Stefano Ermon

TMLR Journal 2025 Journal Article

Calibrated Probabilistic Forecasts for Arbitrary Sequences

• Charles Marx
• Volodymyr Kuleshov
• Stefano Ermon

Real-world data streams can change unpredictably due to distribution shifts, feedback loops and adversarial actors, which challenges the validity of forecasts. We present a forecasting framework ensuring valid uncertainty estimates regardless of how data evolves. Leveraging the concept of Blackwell approachability from game theory, we introduce a forecasting framework that guarantees calibrated uncertainties for outcomes in any compact space (e.g., classification or bounded regression). We extend this framework to recalibrate existing forecasters, guaranteeing calibration without sacrificing predictive performance. We implement both general-purpose gradient-based algorithms and algorithms optimized for popular special cases of our framework. Empirically, our algorithms improve calibration and downstream decision-making for energy systems.

ICLR Conference 2025 Conference Paper

CPSample: Classifier Protected Sampling for Guarding Training Data During Diffusion

• Joshua Kazdan
• Hao Sun
• Jiaqi Han
• Felix Petersen
• Frederick Vu
• Stefano Ermon

Diffusion models have a tendency to exactly replicate their training data, especially when trained on small datasets. Most prior work has sought to mitigate this problem by imposing differential privacy constraints or masking parts of the training data, resulting in a notable substantial decrease in image quality. We present CPSample, a method that modifies the sampling process to prevent training data replication while preserving image quality. CPSample utilizes a classifier that is trained to overfit on random binary labels attached to the training data. CPSample then uses classifier guidance to steer the generation process away from the set of points that can be classified with high certainty, a set that includes the training data. CPSample achieves FID scores of 4.97 and 2.97 on CIFAR-10 and CelebA-64, respectively, without producing exact replicates of the training data. Unlike prior methods intended to guard the training images, CPSample only requires training a classifier rather than retraining a diffusion model, which is computationally cheaper. Moreover, our technique provides diffusion models with greater robustness against membership inference attacks, wherein an adversary attempts to discern which images were in the model's training dataset. We show that CPSample behaves like a built-in rejection sampler, and we demonstrate its capabilities to prevent mode collapse in Stable Diffusion.

ICLR Conference 2025 Conference Paper

Data Unlearning in Diffusion Models

• Silas Alberti
• Kenan Hasanaliyev
• Manav Shah
• Stefano Ermon

Recent work has shown that diffusion models memorize and reproduce training data examples. At the same time, large copyright lawsuits and legislation such as GDPR have highlighted the need for erasing datapoints from diffusion models. However, retraining from scratch is often too expensive. This motivates the setting of data unlearning, i.e., the study of efficient techniques for unlearning specific datapoints from the training set. Existing concept unlearning techniques require an anchor prompt/class/distribution to guide unlearning, which is not available in the data unlearning setting. General-purpose machine unlearning techniques were found to be either unstable or failed to unlearn data. We therefore propose a family of new loss functions called Subtracted Importance Sampled Scores (SISS) that utilize importance sampling and are the first method to unlearn data with theoretical guarantees. SISS is constructed as a weighted combination between simpler objectives that are responsible for preserving model quality and unlearning the targeted datapoints. When evaluated on CelebA-HQ and MNIST, SISS achieved Pareto optimality along the quality and unlearning strength dimensions. On Stable Diffusion, SISS successfully mitigated memorization on nearly 90% of the prompts we tested. We release our code online.

ICLR Conference 2025 Conference Paper

Energy-Based Diffusion Language Models for Text Generation

• Minkai Xu
• Tomas Geffner
• Karsten Kreis
• Weili Nie
• Yilun Xu
• Jure Leskovec
• Stefano Ermon
• Arash Vahdat

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have recently emerged as a promising alternative. Unfortunately, these models still underperform the autoregressive counterparts, with the performance gap increasing when reducing the number of sampling steps. Our analysis reveals that this degradation is a consequence of an imperfect approximation used by diffusion models. In this work, we propose Energy-based Diffusion Language Model (EDLM), an energy-based model operating at the full sequence level for each diffusion step, introduced to improve the underlying approximation used by diffusion models. More specifically, we introduce an EBM in a residual form, and show that its parameters can be obtained by leveraging a pretrained autoregressive model or by finetuning a bidirectional transformer via noise contrastive estimation. We also propose an efficient generation algorithm via parallel important sampling. Comprehensive experiments on language modeling benchmarks show that our model can consistently outperform state-of-the-art diffusion models by a significant margin, and approaches autoregressive models' perplexity. We further show that, without any generation performance drop, our framework offers a 1.3x sampling speedup over existing diffusion models. Reproduced code is available at https://github.com/MinkaiXu/Energy-Diffusion-LLM.

ICML Conference 2025 Conference Paper

ExPLoRA: Parameter-Efficient Extended Pre-Training to Adapt Vision Transformers under Domain Shifts

• Samar Khanna
• Medhanie Irgau
• David B. Lobell
• Stefano Ermon

Parameter-efficient fine-tuning (PEFT) techniques such as low-rank adaptation (LoRA) can effectively adapt large pre-trained foundation models to downstream tasks using only a small fraction (0. 1%-10%) of the original trainable weights. An under-explored question of PEFT is in extending the pre-training phase without supervised labels; that is, can we adapt a pre-trained foundation model to a new domain via efficient self-supervised pre-training on this domain? In this work, we introduce ExPLoRA, a highly effective technique to improve transfer learning of pre-trained vision transformers (ViTs) under domain shifts. Initializing a ViT with pre-trained weights on large, natural-image datasets such as from DinoV2 or MAE, ExPLoRA continues the unsupervised pre-training objective on a new domain, unfreezing 1-2 pre-trained ViT blocks and tuning all other layers with LoRA. We then fine-tune the resulting model only with LoRA on this new domain for supervised learning. Our experiments demonstrate state-of-the-art results on satellite imagery, even outperforming fully pre-training and fine-tuning ViTs. Using the DinoV2 training objective, we demonstrate up to 8% improvement in linear probing top-1 accuracy on downstream tasks while using $<$10% of the number of parameters that are used in prior fully-tuned state-of-the art approaches. Our ablation studies confirm the efficacy of our approach over other baselines such as PEFT. Code is available at: https: //samar-khanna. github. io/ExPLoRA/

NeurIPS Conference 2025 Conference Paper

Exploring Diffusion Transformer Designs via Grafting

• Keshigeyan Chandrasegaran
• Michael Poli
• Dan Fu
• Dongjun Kim
• Lea M. Hadzic
• Manling Li
• Agrim Gupta
• Stefano Massaroli

Designing model architectures requires decisions such as selecting operators (e. g. , attention, convolution) and configurations (e. g. , depth, width). However, evaluating the impact of these decisions on model quality requires costly pretraining, limiting architectural investigation. Inspired by how new software is built on existing code, we ask: can new architecture designs be studied using pretrained models? To this end, we present *grafting*, a simple approach for editing pretrained diffusion transformers (DiTs) to materialize new architectures under small compute budgets. Informed by our analysis of activation behavior and attention locality, we construct a testbed based on the DiT-XL/2 design to study the impact of grafting on model quality. Using this testbed, we develop a family of hybrid designs via grafting: replacing softmax attention with gated convolution, local attention, and linear attention, and replacing MLPs with variable expansion ratio and convolutional variants. Notably, many hybrid designs achieve good quality (FID: 2. 38–2. 64 vs. 2. 27 for DiT-XL/2) using $<2$% pretraining compute. We then graft a text-to-image model (PixArt-$\Sigma$), achieving a 1. 43$\times$ speedup with less than a 2% drop in GenEval score. Finally, we present a case study that restructures DiT-XL/2 by converting every pair of sequential transformer blocks into parallel blocks via grafting. This reduces model depth by 2$\times$ and yields better quality (FID: 2. 77) than other models of comparable depth. Together, we show that new diffusion model designs can be explored by grafting pretrained DiTs, with edits ranging from operator replacement to architecture restructuring. Code and grafted models: https: //grafting. stanford. edu.

TMLR Journal 2025 Journal Article

G2D2: Gradient-Guided Discrete Diffusion for Inverse Problem Solving

• Naoki Murata
• Chieh-Hsin Lai
• Yuhta Takida
• Toshimitsu Uesaka
• Bac Nguyen
• Stefano Ermon
• Yuki Mitsufuji

Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly in modalities suited for discrete compressed representations, such as image and motion generation. However, their discrete and non-differentiable nature has limited their application to inverse problems formulated in continuous spaces. This paper presents a novel method for addressing linear inverse problems by leveraging generative models based on discrete diffusion as priors. We overcome these limitations by approximating the true posterior distribution with a variational distribution constructed from categorical distributions and continuous relaxation techniques. Furthermore, we employ a star-shaped noise process to mitigate the drawbacks of traditional discrete diffusion models with absorbing states, demonstrating that our method performs comparably to continuous diffusion techniques with lower GPU memory consumption.

NeurIPS Conference 2025 Conference Paper

GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters

• Wanjia Zhao
• Jiaqi Han
• Siyi Gu
• Mingjian Jiang
• James Zou
• Stefano Ermon

Geometric diffusion models have shown remarkable success in molecular dynamics and structure generation. However, efficiently fine-tuning them for downstream tasks with varying geometric controls remains underexplored. In this work, we propose an SE(3)-equivariant adapter framework (GeoAda) that enables flexible and parameter-efficient fine-tuning for controlled generative tasks without modifying the original model architecture. GeoAda introduces a structured adapter design: control signals are first encoded through coupling operators, then processed by a trainable copy of selected base model layers, and finally projected back via decoupling operators followed by an equivariant zero-initialized convolution. By fine-tuning only these lightweight adapter modules, GeoAda preserves the model’s geometric consistency while mitigating overfitting and catastrophic forgetting. We theoretically prove that the proposed adapters maintain SE(3)-equivariance, ensuring that the geometric inductive biases of the pretrained diffusion model remain intact during adaptation. We demonstrate the wide applicability of \method across diverse geometric control types, including frame control, global control, subgraph control, and a broad range of application domains such as particle dynamics, molecular dynamics, human motion prediction, and molecule generation. Empirical results show that GeoAda achieves state-of-the-art fine-tuning performance while preserving original task accuracy, whereas other baselines experience significant performance degradation due to overfitting and catastrophic forgetting.

ICML Conference 2025 Conference Paper

Inductive Moment Matching

• Linqi Zhou
• Stefano Ermon
• Jiaming Song

Diffusion models and Flow Matching generate high-quality samples but are slow at inference, and distilling them into few-step models often leads to instability and extensive tuning. To resolve these trade-offs, we propose Moment Matching Self-Distillation (MMSD), a new class of generative models for one- or few-step sampling with a single-stage training procedure. Unlike distillation, MMSD does not require pre-training initialization and optimization of two networks; and unlike Consistency Models, MMSD guarantees distribution-level convergence and remains stable under various hyperparameters and standard model architectures. MMSD surpasses diffusion models on ImageNet-256x256 with 2. 13 FID using only 8 inference steps and achieves state-of-the-art 2-step FID of 2. 05 on CIFAR-10 for a model trained from scratch.

TMLR Journal 2025 Journal Article

Non-Myopic Multi-Objective Bayesian Optimization

• Syrine Belakaria
• Alaleh Ahmadian
• Barbara E Engelhardt
• Stefano Ermon
• Jana Doppa

We consider the problem of finite-horizon sequential experimental design to solve multi-objective optimization (MOO) of expensive black-box objective functions. This problem arises in many real-world applications, including materials design, where we have a small resource budget to make and evaluate candidate materials in the lab. We solve this problem using the framework of Bayesian optimization (BO) and propose the first set of non-myopic methods for MOO problems. Prior work on non-myopic BO for single-objective problems relies on the Bellman optimality principle to handle the lookahead reasoning process. However, this principle does not hold for most MOO problems because the reward function needs to satisfy some conditions: scalar variable, monotonicity, and additivity. We address this challenge by using hypervolume improvement (HVI) as our scalarization approach, which allows us to use a lower-bound on the Bellman equation to approximate the finite-horizon using a batch expected hypervolume improvement (EHVI) acquisition function (AF) for MOO. Our formulation naturally allows us to use other improvement-based scalarizations and compare their efficacy to HVI. We derive three non-myopic AFs for MOBO: 1) the Nested AF, which is based on the exact computation of the lower bound, 2) the Joint AF, which is a lower bound on the nested AF, and 3) the BINOM AF, which is a fast and approximate variant based on batch multi-objective acquisition functions. Our experiments on multiple diverse real-world MO problems demonstrate that our non-myopic AFs substantially improve performance over the existing myopic AFs for MOBO.

NeurIPS Conference 2025 Conference Paper

Preference-Guided Diffusion for Multi-Objective Offline Optimization

• Yashas Annadani
• Syrine Belakaria
• Stefano Ermon
• Stefan Bauer
• Barbara Engelhardt

Offline multi-objective optimization aims to identify Pareto-optimal solutions given a dataset of designs and their objective values. In this work, we propose a preference-guided diffusion model that generates Pareto-optimal designs by leveraging a classifier-based guidance mechanism. Our guidance classifier is a preference model trained to predict the probability that one design dominates another, directing the diffusion model toward optimal regions of the design space. Crucially, this preference model generalizes beyond the training distribution, enabling the discovery of Pareto-optimal solutions outside the observed dataset. We introduce a novel diversity-aware preference guidance, augmenting Pareto dominance preference with diversity criteria. This ensures that generated solutions are optimal and well-distributed across the objective space, a capability absent in prior generative methods for offline multi-objective optimization. We evaluate our approach on various continuous offline multi-objective optimization tasks and find that it consistently outperforms other inverse/generative approaches while remaining competitive with forward/ surrogate-based optimization methods. Our results highlight the effectiveness of classifier-guided diffusion models in generating diverse and high-quality solutions that approximate the Pareto front well.

ICML Conference 2025 Conference Paper

Scaling Probabilistic Circuits via Monarch Matrices

• Honghua Zhang
• Meihua Dang
• Benjie Wang 0001
• Stefano Ermon
• Nanyun Peng 0001
• Guy Van den Broeck

Probabilistic Circuits (PCs) are tractable representations of probability distributions allowing for exact and efficient computation of likelihoods and marginals. Recent advancements have improved the scalability of PCs either by leveraging their sparse properties or through the use of tensorized operations for better hardware utilization. However, no existing method fully exploits both aspects simultaneously. In this paper, we propose a novel sparse and structured parameterization for the sum blocks in PCs. By replacing dense matrices with sparse Monarch matrices, we significantly reduce the memory and computation costs, enabling unprecedented scaling of PCs. From a theory perspective, our construction arises naturally from circuit multiplication; from a practical perspective, compared to previous efforts on scaling up tractable probabilistic models, our approach not only achieves state-of-the-art generative modeling performance on challenging benchmarks like Text8, LM1B and ImageNet, but also demonstrates superior scaling behavior, achieving the same performance with substantially less compute as measured by the number of floating-point operations (FLOPs) during training.

ICML Conference 2025 Conference Paper

Smooth Interpolation for Improved Discrete Graph Generative Models

• Yuxuan Song
• Juntong Shi
• Jingjing Gong
• Minkai Xu
• Stefano Ermon
• Hao Zhou 0012
• Wei-Ying Ma

Though typically represented by the discrete node and edge attributes, the graph topological information can be sufficiently captured by the graph spectrum in a continuous space. It is believed that incorporating the continuity of graph topological information into the generative process design could establish a superior paradigm for graph generative modeling. Motivated by such prior and recent advancements in the generative paradigm, we propose Graph Bayesian Flow Networks (GraphBFN) in this paper, a principled generative framework that designs an alternative generative process emphasizing the dynamics of topological information. Unlike recent discrete-diffusion-based methods, GraphBFNemploys the continuous counts derived from sampling infinite times from a categorical distribution as latent to facilitate a smooth decomposition of topological information, demonstrating enhanced effectiveness. To effectively realize the concept, we further develop an advanced sampling strategy and new time-scheduling techniques to overcome practical barriers and boost performance. Through extensive experimental validation on both generic graph and molecular graph generation tasks, GraphBFN could consistently achieve superior or competitive performance with significantly higher training and sampling efficiency.

ICLR Conference 2025 Conference Paper

TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation

• Juntong Shi
• Minkai Xu
• Harper Hua
• Hengrui Zhang
• Stefano Ermon
• Jure Leskovec

Synthesizing high-quality tabular data is an important topic in many data science tasks, ranging from dataset augmentation to privacy protection. However, developing expressive generative models for tabular data is challenging due to its inherent heterogeneous data types, complex inter-correlations, and intricate column-wise distributions. In this paper, we introduce TabDiff, a joint diffusion framework that models all mixed-type distributions of tabular data in one model. Our key innovation is the development of a joint continuous-time diffusion process for numerical and categorical data, where we propose feature-wise learnable diffusion processes to counter the high disparity of different feature distributions. TabDiff is parameterized by a transformer handling different input types, and the entire framework can be efficiently optimized in an end-to-end fashion. We further introduce a mixed-type stochastic sampler to automatically correct the accumulated decoding error during sampling, and propose classifier-free guidance for conditional missing column value imputation. Comprehensive experiments on seven datasets demonstrate that TabDiff achieves superior average performance over existing competitive baselines across all eight metrics, with up to $22.5\%$ improvement over the state-of-the-art model on pair-wise column correlation estimations. Code is available at https://github.com/MinkaiXu/TabDiff.

ICLR Conference 2025 Conference Paper

TEOChat: A Large Vision-Language Assistant for Temporal Earth Observation Data

• Jeremy Andrew Irvin
• Emily Ruoyu Liu
• Joyce Chuyi Chen
• Ines Dormoy
• Jin-Young Kim
• Samar Khanna
• Zhuo Zheng
• Stefano Ermon

Large vision and language assistants have enabled new capabilities for interpreting natural images. These approaches have recently been adapted to earth observation data, but they are only able to handle single image inputs, limiting their use for many real-world tasks. In this work, we develop a new vision and language assistant called TEOChat that can engage in conversations about temporal sequences of earth observation data. To train TEOChat, we curate an instruction-following dataset composed of many single image and temporal tasks including building change and damage assessment, semantic change detection, and temporal scene classification. We show that TEOChat can perform a wide variety of spatial and temporal reasoning tasks, substantially outperforming previous vision and language assistants, and even achieving comparable or better performance than several specialist models trained to perform specific tasks. Furthermore, TEOChat achieves impressive zero-shot performance on a change detection and change question answering dataset, outperforms GPT-4o and Gemini 1.5 Pro on multiple temporal tasks, and exhibits stronger single image capabilities than a comparable single image instruction-following model on scene classification, visual question answering, and captioning. We publicly release our data, models, and code at https://github.com/ermongroup/TEOChat .

ICLR Conference 2025 Conference Paper

TFG-Flow: Training-free Guidance in Multimodal Generative Flow

• Haowei Lin
• Shanda Li
• Haotian Ye
• Yiming Yang
• Stefano Ermon
• Yitao Liang
• Jianzhu Ma

Given an unconditional generative model and a predictor for a target property (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. As a highly efficient technique for steering generative models toward flexible outcomes, training-free guidance has gained increasing attention in diffusion models. However, existing methods only handle data in continuous spaces, while many scientific applications involve both continuous and discrete data (referred to as multimodality). Another emerging trend is the growing use of the simple and general flow matching framework in building generative foundation models, where guided generation remains under-explored. To address this, we introduce TFG-Flow, a novel training-free guidance method for multimodal generative flow. TFG-Flow addresses the curse-of-dimensionality while maintaining the property of unbiased sampling in guiding discrete variables. We validate TFG-Flow on four molecular design tasks and show that TFG-Flow has great potential in drug design by generating molecules with desired properties.

NeurIPS Conference 2025 Conference Paper

Training-Free Safe Denoisers for Safe Use of Diffusion Models

• Mingyu Kim
• Dongjun Kim
• Amman Yusuf
• Stefano Ermon
• Mi Jung Park

There is growing concern over the safety of powerful diffusion models, as they are often misused to produce inappropriate, not-safe-for-work content or generate copyrighted material or data of individuals who wish to be forgotten. Many existing methods tackle these issues by heavily relying on text-based negative prompts or retraining the model to eliminate certain features or samples. In this paper, we take a radically different approach, directly modifying the sampling trajectory by leveraging a negation set (e. g. , unsafe images, copyrighted data, or private data) to avoid specific regions of data distribution, without needing to retrain or fine-tune the model. We formally derive the relationship between the expected denoised samples that are safe and those that are unsafe, leading to our safe denoiser, which ensures its final samples are away from the area to be negated. We achieve state-of-the-art safety performance in large-scale datasets such as the CoPro dataset while also enabling significantly more cost-effective sampling than existing methodologies.

ICML Conference 2025 Conference Paper

Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints

• Dapeng Jiang
• Xiangzhe Kong
• Jiaqi Han
• Mingyu Li
• Rui Jiao
• Wenbing Huang 0001
• Stefano Ermon
• Jianzhu Ma

Cyclic peptides, characterized by geometric constraints absent in linear peptides, offer enhanced biochemical properties, presenting new opportunities to address unmet medical needs. However, designing target-specific cyclic peptides remains underexplored due to limited training data. To bridge the gap, we propose CP-Composer, a novel generative framework that enables zero-shot cyclic peptide generation via composable geometric constraints. Our approach decomposes complex cyclization patterns into unit constraints, which are incorporated into a diffusion model through geometric conditioning on nodes and edges. During training, the model learns from unit constraints and their random combinations in linear peptides, while at inference, novel constraint combinations required for cyclization are imposed as input. Experiments show that our model, despite trained with linear peptides, is capable of generating diverse target-binding cyclic peptides, reaching success rates from 38% to 84% on different cyclization strategies.

NeurIPS Conference 2024 Conference Paper

Active Learning for Derivative-Based Global Sensitivity Analysis with Gaussian Processes

• Syrine Belakaria
• Benjamin Letham
• Janardhan R. Doppa
• Barbara Engelhardt
• Stefano Ermon
• Eytan Bakshy

We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e. g. , in vehicle safety experimentation, we study the impact of the thickness of various components on safety objectives. Since function evaluations are expensive, we use active learning to prioritize experimental resources where they yield the most value. We propose novel active learning acquisition functions that directly target key quantities of derivative-based global sensitivity measures (DGSMs) under Gaussian process surrogate models. We showcase the first application of active learning directly to DGSMs, and develop tractable uncertainty reduction and information gain acquisition functions for these measures. Through comprehensive evaluation on synthetic and real-world problems, our study demonstrates how these active learning acquisition strategies substantially enhance the sample efficiency of DGSM estimation, particularly with limited evaluation budgets. Our work paves the way for more efficient and accurate sensitivity analysis in various scientific and engineering applications.

NeurIPS Conference 2024 Conference Paper

Aligning Target-Aware Molecule Diffusion Models with Exact Energy Optimization

• Siyi Gu
• Minkai Xu
• Alexander Powers
• Weili Nie
• Tomas Geffner
• Karsten Kreis
• Jure Leskovec
• Arash Vahdat

Generating ligand molecules for specific protein targets, known as structure-based drug design, is a fundamental problem in therapeutics development and biological discovery. Recently, target-aware generative models, especially diffusion models, have shown great promise in modeling protein-ligand interactions and generating candidate drugs. However, existing models primarily focus on learning the chemical distribution of all drug candidates, which lacks effective steerability on the chemical quality of model generations. In this paper, we propose a novel and general alignment framework to align pretrained target diffusion models with preferred functional properties, named AliDiff. AliDiff shifts the target-conditioned chemical distribution towards regions with higher binding affinity and structural rationality, specified by user-defined reward functions, via the preference optimization approach. To avoid the overfitting problem in common preference optimization objectives, we further develop an improved Exact Energy Preference Optimization method to yield an exact and efficient alignment of the diffusion models, and provide the closed-form expression for the converged distribution. Empirical studies on the CrossDocked2020 benchmark show that AliDiff can generate molecules with state-of-the-art binding energies with up to -7. 07 Avg. Vina Score, while maintaining strong molecular properties. Code is available at https: //github. com/MinkaiXu/AliDiff.

ICLR Conference 2024 Conference Paper

Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion

• Dongjun Kim
• Chieh-Hsin Lai
• Wei-Hsiang Liao 0001
• Naoki Murata
• Yuhta Takida
• Toshimitsu Uesaka
• Yutong He
• Yuki Mitsufuji

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory Model (CTM), a generalization encompassing CM and score-based models as special cases. CTM trains a single neural network that can -- in a single forward pass -- output scores (i.e., gradients of log-density) and enables unrestricted traversal between any initial and final time along the Probability Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance and achieves new state-of-the-art FIDs for single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at 64X64 resolution (FID 1.92). CTM also enables a new family of sampling schemes, both deterministic and stochastic, involving long jumps along the ODE solution trajectories. It consistently improves sample quality as computational budgets increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods from the diffusion community. This access also enables the computation of likelihood. The code is available at https://github.com/sony/ctm.

NeurIPS Conference 2024 Conference Paper

Convolutional Differentiable Logic Gate Networks

• Felix Petersen
• Hilde Kuehne
• Christian Borgelt
• Julian Welzel
• Stefano Ermon

With the increasing inference cost of machine learning models, there is a growing interest in models with fast and efficient inference. Recently, an approach for learning logic gate networks directly via a differentiable relaxation was proposed. Logic gate networks are faster than conventional neural network approaches because their inference only requires logic gate operators such as NAND, OR, and XOR, which are the underlying building blocks of current hardware and can be efficiently executed. We build on this idea, extending it by deep logic gate tree convolutions, logical OR pooling, and residual initializations. This allows scaling logic gate networks up by over one order of magnitude and utilizing the paradigm of convolution. On CIFAR-10, we achieve an accuracy of 86. 29% using only 61 million logic gates, which improves over the SOTA while being 29x smaller.

ICLR Conference 2024 Conference Paper

Cross-Modal Contextualized Diffusion Models for Text-Guided Visual Generation and Editing

• Ling Yang 0006
• Zhilong Zhang
• Zhaochen Yu
• Jingwei Liu
• Minkai Xu
• Stefano Ermon
• Bin Cui 0001

Conditional diffusion models have exhibited superior performance in high-fidelity text-guided visual generation and editing. Nevertheless, prevailing text-guided visual diffusion models primarily focus on incorporating text-visual relationships exclusively into the reverse process, often disregarding their relevance in the forward process. This inconsistency between forward and reverse processes may limit the precise conveyance of textual semantics in visual synthesis results. To address this issue, we propose a novel and general contextualized diffusion model (ContextDiff) by incorporating the cross-modal context encompassing interactions and alignments between text condition and visual sample into forward and reverse processes. We propagate this context to all timesteps in the two processes to adapt their trajectories, thereby facilitating cross-modal conditional modeling. We generalize our contextualized diffusion to both DDPMs and DDIMs with theoretical derivations, and demonstrate the effectiveness of our model in evaluations with two challenging tasks: text-to-image generation, and text-to-video editing. In each task, our ContextDiff achieves new state-of-the-art performance, significantly enhancing the semantic alignment between text condition and generated samples, as evidenced by quantitative and qualitative evaluations. Our code is available at https://github.com/YangLing0818/ContextDiff

ICLR Conference 2024 Conference Paper

Denoising Diffusion Bridge Models

• Linqi Zhou
• Aaron Lou
• Samar Khanna
• Stefano Ermon

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion models must rely on cumbersome methods like guidance or projected sampling to incorporate this information in the generative process. In our work, we propose Denoising Diffusion Bridge Models (DDBMs), a natural alternative to this paradigm based on *diffusion bridges*, a family of processes that interpolate between two paired distributions given as endpoints. Our method learns the score of the diffusion bridge from data and maps from one endpoint distribution to the other by solving a (stochastic) differential equation based on the learned score. Our method naturally unifies several classes of generative models, such as score-based diffusion models and OT-Flow-Matching, allowing us to adapt existing design and architectural choices to our more general problem. Empirically, we apply DDBMs to challenging image datasets in both pixel and latent space. On standard image translation problems, DDBMs achieve significant improvement over baseline methods, and, when we reduce the problem to image generation by setting the source distribution to random noise, DDBMs achieve comparable FID scores to state-of-the-art methods despite being built for a more general task.

ICLR Conference 2024 Conference Paper

DiffusionSat: A Generative Foundation Model for Satellite Imagery

• Samar Khanna
• Patrick Liu
• Linqi Zhou
• Chenlin Meng
• Robin Rombach
• Marshall Burke
• David B. Lobell
• Stefano Ermon

Diffusion models have achieved state-of-the-art results on many modalities including images, speech, and video. However, existing models are not tailored to support remote sensing data, which is widely used in important applications including environmental monitoring and crop-yield prediction. Satellite images are significantly different from natural images -- they can be multi-spectral, irregularly sampled across time -- and existing diffusion models trained on images from the Web do not support them. Furthermore, remote sensing data is inherently spatio-temporal, requiring conditional generation tasks not supported by traditional methods based on captions or images. In this paper, we present DiffusionSat, to date the largest generative foundation model trained on a collection of publicly available large, high-resolution remote sensing datasets . As text-based captions are sparsely available for satellite images, we incorporate the associated metadata such as geolocation as conditioning information. Our method produces realistic samples and can be used to solve multiple generative tasks including temporal generation, multi-spectral superrresolution and in-painting. Our method outperforms previous state-of-the-art methods for satellite image generation and is the first large-scale _generative_ foundation model for satellite imagery. The project website can be found here: https://samar-khanna.github.io/DiffusionSat/

ICML Conference 2024 Conference Paper

Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution

• Aaron Lou
• Chenlin Meng
• Stefano Ermon

Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of score matching, but efforts to generalize this to discrete structures have not yielded the same empirical gains. In this work, we bridge this gap by proposing score entropy, a novel loss that naturally extends score matching to discrete spaces, integrates seamlessly to build discrete diffusion models, and significantly boosts performance. Experimentally, we test our Score Entropy Discrete Diffusion models (SEDD) on standard language modeling tasks. For comparable model sizes, SEDD beats existing language diffusion paradigms (reducing perplexity by $25$-$75$%) and is competitive with autoregressive models, in particular outperforming GPT-2. Furthermore, compared to autoregressive mdoels, SEDD generates faithful text without requiring distribution annealing techniques like temperature scaling (around $6$-$8\times$ better generative perplexity than un-annealed GPT-2), can trade compute and quality (similar quality with $32\times$ fewer network evaluations), and enables controllable infilling (matching nucleus sampling quality while enabling other strategies besides left to right prompting).

ICML Conference 2024 Conference Paper

Equivariant Graph Neural Operator for Modeling 3D Dynamics

• Minkai Xu
• Jiaqi Han
• Aaron Lou
• Jean Kossaifi
• Arvind Ramanathan
• Kamyar Azizzadenesheli
• Jure Leskovec
• Stefano Ermon

Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved good success by learning graph neural networks to model spatial interactions. However, these approaches do not faithfully capture temporal correlations since they only model next-step predictions. In this work, we propose Equivariant Graph Neural Operator (EGNO), a novel and principled method that directly models dynamics as trajectories instead of just next-step prediction. Different from existing methods, EGNO explicitly learns the temporal evolution of 3D dynamics where we formulate the dynamics as a function over time and learn neural operators to approximate it. To capture the temporal correlations while keeping the intrinsic SE(3)-equivariance, we develop equivariant temporal convolutions parameterized in the Fourier space and build EGNO by stacking the Fourier layers over equivariant networks. EGNO is the first operator learning framework that is capable of modeling solution dynamics functions over time while retaining 3D equivariance. Comprehensive experiments in multiple domains, including particle simulations, human motion capture, and molecular dynamics, demonstrate the significantly superior performance of EGNO against existing methods, thanks to the equivariant temporal modeling. Our code is available at https: //github. com/MinkaiXu/egno.

NeurIPS Conference 2024 Conference Paper

Generative Fractional Diffusion Models

• Gabriel Nobis
• Maximilian Springenberg
• Marco Aversa
• Michael Detzel
• Rembert Daems
• Roderick Murray-Smith
• Shinichi Nakajima
• Sebastian Lapuschkin

We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion models have excelled at capturing data distributions, they still suffer from various limitations such as slow convergence, mode-collapse on imbalanced data, and lack of diversity. These issues are partially linked to the use of light-tailed Brownian motion (BM) with independent increments. In this paper, we replace BM with an approximation of its non-Markovian counterpart, fractional Brownian motion (fBM), characterized by correlated increments and Hurst index $H \in (0, 1)$, where $H=0. 5$ recovers the classical BM. To ensure tractable inference and learning, we employ a recently popularized Markov approximation of fBM (MA-fBM) and derive its reverse-time model, resulting in *generative fractional diffusion models* (GFDM). We characterize the forward dynamics using a continuous reparameterization trick and propose *augmented score matching* to efficiently learn the score function, which is partly known in closed form, at minimal added cost. The ability to drive our diffusion model via MA-fBM offers flexibility and control. $H \leq 0. 5$ enters the regime of *rough paths* whereas $H>0. 5$ regularizes diffusion paths and invokes long-term memory. The Markov approximation allows added control by varying the number of Markov processes linearly combined to approximate fBM. Our evaluations on real image datasets demonstrate that GFDM achieves greater pixel-wise diversity and enhanced image quality, as indicated by a lower FID, offering a promising alternative to traditional diffusion models

ICLR Conference 2024 Conference Paper

GeoLLM: Extracting Geospatial Knowledge from Large Language Models

• Rohin Manvi
• Samar Khanna
• Gengchen Mai
• Marshall Burke
• David B. Lobell
• Stefano Ermon

The application of machine learning (ML) in a range of geospatial tasks is increasingly common but often relies on globally available covariates such as satellite imagery that can either be expensive or lack predictive power. Here we explore the question of whether the vast amounts of knowledge found in Internet language corpora, now compressed within large language models (LLMs), can be leveraged for geospatial prediction tasks. We first demonstrate that LLMs embed remarkable spatial information about locations, but naively querying LLMs using geographic coordinates alone is ineffective in predicting key indicators like population density. We then present GeoLLM, a novel method that can effectively extract geospatial knowledge from LLMs with auxiliary map data from OpenStreetMap. We demonstrate the utility of our approach across multiple tasks of central interest to the international community, including the measurement of population density and economic livelihoods. Across these tasks, our method demonstrates a 70\% improvement in performance (measured using Pearson's $r^2$) relative to baselines that use nearest neighbors or use information directly from the prompt, and performance equal to or exceeding satellite-based benchmarks in the literature. With GeoLLM, we observe that GPT-3.5 outperforms Llama 2 and RoBERTa by 19\% and 51\% respectively, suggesting that the performance of our method scales well with the size of the model and its pretraining dataset. Our experiments reveal that LLMs are remarkably sample-efficient, rich in geospatial information, and robust across the globe. Crucially, GeoLLM shows promise in mitigating the limitations of existing geospatial covariates and complementing them well. Code is available on the project website: https://rohinmanvi.github.io/GeoLLM

NeurIPS Conference 2024 Conference Paper

Geometric Trajectory Diffusion Models

• Jiaqi Han
• Minkai Xu
• Aaron Lou
• Haotian Ye
• Stefano Ermon

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

AAAI Conference 2024 Conference Paper

HarvestNet: A Dataset for Detecting Smallholder Farming Activity Using Harvest Piles and Remote Sensing

• Jonathan Xu
• Amna Elmustafa
• Liya Weldegebriel
• Emnet Negash
• Richard Lee
• Chenlin Meng
• Stefano Ermon
• David Lobell

Small farms contribute to a large share of the productive land in developing countries. In regions such as sub-Saharan Africa, where 80% of farms are small (under 2 ha in size), the task of mapping smallholder cropland is an important part of tracking sustainability measures such as crop productivity. However, the visually diverse and nuanced appearance of small farms has limited the effectiveness of traditional approaches to cropland mapping. Here we introduce a new approach based on the detection of harvest piles characteristic of many smallholder systems throughout the world. We present HarvestNet, a dataset for mapping the presence of farms in the Ethiopian regions of Tigray and Amhara during 2020-2023, collected using expert knowledge and satellite images, totalling 7k hand-labeled images and 2k ground-collected labels. We also benchmark a set of baselines, including SOTA models in remote sensing, with our best models having around 80% classification performance on hand labelled data and 90% and 98% accuracy on ground truth data for Tigray and Amhara, respectively. We also perform a visual comparison with a widely used pre-existing coverage map and show that our model detects an extra 56,621 hectares of cropland in Tigray. We conclude that remote sensing of harvest piles can contribute to more timely and accurate cropland assessments in food insecure regions. The dataset can be accessed through https://figshare.com/s/45a7b45556b90a9a11d2, while the code for the dataset and benchmarks is publicly available at https://github.com/jonxuxu/harvest-piles

ICLR Conference 2024 Conference Paper

Language Model Detectors Are Easily Optimized Against

• Charlotte Nicks
• Eric Mitchell
• Rafael Rafailov
• Archit Sharma
• Christopher D. Manning
• Chelsea Finn
• Stefano Ermon

The fluency and general applicability of large language models (LLMs) has motivated significant interest in detecting whether a piece of text was written by a language model. While both academic and commercial detectors have been deployed in some settings, particularly education, other research has highlighted the fragility of these systems. In this paper, we demonstrate a data-efficient attack that fine-tunes language models to confuse existing detectors, leveraging recent developments in reinforcement learning of language models. We use the `human-ness' score (often just a log probability) of various open-source and commercial detectors as a reward function for reinforcement learning, subject to a KL-divergence constraint that the resulting model does not differ significantly from the original. For a 7B parameter Llama-2 model, fine-tuning for under a day reduces the AUROC of the OpenAI RoBERTa-Large detector from 0.84 to 0.63, while perplexity on OpenWebText increases from 8.7 to only 9.0; with a larger perplexity budget, we can drive AUROC to 0.30 (worse than random). Similar to traditional adversarial attacks, we find that this increase in 'detector evasion' generalizes to other detectors not used during training. In light of our empirical results, we advise against continued reliance on LLM-generated text detectors. Models, datasets, and selected experiment code will be released at https://github.com/charlottttee/llm-detector-evasion.

ICML Conference 2024 Conference Paper

Large Language Models are Geographically Biased

• Rohin Manvi
• Samar Khanna
• Marshall Burke
• David B. Lobell
• Stefano Ermon

Large Language Models (LLMs) inherently carry the biases contained in their training corpora, which can lead to the perpetuation of societal harm. As the impact of these foundation models grows, understanding and evaluating their biases becomes crucial to achieving fairness and accuracy. We propose to study what LLMs know about the world we live in through the lens of geography. This approach is particularly powerful as there is ground truth for the numerous aspects of human life that are meaningfully projected onto geographic space such as culture, race, language, politics, and religion. We show various problematic geographic biases, which we define as systemic errors in geospatial predictions. Initially, we demonstrate that LLMs are capable of making accurate zero-shot geospatial predictions in the form of ratings that show strong monotonic correlation with ground truth (Spearman’s $\rho$ of up to 0. 89). We then show that LLMs exhibit common biases across a range of objective and subjective topics. In particular, LLMs are clearly biased against locations with lower socioeconomic conditions (e. g. most of Africa) on a variety of sensitive subjective topics such as attractiveness, morality, and intelligence (Spearman’s $\rho$ of up to 0. 70). Finally, we introduce a bias score to quantify this and find that there is significant variation in the magnitude of bias across existing LLMs. Code is available on the project website: https: //rohinmanvi. github. io/GeoLLM.

NeurIPS Conference 2024 Conference Paper

MADiff: Offline Multi-agent Learning with Diffusion Models

• Zhengbang Zhu
• Minghuan Liu
• Liyuan Mao
• Bingyi Kang
• Minkai Xu
• Yong Yu
• Stefano Ermon
• Weinan Zhang

Offline reinforcement learning (RL) aims to learn policies from pre-existing datasets without further interactions, making it a challenging task. Q-learning algorithms struggle with extrapolation errors in offline settings, while supervised learning methods are constrained by model expressiveness. Recently, diffusion models (DMs) have shown promise in overcoming these limitations in single-agent learning, but their application in multi-agent scenarios remains unclear. Generating trajectories for each agent with independent DMs may impede coordination, while concatenating all agents’ information can lead to low sample efficiency. Accordingly, we propose MADiff, which is realized with an attention-based diffusion model to model the complex coordination among behaviors of multiple agents. To our knowledge, MADiff is the first diffusion-based multi-agent learning framework, functioning as both a decentralized policy and a centralized controller. During decentralized executions, MADiff simultaneously performs teammate modeling, and the centralized controller can also be applied in multi-agent trajectory predictions. Our experiments demonstrate that MADiff outperforms baseline algorithms across various multi-agent learning tasks, highlighting its effectiveness in modeling complex multi-agent interactions.

ICLR Conference 2024 Conference Paper

Manifold Preserving Guided Diffusion

• Yutong He
• Naoki Murata
• Chieh-Hsin Lai
• Yuhta Takida
• Toshimitsu Uesaka
• Dongjun Kim
• Wei-Hsiang Liao 0001
• Yuki Mitsufuji

Despite the recent advancements, conditional image generation still faces challenges of cost, generalizability, and the need for task-specific training. In this paper, we propose Manifold Preserving Guided Diffusion (MPGD), a training-free conditional generation framework that leverages pretrained diffusion models and off-the-shelf neural networks with minimal additional inference cost for a broad range of tasks. Specifically, we leverage the manifold hypothesis to refine the guided diffusion steps and introduce a shortcut algorithm in the process. We then propose two methods for on-manifold training-free guidance using pre-trained autoencoders and demonstrate that our shortcut inherently preserves the manifolds when applied to latent diffusion models. Our experiments show that MPGD is efficient and effective for solving a variety of conditional generation applications in low-compute settings, and can consistently offer up to 3.8× speed-ups with the same number of diffusion steps while maintaining high sample quality compared to the baselines.

ICML Conference 2024 Conference Paper

Mastering Text-to-Image Diffusion: Recaptioning, Planning, and Generating with Multimodal LLMs

• Ling Yang 0006
• Zhaochen Yu
• Chenlin Meng
• Minkai Xu
• Stefano Ermon
• Bin Cui 0001

Diffusion models have exhibit exceptional performance in text-to-image generation and editing. However, existing methods often face challenges when handling complex text prompts that involve multiple objects with multiple attributes and relationships. In this paper, we propose a brand new training-free text-to-image generation/editing framework, namely Recaption, Plan and Generate (RPG), harnessing the powerful chain-of-thought reasoning ability of multimodal LLMs to enhance the compositionality of text-to-image diffusion models. Our approach employs the MLLM as a global planner to decompose the process of generating complex images into multiple simpler generation tasks within subregions. We propose complementary regional diffusion to enable region-wise compositional generation. Furthermore, we integrate text-guided image generation and editing within the proposed RPG in a closed-loop fashion, thereby enhancing generalization ability. Extensive experiments demonstrate our RPG outperforms state-of-the-art text-to-image models, including DALL-E 3 and SDXL, particularly in multi-category object composition and text-image semantic alignment. Notably, our RPG framework exhibits wide compatibility with various MLLM architectures and diffusion backbones. Our code is available at https: //github. com/YangLing0818/RPG-DiffusionMaster

ICML Conference 2024 Conference Paper

Mechanistic Design and Scaling of Hybrid Architectures

• Michael Poli
• Armin W. Thomas
• Eric Nguyen
• Pragaash Ponnusamy
• Björn Deiseroth
• Kristian Kersting
• Taiji Suzuki
• Brian L. Hie

The development of deep learning architectures is a resource-demanding process, due to a vast design space, long prototyping times, and high compute costs associated with at-scale model training and evaluation. We set out to simplify this process by grounding it in an end-to-end mechanistic architecture design (MAD) pipeline, encompassing small-scale capability unit tests predictive of scaling laws. Through a suite of synthetic token manipulation tasks such as compression and recall, designed to probe capabilities, we identify and test new hybrid architectures constructed from a variety of computational primitives. We experimentally validate the resulting architectures via an extensive compute-optimal and a new state-optimal scaling law analysis, training over 500 language models between 70M to 7B parameters. Surprisingly, we find MAD synthetics to correlate with compute-optimal perplexity, enabling accurate evaluation of new architectures via isolated proxy tasks. The new architectures found via MAD, based on simple ideas such as hybridization and sparsity, outperform state-of-the-art Transformer, convolutional, and recurrent architectures (Transformer++, Hyena, Mamba) in scaling, both at compute-optimal budgets and in overtrained regimes. Overall, these results provide evidence that performance on curated synthetic tasks can be predictive of scaling laws, and that an optimal architecture should leverage specialized layers via a hybrid topology.

NeurIPS Conference 2024 Conference Paper

Newton Losses: Using Curvature Information for Learning with Differentiable Algorithms

• Felix Petersen
• Christian Borgelt
• Tobias Sutter
• Hilde Kuehne
• Oliver Deussen
• Stefano Ermon

When training neural networks with custom objectives, such as ranking losses and shortest-path losses, a common problem is that they are, per se, non-differentiable. A popular approach is to continuously relax the objectives to provide gradients, enabling learning. However, such differentiable relaxations are often non-convex and can exhibit vanishing and exploding gradients, making them (already in isolation) hard to optimize. Here, the loss function poses the bottleneck when training a deep neural network. We present Newton Losses, a method for improving the performance of existing hard to optimize losses by exploiting their second-order information via their empirical Fisher and Hessian matrices. Instead of training the neural network with second-order techniques, we only utilize the loss function's second-order information to replace it by a Newton Loss, while training the network with gradient descent. This makes our method computationally efficient. We apply Newton Losses to eight differentiable algorithms for sorting and shortest-paths, achieving significant improvements for less-optimized differentiable algorithms, and consistent improvements, even for well-optimized differentiable algorithms.

NeurIPS Conference 2024 Conference Paper

PaGoDA: Progressive Growing of a One-Step Generator from a Low-Resolution Diffusion Teacher

• Dongjun Kim
• Chieh-Hsin Lai
• Wei-Hsiang Liao
• Yuhta Takida
• Naoki Murata
• Toshimitsu Uesaka
• Yuki Mitsufuji
• Stefano Ermon

The diffusion model performs remarkable in generating high-dimensional content but is computationally intensive, especially during training. We propose Progressive Growing of Diffusion Autoencoder (PaGoDA), a novel pipeline that reduces the training costs through three stages: training diffusion on downsampled data, distilling the pretrained diffusion, and progressive super-resolution. With the proposed pipeline, PaGoDA achieves a $64\times$ reduced cost in training its diffusion model on $8\times$ downsampled data; while at the inference, with the single-step, it performs state-of-the-art on ImageNet across all resolutions from $64\times64$ to $512\times512$, and text-to-image. PaGoDA's pipeline can be applied directly in the latent space, adding compression alongside the pre-trained autoencoder in Latent Diffusion Models (e. g. , Stable Diffusion). The code is available at https: //github. com/sony/pagoda.

ICML Conference 2024 Conference Paper

Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data

• Fahim Tajwar
• Anikait Singh
• Archit Sharma
• Rafael Rafailov
• Jeff G. Schneider
• Tengyang Xie
• Stefano Ermon
• Chelsea Finn

Learning from preference labels plays a crucial role in fine-tuning large language models — this is done via supervised learning, on-policy reinforcement learning (RL), or contrastive learning. Different methods come with different implementation tradeoffs, and existing empirical findings present different conclusions, for instance, some results show that online RL is quite important to attain good fine-tuning results, while others find offline methods sufficient. This raises a question: what kind of approaches are important for fine-tuning with preference data and why? In this paper, we answer this question by performing a rigorous analysis of a number of fine-tuning techniques on didactic and full-scale LLM problems. Our main finding is that approaches that use on-policy sampling and attempt to push down the likelihood on certain responses (i. e. , employ a ”negative gradient”) outperform offline and maximum likelihood objectives. We conceptualize our insights and unify methods that use on-policy sampling or negative gradient under a notion of mode-seeking objectives for categorical distributions. Mode-seeking objectives are able to alter probability mass on specific bins of a categorical distribution at a fast rate compared to maximum likelihood, allowing them to relocate masses across bins more effectively. Our analysis prescribes actionable insights for preference fine-tuning of LLMs and informs how data should be collected for maximal improvement.

NeurIPS Conference 2024 Conference Paper

Segment Any Change

• Zhuo Zheng
• Yanfei Zhong
• Liangpei Zhang
• Stefano Ermon

Visual foundation models have achieved remarkable results in zero-shot image classification and segmentation, but zero-shot change detection remains an open problem. In this paper, we propose the segment any change models (AnyChange), a new type of change detection model that supports zero-shot prediction and generalization on unseen change types and data distributions. AnyChange is built on the segment anything model (SAM) via our training-free adaptation method, bitemporal latent matching. By revealing and exploiting intra-image and inter-image semantic similarities in SAM's latent space, bitemporal latent matching endows SAM with zero-shot change detection capabilities in a training-free way. We also propose a point query mechanism to enable AnyChange's zero-shot object-centric change detection capability. We perform extensive experiments to confirm the effectiveness of AnyChange for zero-shot change detection. AnyChange sets a new record on the SECOND benchmark for unsupervised change detection, exceeding the previous SOTA by up to 4. 4\% F$_1$ score, and achieving comparable accuracy with negligible manual annotations (1 pixel per image) for supervised change detection. Code is available at https: //github. com/Z-Zheng/pytorch-change-models.

NeurIPS Conference 2024 Conference Paper

Self-Refining Diffusion Samplers: Enabling Parallelization via Parareal Iterations

• Nikil R. Selvam
• Amil Merchant
• Stefano Ermon

In diffusion models, samples are generated through an iterative refinement process, requiring hundreds of sequential model evaluations. Several recent methods have introduced approximations (fewer discretization steps or distillation) to trade off speed at the cost of sample quality. In contrast, we introduce Self-Refining Diffusion Samplers (SRDS) that retain sample quality and can improve latency at the cost of additional parallel compute. We take inspiration from the Parareal algorithm, a popular numerical method for parallel-in-time integration of differential equations. In SRDS, a quick but rough estimate of a sample is first created and then iteratively refined in parallel through Parareal iterations. SRDS is not only guaranteed to accurately solve the ODE and converge to the serial solution but also benefits from parallelization across the diffusion trajectory, enabling batched inference and pipelining. As we demonstrate for pre-trained diffusion models, the early convergence of this refinement procedure drastically reduces the number of steps required to produce a sample, speeding up generation for instance by up to 1. 7x on a 25-step StableDiffusion-v2 benchmark and up to 4. 3x on longer trajectories.

ICLR Conference 2024 Conference Paper

SequenceMatch: Imitation Learning for Autoregressive Sequence Modelling with Backtracking

• Chris Cundy
• Stefano Ermon

In many domains, autoregressive models can attain high likelihood on the task of predicting the next observation. However, this maximum-likelihood (MLE) objective does not necessarily match a downstream use-case of autoregressively generating high-quality sequences. The MLE objective weights sequences proportionally to their frequency under the data distribution, with no guidance for the model's behaviour out of distribution (OOD): leading to compounding error during autoregressive generation. In order to address this compounding error problem, we formulate sequence generation as an imitation learning (IL) problem. This allows us to minimize a variety of divergences between the distribution of sequences generated by an autoregressive model and sequences from a dataset, including divergences with weight on OOD generated sequences. The IL framework also allows us to incorporate backtracking by introducing a backspace action into the generation process. This further mitigates the compounding error problem by allowing the model to revert a sampled token if it takes the sequence OOD. Our resulting method, SequenceMatch, can be implemented without adversarial training or major architectural changes. We identify the SequenceMatch-χ2 divergence as a more suitable training objective for autoregressive models which are used for generation. We show that empirically, SequenceMatch training leads to improvements over MLE on text generation with language models and arithmetic

ICML Conference 2024 Conference Paper

State-Free Inference of State-Space Models: The *Transfer Function* Approach

• Rom N. Parnichkun
• Stefano Massaroli
• Alessandro Moro
• Jimmy T. H. Smith
• Ramin M. Hasani
• Mathias Lechner
• Qi An
• Christopher Ré

We approach designing a state-space model for deep learning applications through its dual representation, the transfer function, and uncover a highly efficient sequence parallel inference algorithm that is state-free: unlike other proposed algorithms, state-free inference does not incur any significant memory or computational cost with an increase in state size. We achieve this using properties of the proposed frequency domain transfer function parametrization, which enables direct computation of its corresponding convolutional kernel’s spectrum via a single Fast Fourier Transform. Our experimental results across multiple sequence lengths and state sizes illustrates, on average, a 35% training speed improvement over S4 layers – parametrized in time-domain – on the Long Range Arena benchmark, while delivering state-of-the-art downstream performances over other attention-free approaches. Moreover, we report improved perplexity in language modeling over a long convolutional Hyena baseline, by simply introducing our transfer function parametrization. Our code is available at https: //github. com/ruke1ire/RTF.

NeurIPS Conference 2024 Conference Paper

TFG: Unified Training-Free Guidance for Diffusion Models

• Haotian Ye
• Haowei Lin
• Jiaqi Han
• Minkai Xu
• Sheng Liu
• Yitao Liang
• Jianzhu Ma
• James Zou

Given an unconditional diffusion model and a predictor for a target property of interest (e. g. , a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8. 5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

NeurIPS Conference 2024 Conference Paper

TorchSpatial: A Location Encoding Framework and Benchmark for Spatial Representation Learning

• Nemin Wu
• Qian Cao
• Zhangyu Wang
• Zeping Liu
• Yanlin Qi
• Jielu Zhang
• Joshua Ni
• Xiaobai Yao

Spatial representation learning (SRL) aims at learning general-purpose neural network representations from various types of spatial data (e. g. , points, polylines, polygons, networks, images, etc. ) in their native formats. Learning good spatial representations is a fundamental problem for various downstream applications such as species distribution modeling, weather forecasting, trajectory generation, geographic question answering, etc. Even though SRL has become the foundation of almost all geospatial artificial intelligence (GeoAI) research, we have not yet seen significant efforts to develop an extensive deep learning framework and benchmark to support SRL model development and evaluation. To fill this gap, we propose TorchSpatial, a learning framework and benchmark for location (point) encoding, which is one of the most fundamental data types of spatial representation learning. TorchSpatial contains three key components: 1) a unified location encoding framework that consolidates 15 commonly recognized location encoders, ensuring scalability and reproducibility of the implementations; 2) the LocBench benchmark tasks encompassing 7 geo-aware image classification and 10 geo-aware imageregression datasets; 3) a comprehensive suite of evaluation metrics to quantify geo-aware models’ overall performance as well as their geographic bias, with a novel Geo-Bias Score metric. Finally, we provide a detailed analysis and insights into the model performance and geographic bias of different location encoders. We believe TorchSpatial will foster future advancement of spatial representationlearning and spatial fairness in GeoAI research. The TorchSpatial model framework and LocBench benchmark are available at https: //github. com/seai-lab/TorchSpatial, and the Geo-Bias Score evaluation framework is available at https: //github. com/seai-lab/PyGBS.

NeurIPS Conference 2024 Conference Paper

TrAct: Making First-layer Pre-Activations Trainable

• Felix Petersen
• Christian Borgelt
• Stefano Ermon

We consider the training of the first layer of vision models and notice the clear relationship between pixel values and gradient update magnitudes: the gradients arriving at the weights of a first layer are by definition directly proportional to (normalized) input pixel values. Thus, an image with low contrast has a smaller impact on learning than an image with higher contrast, and a very bright or very dark image has a stronger impact on the weights than an image with moderate brightness. In this work, we propose performing gradient descent on the embeddings produced by the first layer of the model. However, switching to discrete inputs with an embedding layer is not a reasonable option for vision models. Thus, we propose the conceptual procedure of (i) a gradient descent step on first layer activations to construct an activation proposal, and (ii) finding the optimal weights of the first layer, i. e. , those weights which minimize the squared distance to the activation proposal. We provide a closed form solution of the procedure and adjust it for robust stochastic training while computing everything efficiently. Empirically, we find that TrAct (Training Activations) speeds up training by factors between 1. 25x and 4x while requiring only a small computational overhead. We demonstrate the utility of TrAct with different optimizers for a range of different vision models including convolutional and transformer architectures.

AAAI Conference 2024 Conference Paper

Uncertainty Quantification for Forward and Inverse Problems of PDEs via Latent Global Evolution

• Tailin Wu
• Willie Neiswanger
• Hongtao Zheng
• Stefano Ermon
• Jure Leskovec

Deep learning-based surrogate models have demonstrated remarkable advantages over classical solvers in terms of speed, often achieving speedups of 10 to 1000 times over traditional partial differential equation (PDE) solvers. However, a significant challenge hindering their widespread adoption in both scientific and industrial domains is the lack of understanding about their prediction uncertainties, particularly in scenarios that involve critical decision making. To address this limitation, we propose a method that integrates efficient and precise uncertainty quantification into a deep learning-based surrogate model. Our method, termed Latent Evolution of PDEs with Uncertainty Quantification (LE-PDE-UQ), endows deep learning-based surrogate models with robust and efficient uncertainty quantification capabilities for both forward and inverse problems. LE-PDE-UQ leverages latent vectors within a latent space to evolve both the system's state and its corresponding uncertainty estimation. The latent vectors are decoded to provide predictions for the system's state as well as estimates of its uncertainty. In extensive experiments, we demonstrate the accurate uncertainty quantification performance of our approach, surpassing that of strong baselines including deep ensembles, Bayesian neural network layers, and dropout. Our method excels at propagating uncertainty over extended auto-regressive rollouts, making it suitable for scenarios involving long-term predictions. Our code is available at: https://github.com/AI4Science-WestlakeU/le-pde-uq.

TMLR Journal 2023 Journal Article

Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models

• Aarohi Srivastava
• Abhinav Rastogi
• Abhishek Rao
• Abu Awal Md Shoeb
• Abubakar Abid
• Adam Fisch
• Adam R. Brown
• Adam Santoro

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG- bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood develop- ment, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google- internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

NeurIPS Conference 2023 Conference Paper

Calibration by Distribution Matching: Trainable Kernel Calibration Metrics

• Charlie Marx
• Sofian Zalouk
• Stefano Ermon

Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc recalibration, which can worsen the sharpness of forecasts. Drawing on the insight that calibration can be viewed as a distribution matching task, we introduce kernel-based calibration metrics that unify and generalize popular forms of calibration for both classification and regression. These metrics admit differentiable sample estimates, making it easy to incorporate a calibration objective into empirical risk minimization. Furthermore, we provide intuitive mechanisms to tailor calibration metrics to a decision task, and enforce accurate loss estimation and no regret decisions. Our empirical evaluation demonstrates that employing these metrics as regularizers enhances calibration, sharpness, and decision-making across a range of regression and classification tasks, outperforming methods relying solely on post-hoc recalibration.

ICML Conference 2023 Conference Paper

CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations

• Gengchen Mai
• Ni Lao
• Yutong He
• Jiaming Song
• Stefano Ermon

Geo-tagged images are publicly available in large quantities, whereas labels such as object classes are rather scarce and expensive to collect. Meanwhile, contrastive learning has achieved tremendous success in various natural image and language tasks with limited labeled data. However, existing methods fail to fully leverage geospatial information, which can be paramount to distinguishing objects that are visually similar. To directly leverage the abundant geospatial information associated with images in pre-training, fine-tuning, and inference stages, we present Contrastive Spatial Pre-Training (CSP), a self-supervised learning framework for geo-tagged images. We use a dual-encoder to separately encode the images and their corresponding geo-locations, and use contrastive objectives to learn effective location representations from images, which can be transferred to downstream supervised tasks such as image classification. Experiments show that CSP can improve model performance on both iNat2018 and fMoW datasets. Especially, on iNat2018, CSP significantly boosts the model performance with 10-34% relative improvement with various labeled training data sampling ratios.

ICML Conference 2023 Conference Paper

Deep Latent State Space Models for Time-Series Generation

• Linqi Zhou
• Michael Poli
• Winnie Xu
• Stefano Massaroli
• Stefano Ermon

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.

NeurIPS Conference 2023 Conference Paper

Direct Preference Optimization: Your Language Model is Secretly a Reward Model

• Rafael Rafailov
• Archit Sharma
• Eric Mitchell
• Christopher D Manning
• Stefano Ermon
• Chelsea Finn

While large-scale unsupervised language models (LMs) learn broad world knowledge and some reasoning skills, achieving precise control of their behavior is difficult due to the completely unsupervised nature of their training. Existing methods for gaining such steerability collect human labels of the relative quality of model generations and fine-tune the unsupervised LM to align with these preferences, often with reinforcement learning from human feedback (RLHF). However, RLHF is a complex and often unstable procedure, first fitting a reward model that reflects the human preferences, and then fine-tuning the large unsupervised LM using reinforcement learning to maximize this estimated reward without drifting too far from the original model. In this paper, we leverage a mapping between reward functions and optimal policies to show that this constrained reward maximization problem can be optimized exactly with a single stage of policy training, essentially solving a classification problem on the human preference data. The resulting algorithm, which we call Direct Preference Optimization (DPO), is stable, performant, and computationally lightweight, eliminating the need for fitting a reward model, sampling from the LM during fine-tuning, or performing significant hyperparameter tuning. Our experiments show that DPO can fine-tune LMs to align with human preferences as well as or better than existing methods. Notably, fine-tuning with DPO exceeds RLHF's ability to control sentiment of generations and improves response quality in summarization and single-turn dialogue while being substantially simpler to implement and train.

ICLR Conference 2023 Conference Paper

Dual Diffusion Implicit Bridges for Image-to-Image Translation

• Xuan Su
• Jiaming Song
• Chenlin Meng
• Stefano Ermon

Common image-to-image translation methods rely on joint training over data from both source and target domains. The training process requires concurrent access to both datasets, which hinders data separation and privacy protection; and existing models cannot be easily adapted for translation of new domain pairs. We present Dual Diffusion Implicit Bridges (DDIBs), an image translation method based on diffusion models, that circumvents training on domain pairs. Image translation with DDIBs relies on two diffusion models trained independently on each domain, and is a two-step process: DDIBs first obtain latent encodings for source images with the source diffusion model, and then decode such encodings using the target model to construct target images. Both steps are defined via ordinary differential equations (ODEs), thus the process is cycle consistent only up to discretization errors of the ODE solvers. Theoretically, we interpret DDIBs as concatenation of source to latent, and latent to target Schrodinger Bridges, a form of entropy-regularized optimal transport, to explain the efficacy of the method. Experimentally, we apply DDIBs on synthetic and high-resolution image datasets, to demonstrate their utility in a wide variety of translation tasks and their inherent optimal transport properties.

NeurIPS Conference 2023 Conference Paper

Equivariant Flow Matching with Hybrid Probability Transport for 3D Molecule Generation

• Yuxuan Song
• Jingjing Gong
• Minkai Xu
• Ziyao Cao
• Yanyan Lan
• Stefano Ermon
• Hao Zhou
• Wei-Ying Ma

The generation of 3D molecules requires simultaneously deciding the categorical features (atom types) and continuous features (atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in generating feature-rich geometries. However, existing DMs typically suffer from unstable probability dynamics with inefficient sampling speed. In this paper, we introduce geometric flow matching, which enjoys the advantages of both equivariant modeling and stabilized probability dynamics. More specifically, we propose a hybrid probability path where the coordinates probability path is regularized by an equivariant optimal transport, and the information between different modalities is aligned. Experimentally, the proposed method could consistently achieve better performance on multiple molecule generation benchmarks with 4. 75$\times$ speed up of sampling on average.

ICLR Conference 2023 Conference Paper

Extreme Q-Learning: MaxEnt RL without Entropy

• Divyansh Garg
• Joey Hejna
• Matthieu Geist
• Stefano Ermon

Modern Deep Reinforcement Learning (RL) algorithms require estimates of the maximal Q-value, which are difficult to compute in continuous domains with an infinite number of possible actions. In this work, we introduce a new update rule for online and offline RL which directly models the maximal value using Extreme Value Theory (EVT), drawing inspiration from economics. By doing so, we avoid computing Q-values using out-of-distribution actions which is often a substantial source of error. Our key insight is to introduce an objective that directly estimates the optimal soft-value functions (LogSumExp) in the maximum entropy RL setting without needing to sample from a policy. Using EVT, we derive our \emph{Extreme Q-Learning} framework and consequently online and, for the first time, offline MaxEnt Q-learning algorithms, that do not explicitly require access to a policy or its entropy. Our method obtains consistently strong performance in the D4RL benchmark, outperforming prior works by \emph{10+ points} on the challenging Franka Kitchen tasks while offering moderate improvements over SAC and TD3 on online DM Control tasks. Visualizations and code can be found on our website.

ICML Conference 2023 Conference Paper

FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation

• Chieh-Hsin Lai
• Yuhta Takida
• Naoki Murata
• Toshimitsu Uesaka
• Yuki Mitsufuji
• Stefano Ermon

Score-based generative models (SGMs) learn a family of noise-conditional score functions corresponding to the data density perturbed with increasingly large amounts of noise. These perturbed data densities are linked together by the Fokker-Planck equation (FPE), a partial differential equation (PDE) governing the spatial-temporal evolution of a density undergoing a diffusion process. In this work, we derive a corresponding equation called the score FPE that characterizes the noise-conditional scores of the perturbed data densities (i. e. , their gradients). Surprisingly, despite the impressive empirical performance, we observe that scores learned through denoising score matching (DSM) fail to fulfill the underlying score FPE, which is an inherent self-consistency property of the ground truth score. We prove that satisfying the score FPE is desirable as it improves the likelihood and the degree of conservativity. Hence, we propose to regularize the DSM objective to enforce satisfaction of the score FPE, and we show the effectiveness of this approach across various datasets.

ICLR Conference 2023 Conference Paper

Generative Modeling Helps Weak Supervision (and Vice Versa)

• Benedikt Boecking
• Nicholas Carl Roberts
• Willie Neiswanger
• Stefano Ermon
• Frederic Sala
• Artur Dubrawski

Many promising applications of supervised machine learning face hurdles in the acquisition of labeled data in sufficient quantity and quality, creating an expensive bottleneck. To overcome such limitations, techniques that do not depend on ground truth labels have been studied, including weak supervision and generative modeling. While these techniques would seem to be usable in concert, improving one another, how to build an interface between them is not well-understood. In this work, we propose a model fusing programmatic weak supervision and generative adversarial networks and provide theoretical justification motivating this fusion. The proposed approach captures discrete latent variables in the data alongside the weak supervision derived label estimate. Alignment of the two allows for better modeling of sample-dependent accuracies of the weak supervision sources, improving the estimate of unobserved labels. It is the first approach to enable data augmentation through weakly supervised synthetic images and pseudolabels. Additionally, its learned latent variables can be inspected qualitatively. The model outperforms baseline weak supervision label models on a number of multiclass image classification datasets, improves the quality of generated images, and further improves end-model performance through data augmentation with synthetic samples.

NeurIPS Conference 2023 Conference Paper

GEO-Bench: Toward Foundation Models for Earth Monitoring

• Alexandre Lacoste
• Nils Lehmann
• Pau Rodriguez
• Evan Sherwin
• Hannah Kerner
• Björn Lütjens
• Jeremy Irvin
• David Dao

Recent progress in self-supervision has shown that pre-training large neural networks on vast amounts of unsupervised data can lead to substantial increases in generalization to downstream tasks. Such models, recently coined foundation models, have been transformational to the field of natural language processing. Variants have also been proposed for image data, but their applicability to remote sensing tasks is limited. To stimulate the development of foundation models for Earth monitoring, we propose a benchmark comprised of six classification and six segmentation tasks, which were carefully curated and adapted to be both relevant to the field and well-suited for model evaluation. We accompany this benchmark with a robust methodology for evaluating models and reporting aggregated results to enable a reliable assessment of progress. Finally, we report results for 20 baselines to gain information about the performance of existing models. We believe that this benchmark will be a driver of progress across a variety of Earth monitoring tasks.

ICML Conference 2023 Conference Paper

Geometric Latent Diffusion Models for 3D Molecule Generation

• Minkai Xu
• Alexander S. Powers
• Ron O. Dror
• Stefano Ermon
• Jure Leskovec

Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we propose a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM’s higher capacity for controllable generation thanks to the latent modeling. Code is provided at https: //github. com/MinkaiXu/GeoLDM.

ICML Conference 2023 Conference Paper

GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration

• Naoki Murata
• Koichi Saito
• Chieh-Hsin Lai
• Yuhta Takida
• Toshimitsu Uesaka
• Yuki Mitsufuji
• Stefano Ermon

Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine-tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.

NeurIPS Conference 2023 Conference Paper

Holistic Evaluation of Text-to-Image Models

• Tony Lee
• Michihiro Yasunaga
• Chenlin Meng
• Yifan Mai
• Joon Sung Park
• Agrim Gupta
• Yunzhi Zhang
• Deepak Narayanan

The stunning qualitative improvement of text-to-image models has led to their widespread attention and adoption. However, we lack a comprehensive quantitative understanding of their capabilities and risks. To fill this gap, we introduce a new benchmark, Holistic Evaluation of Text-to-Image Models (HEIM). Whereas previous evaluations focus mostly on image-text alignment and image quality, we identify 12 aspects, including text-image alignment, image quality, aesthetics, originality, reasoning, knowledge, bias, toxicity, fairness, robustness, multilinguality, and efficiency. We curate 62 scenarios encompassing these aspects and evaluate 26 state-of-the-art text-to-image models on this benchmark. Our results reveal that no single model excels in all aspects, with different models demonstrating different strengths. We release the generated images and human evaluation results for full transparency at https: //crfm. stanford. edu/heim/latest and the code at https: //github. com/stanford-crfm/helm, which is integrated with the HELM codebase

ICML Conference 2023 Conference Paper

Hyena Hierarchy: Towards Larger Convolutional Language Models

• Michael Poli
• Stefano Massaroli
• Eric Nguyen
• Daniel Y. Fu
• Tri Dao
• Stephen Baccus
• Yoshua Bengio
• Stefano Ermon

Recent advances in deep learning have relied heavily on the use of large Transformers due to their ability to learn at scale. However, the core building block of Transformers, the attention operator, exhibits quadratic cost in sequence length, limiting the amount of context accessible. Existing subquadratic methods based on low-rank and sparse approximations need to be combined with dense attention layers to match Transformers at scale, indicating a gap in capability. In this work, we propose Hyena, a subquadratic drop-in replacement for attention constructed by interleaving implicitly parametrized long convolutions and data-controlled gating. In challenging reasoning tasks on sequences of thousands to hundreds of thousands of tokens, Hyena improves accuracy by more than 50 points over operators relying on state-space models, transfer functions, and other implicit and explicit methods, matching attention-based models. We set a new state-of-the-art for dense-attention-free architectures on language modeling in standard datasets WikiText103 and The Pile, reaching Transformer quality with a 20% reduction in training compute required at sequence length 2k. Hyena operators are 2x faster than highly optimized attention at sequence length 8k, with speedups of 100x at 64k.

NeurIPS Conference 2023 Conference Paper

HyenaDNA: Long-Range Genomic Sequence Modeling at Single Nucleotide Resolution

• Eric Nguyen
• Michael Poli
• Marjan Faizi
• Armin Thomas
• Michael Wornow
• Callum Birch-Sykes
• Stefano Massaroli
• Aman Patel

Genomic (DNA) sequences encode an enormous amount of information for gene regulation and protein synthesis. Similar to natural language models, researchers have proposed foundation models in genomics to learn generalizable features from unlabeled genome data that can then be fine-tuned for downstream tasks such as identifying regulatory elements. Due to the quadratic scaling of attention, previous Transformer-based genomic models have used 512 to 4k tokens as context (<0. 001% of the human genome), significantly limiting the modeling of long-range interactions in DNA. In addition, these methods rely on tokenizers or fixed k-mers to aggregate meaningful DNA units, losing single nucleotide resolution (i. e. DNA "characters") where subtle genetic variations can completely alter protein function via single nucleotide polymorphisms (SNPs). Recently, Hyena, a large language model based on implicit convolutions was shown to match attention in quality while allowing longer context lengths and lower time complexity. Leveraging Hyena’s new long-range capabilities, we present HyenaDNA, a genomic foundation model pretrained on the human reference genome with context lengths of up to 1 million tokens at the single nucleotide-level – an up to 500x increase over previous dense attention-based models. HyenaDNA scales sub-quadratically in sequence length (training up to 160x faster than Transformer), uses single nucleotide tokens, and has full global context at each layer. We explore what longer context enables - including the first use of in-context learning in genomics for simple adaptation to novel tasks without updating pretrained model weights. On fine-tuned benchmarks from the Nucleotide Transformer, HyenaDNA reaches state-of-the-art (SotA) on 12 of 18 datasets using a model with orders of magnitude less parameters and pretraining data. 1 On the GenomicBenchmarks, HyenaDNA surpasses SotA on 7 of 8 datasets on average by +10 accuracy points. Code at https: //github. com/HazyResearch/hyena-dna.

NeurIPS Conference 2023 Conference Paper

Laughing Hyena Distillery: Extracting Compact Recurrences From Convolutions

• Stefano Massaroli
• Michael Poli
• Dan Fu
• Hermann Kumbong
• Rom Parnichkun
• David Romero
• Aman Timalsina
• Quinn McIntyre

Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In particular, long convolution sequence models have achieved state-of-the-art performance in many domains, but incur a significant cost during auto-regressive inference workloads -- naively requiring a full pass (or caching of activations) over the input sequence for each generated token -- similarly to attention-based models. In this paper, we seek to enable $\mathcal O(1)$ compute and memory cost per token in any pre-trained long convolution architecture to reduce memory footprint and increase throughput during generation. Concretely, our methods consist in extracting low-dimensional linear state-space models from each convolution layer, building upon rational interpolation and model-order reduction techniques. We further introduce architectural improvements to convolution-based layers such as Hyena: by weight-tying the filters across channels into heads, we achieve higher pre-training quality and reduce the number of filters to be distilled. The resulting model achieves 10x higher throughput than Transformers and 1. 5x higher than Hyena at 1. 3B parameters, without any loss in quality after distillation.

ICML Conference 2023 Conference Paper

Long Horizon Temperature Scaling

• Andy Shih
• Dorsa Sadigh
• Stefano Ermon

Temperature scaling is a popular technique for tuning the sharpness of a model distribution. It is used extensively for sampling likely generations and calibrating model uncertainty, and even features as a controllable parameter to many large language models in deployment. However, autoregressive models rely on myopic temperature scaling that greedily optimizes the next token. To address this, we propose Long Horizon Temperature Scaling (LHTS), a novel approach for sampling from temperature-scaled joint distributions. LHTS is compatible with all likelihood-based models, and optimizes for the long-horizon likelihood of samples. We derive a temperature-dependent LHTS objective, and show that fine-tuning a model on a range of temperatures produces a single model capable of generation with a controllable long-horizon temperature parameter. We experiment with LHTS on image diffusion models and character/language autoregressive models, demonstrating its advantages over myopic temperature scaling in likelihood and sample quality, and showing improvements in accuracy of a multiple choice analogy by $10$%.

TMLR Journal 2023 Journal Article

MERMAIDE: Learning to Align Learners using Model-Based Meta-Learning

• Arundhati Banerjee
• Soham Rajesh Phade
• Stefano Ermon
• Stephan Zheng

We study how a principal can efficiently and effectively intervene on the rewards of a previously unseen learning agent in order to induce desirable outcomes. This is relevant to many real-world settings like auctions or taxation, where the principal may not know the learning behavior nor the rewards of real people. Moreover, the principal should be few-shot adaptable and minimize the number of interventions, because interventions are often costly. We introduce MERMAIDE, a model-based meta-learning framework to train a principal that can quickly adapt to out-of-distribution agents with different learning strategies and reward functions. We validate this approach step-by-step. First, in a Stackelberg setting with a best-response agent, we show that meta-learning enables quick convergence to the theoretically known Stackelberg equilibrium at test time, although noisy observations severely increase the sample complexity. We then show that our model-based meta-learning approach is cost-effective in intervening on bandit agents with unseen explore-exploit strategies. Finally, we outperform baselines that use either meta-learning or agent behavior modeling, in both $0$-shot and $1$-shot settings with partial agent information.

AAAI Conference 2023 Conference Paper

Offline Imitation Learning with Suboptimal Demonstrations via Relaxed Distribution Matching

• Lantao Yu
• Tianhe Yu
• Jiaming Song
• Willie Neiswanger
• Stefano Ermon

Offline imitation learning (IL) promises the ability to learn performant policies from pre-collected demonstrations without interactions with the environment. However, imitating behaviors fully offline typically requires numerous expert data. To tackle this issue, we study the setting where we have limited expert data and supplementary suboptimal data. In this case, a well-known issue is the distribution shift between the learned policy and the behavior policy that collects the offline data. Prior works mitigate this issue by regularizing the KL divergence between the stationary state-action distributions of the learned policy and the behavior policy. We argue that such constraints based on exact distribution matching can be overly conservative and hamper policy learning, especially when the imperfect offline data is highly suboptimal. To resolve this issue, we present RelaxDICE, which employs an asymmetrically-relaxed f-divergence for explicit support regularization. Specifically, instead of driving the learned policy to exactly match the behavior policy, we impose little penalty whenever the density ratio between their stationary state-action distributions is upper bounded by a constant. Note that such formulation leads to a nested min-max optimization problem, which causes instability in practice. RelaxDICE addresses this challenge by supporting a closed-form solution for the inner maximization problem. Extensive empirical study shows that our method significantly outperforms the best prior offline IL method in six standard continuous control environments with over 30% performance gain on average, across 22 settings where the imperfect dataset is highly suboptimal.

NeurIPS Conference 2023 Conference Paper

Parallel Sampling of Diffusion Models

• Andy Shih
• Suneel Belkhale
• Stefano Ermon
• Dorsa Sadigh
• Nima Anari

Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0. 2s on 100-step DiffusionPolicy and 14. 6s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.

ICML Conference 2023 Conference Paper

Reflected Diffusion Models

• Aaron Lou
• Stefano Ermon

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

NeurIPS Conference 2023 Conference Paper

Scaling Riemannian Diffusion Models

• Aaron Lou
• Minkai Xu
• Adam Farris
• Stefano Ermon

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement and is competitive with other techniques. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds, including $SU(n)$ lattices in the context of lattice quantum chromodynamics (QCD). Finally, we apply our models to contrastively learned hyperspherical embeddings, curbing the representation collapse problem in the projection head and closing the gap between theory and practice.

ICLR Conference 2023 Conference Paper

Understanding and Adopting Rational Behavior by Bellman Score Estimation

• Kuno Kim
• Stefano Ermon

We are interested in solving a class of problems that seek to understand and adopt rational behavior from demonstrations. We may broadly classify these problems into four categories of reward identification, counterfactual analysis, behavior imitation, and behavior transfer. In this work, we make a key observation that knowing how changes in the underlying rewards affect the optimal behavior allows one to solve a variety of aforementioned problems. To a local approximation, this quantity is precisely captured by what we term the Bellman score, i.e gradient of log probabilities of the optimal policy with respect to the reward. We introduce the Bellman score operator which provably converges to the gradient of the infinite-horizon optimal Q-values with respect to the reward which can then be used to directly estimate the score. Guided by our theory, we derive a practical score-learning algorithm which can be used for score estimation in high-dimensional state-actions spaces. We show that score-learning can be used to reliably identify rewards, perform counterfactual predictions, achieve state-of-the-art behavior imitation, and transfer policies across environments.

NeurIPS Conference 2023 Conference Paper

UniControl: A Unified Diffusion Model for Controllable Visual Generation In the Wild

• Can Qin
• Shu Zhang
• Ning Yu
• Yihao Feng
• Xinyi Yang
• Yingbo Zhou
• Huan Wang
• Juan Carlos Niebles

Achieving machine autonomy and human control often represent divergent objectives in the design of interactive AI systems. Visual generative foundation models such as Stable Diffusion show promise in navigating these goals, especially when prompted with arbitrary languages. However, they often fall short in generating images with spatial, structural, or geometric controls. The integration of such controls, which can accommodate various visual conditions in a single unified model, remains an unaddressed challenge. In response, we introduce UniControl, a new generative foundation model that consolidates a wide array of controllable condition-to-image (C2I) tasks within a singular framework, while still allowing for arbitrary language prompts. UniControl enables pixel-level-precise image generation, where visual conditions primarily influence the generated structures and language prompts guide the style and context. To equip UniControl with the capacity to handle diverse visual conditions, we augment pretrained text-to-image diffusion models and introduce a task-aware HyperNet to modulate the diffusion models, enabling the adaptation to different C2I tasks simultaneously. Trained on nine unique C2I tasks, UniControl demonstrates impressive zero-shot generation abilities with unseen visual conditions. Experimental results show that UniControl often surpasses the performance of single-task-controlled methods of comparable model sizes. This control versatility positions UniControl as a significant advancement in the realm of controllable visual generation.

ICML Conference 2022 Conference Paper

A General Recipe for Likelihood-free Bayesian Optimization

• Jiaming Song
• Lantao Yu
• Willie Neiswanger
• Stefano Ermon

The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem, which extends an existing likelihood-free density ratio estimation method related to probability of improvement (PI). By choosing the utility function for expected improvement (EI), LFBO outperforms the aforementioned method, as well as various state-of-the-art black-box optimization methods on several real-world optimization problems. LFBO can also leverage composite structures of the objective function, which further improves its regret by several orders of magnitude.

ICLR Conference 2022 Conference Paper

An Experimental Design Perspective on Model-Based Reinforcement Learning

• Viraj Mehta
• Biswajit Paria
• Jeff G. Schneider
• Stefano Ermon
• Willie Neiswanger

In many practical applications of RL, it is expensive to observe state transitions from the environment. For example, in the problem of plasma control for nuclear fusion, computing the next state for a given state-action pair requires querying an expensive transition function which can lead to many hours of computer simulation or dollars of scientific research. Such expensive data collection prohibits application of standard RL algorithms which usually require a large number of observations to learn. In this work, we address the problem of efficiently learning a policy while making a minimal number of state-action queries to the transition function. In particular, we leverage ideas from Bayesian optimal experimental design to guide the selection of state-action queries for efficient learning. We propose an \emph{acquisition function} that quantifies how much information a state-action pair would provide about the optimal solution to a Markov decision process. At each iteration, our algorithm maximizes this acquisition function, to choose the most informative state-action pair to be queried, thus yielding a data-efficient RL approach. We experiment with a variety of simulated continuous control problems and show that our approach learns an optimal policy with up to $5$ -- $1,000\times$ less data than model-based RL baselines and $10^3$ -- $10^5\times$ less data than model-free RL baselines. We also provide several ablated comparisons which point to substantial improvements arising from the principled method of obtaining data.

ICML Conference 2022 Conference Paper

Bit Prioritization in Variational Autoencoders via Progressive Coding

• Rui Shu
• Stefano Ermon

The hierarchical variational autoencoder (HVAE) is a popular generative model used for many representation learning tasks. However, its application to image synthesis often yields models with poor sample quality. In this work, we treat image synthesis itself as a hierarchical representation learning problem and regularize an HVAE toward representations that improve the model’s image synthesis performance. We do so by leveraging the progressive coding hypothesis, which claims hierarchical latent variable models that are good at progressive lossy compression will generate high-quality samples. To test this hypothesis, we first show empirically that conventionally-trained HVAEs are not good progressive coders. We then propose a simple method that constrains the hierarchical representations to prioritize the encoding of information beneficial for lossy compression, and show that this modification leads to improved sample quality. Our work lends further support to the progressive coding hypothesis and demonstrates that this hypothesis should be exploited when designing variational autoencoders.

ICML Conference 2022 Conference Paper

ButterflyFlow: Building Invertible Layers with Butterfly Matrices

• Chenlin Meng
• Linqi Zhou
• Kristy Choi
• Tri Dao
• Stefano Ermon

Normalizing flows model complex probability distributions using maps obtained by composing invertible layers. Special linear layers such as masked and 1{\texttimes}1 convolutions play a key role in existing architectures because they increase expressive power while having tractable Jacobians and inverses. We propose a new family of invertible linear layers based on butterfly layers, which are known to theoretically capture complex linear structures including permutations and periodicity, yet can be inverted efficiently. This representational power is a key advantage of our approach, as such structures are common in many real-world datasets. Based on our invertible butterfly layers, we construct a new class of normalizing flow mod- els called ButterflyFlow. Empirically, we demonstrate that ButterflyFlows not only achieve strong density estimation results on natural images such as MNIST, CIFAR-10, and ImageNet-32{\texttimes}32, but also obtain significantly better log-likelihoods on structured datasets such as galaxy images and MIMIC-III patient cohorts{—}all while being more efficient in terms of memory and computation than relevant baselines.

ICLR Conference 2022 Conference Paper

Comparing Distributions by Measuring Differences that Affect Decision Making

• Shengjia Zhao
• Abhishek Sinha
• Yutong He
• Aidan Perreault
• Jiaming Song
• Stefano Ermon

Measuring the discrepancy between two probability distributions is a fundamental problem in machine learning and statistics. We propose a new class of discrepancies based on the optimal loss for a decision task -- two distributions are different if the optimal decision loss is higher on their mixture than on each individual distribution. By suitably choosing the decision task, this generalizes the Jensen-Shannon divergence and the maximum mean discrepancy family. We apply our approach to two-sample tests, and on various benchmarks, we achieve superior test power compared to competing methods. In addition, a modeler can directly specify their preferences when comparing distributions through the decision loss. We apply this property to understanding the effects of climate change on different social and economic activities, evaluating sample quality, and selecting features targeting different decision tasks.

NeurIPS Conference 2022 Conference Paper

Concrete Score Matching: Generalized Score Matching for Discrete Data

• Chenlin Meng
• Kristy Choi
• Jiaming Song
• Stefano Ermon

Representing probability distributions by the gradient of their density functions has proven effective in modeling a wide range of continuous data modalities. However, this representation is not applicable in discrete domains where the gradient is undefined. To this end, we propose an analogous score function called the “Concrete score”, a generalization of the (Stein) score for discrete settings. Given a predefined neighborhood structure, the Concrete score of any input is defined by the rate of change of the probabilities with respect to local directional changes of the input. This formulation allows us to recover the (Stein) score in continuous domains when measuring such changes by the Euclidean distance, while using the Manhattan distance leads to our novel score function in discrete domains. Finally, we introduce a new framework to learn such scores from samples called Concrete Score Matching (CSM), and propose an efficient training objective to scale our approach to high dimensions. Empirically, we demonstrate the efficacy of CSM on density estimation tasks on a mixture of synthetic, tabular, and high-dimensional image datasets, and demonstrate that it performs favorably relative to existing baselines for modeling discrete data.

NeurIPS Conference 2022 Conference Paper

Denoising Diffusion Restoration Models

• Bahjat Kawar
• Michael Elad
• Stefano Ermon
• Jiaming Song

Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the measurements. However, efficient solutions often require problem-specific supervised training to model the posterior, whereas unsupervised methods that are not problem-specific typically rely on inefficient iterative methods. This work addresses these issues by introducing Denoising Diffusion Restoration Models (DDRM), an efficient, unsupervised posterior sampling method. Motivated by variational inference, DDRM takes advantage of a pre-trained denoising diffusion generative model for solving any linear inverse problem. We demonstrate DDRM's versatility on several image datasets for super-resolution, deblurring, inpainting, and colorization under various amounts of measurement noise. DDRM outperforms the current leading unsupervised methods on the diverse ImageNet dataset in reconstruction quality, perceptual quality, and runtime, being $5\times$ faster than the nearest competitor. DDRM also generalizes well for natural images out of the distribution of the observed ImageNet training set.

NeurIPS Conference 2022 Conference Paper

Efficient Spatially Sparse Inference for Conditional GANs and Diffusion Models

• Muyang Li
• Ji Lin
• Chenlin Meng
• Stefano Ermon
• Song Han
• Jun-Yan Zhu

During image editing, existing deep generative models tend to re-synthesize the entire output from scratch, including the unedited regions. This leads to a significant waste of computation, especially for minor editing operations. In this work, we present Spatially Sparse Inference (SSI), a general-purpose technique that selectively performs computation for edited regions and accelerates various generative models, including both conditional GANs and diffusion models. Our key observation is that users tend to make gradual changes to the input image. This motivates us to cache and reuse the feature maps of the original image. Given an edited image, we sparsely apply the convolutional filters to the edited regions while reusing the cached features for the unedited regions. Based on our algorithm, we further propose Sparse Incremental Generative Engine (SIGE) to convert the computation reduction to latency reduction on off-the-shelf hardware. With 1. 2%-area edited regions, our method reduces the computation of DDIM by $7. 5\times$ and GauGAN by $18\times$ while preserving the visual fidelity. With SIGE, we accelerate the inference time of DDIM by $3. 0\times$ on RTX 3090 and $6. 6\times$ on Apple M1 Pro CPU, and GauGAN by $4. 2\times$ on RTX 3090 and $14\times$ on Apple M1 Pro CPU.

NeurIPS Conference 2022 Conference Paper

Exploration via Planning for Information about the Optimal Trajectory

• Viraj Mehta
• Ian Char
• Joseph Abbate
• Rory Conlin
• Mark Boyer
• Stefano Ermon
• Jeff Schneider
• Willie Neiswanger

Many potential applications of reinforcement learning (RL) are stymied by the large numbers of samples required to learn an effective policy. This is especially true when applying RL to real-world control tasks, e. g. in the sciences or robotics, where executing a policy in the environment is costly. In popular RL algorithms, agents typically explore either by adding stochasticity to a reward-maximizing policy or by attempting to gather maximal information about environment dynamics without taking the given task into account. In this work, we develop a method that allows us to plan for exploration while taking both the task and the current knowledge about the dynamics into account. The key insight to our approach is to plan an action sequence that maximizes the expected information gain about the optimal trajectory for the task at hand. We demonstrate that our method learns strong policies with 2x fewer samples than strong exploration baselines and 200x fewer samples than model free methods on a diverse set of low-to-medium dimensional control tasks in both the open-loop and closed-loop control settings.

NeurIPS Conference 2022 Conference Paper

FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness

• Tri Dao
• Dan Fu
• Stefano Ermon
• Atri Rudra
• Christopher Ré

Transformers are slow and memory-hungry on long sequences, since the time and memory complexity of self-attention are quadratic in sequence length. Approximate attention methods have attempted to address this problem by trading off model quality to reduce the compute complexity, but often do not achieve wall-clock speedup. We argue that a missing principle is making attention algorithms IO-aware---accounting for reads and writes between levels of GPU memory. We propose FlashAttention, an IO-aware exact attention algorithm that uses tiling to reduce the number of memory reads/writes between GPU high bandwidth memory (HBM) and GPU on-chip SRAM. We analyze the IO complexity of FlashAttention, showing that it requires fewer HBM accesses than standard attention, and is optimal for a range of SRAM sizes. We also extend FlashAttention, yielding an approximate attention algorithm that is faster than any existing approximate attention method. FlashAttention, 3x speedup on GPT-2 (seq. length 1K), and 2. 4x speedup on long-range arena (seq. length 1K-4K). FlashAttention, yielding higher quality models (0. 7 better perplexity on GPT-2 and 6. 4 points of lift on long-document classification) and entirely new capabilities: the first Transformers to achieve better-than-chance performance on the Path-X challenge (seq. length 16K, 61. 4% accuracy) and Path-256 (seq. length 64K, 63. 1% accuracy).

NeurIPS Conference 2022 Conference Paper

Generalizing Bayesian Optimization with Decision-theoretic Entropies

• Willie Neiswanger
• Lantao Yu
• Shengjia Zhao
• Chenlin Meng
• Stefano Ermon

Bayesian optimization (BO) is a popular method for efficiently inferring optima of an expensive black-box function via a sequence of queries. Existing information-theoretic BO procedures aim to make queries that most reduce the uncertainty about optima, where the uncertainty is captured by Shannon entropy. However, an optimal measure of uncertainty would, ideally, factor in how we intend to use the inferred quantity in some downstream procedure. In this paper, we instead consider a generalization of Shannon entropy from work in statistical decision theory (DeGroot 1962, Rao 1984), which contains a broad class of uncertainty measures parameterized by a problem-specific loss function corresponding to a downstream task. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures such as knowledge gradient, expected improvement, and entropy search. We then show how alternative choices for the loss yield a flexible family of acquisition functions that can be customized for use in novel optimization settings. Additionally, we develop gradient-based methods to efficiently optimize our proposed family of acquisition functions, and demonstrate strong empirical performance on a diverse set of sequential decision making tasks, including variants of top-$k$ optimization, multi-level set estimation, and sequence search.

ICLR Conference 2022 Conference Paper

GeoDiff: A Geometric Diffusion Model for Molecular Conformation Generation

• Minkai Xu
• Lantao Yu
• Yang Song 0011
• Chence Shi
• Stefano Ermon
• Jian Tang 0005

Predicting molecular conformations from molecular graphs is a fundamental problem in cheminformatics and drug discovery. Recently, significant progress has been achieved with machine learning approaches, especially with deep generative models. Inspired by the diffusion process in classical non-equilibrium thermodynamics where heated particles will diffuse from original states to a noise distribution, in this paper, we propose a novel generative model named GeoDiff for molecular conformation prediction. GeoDiff treats each atom as a particle and learns to directly reverse the diffusion process (i.e., transforming from a noise distribution to stable conformations) as a Markov chain. Modeling such a generation process is however very challenging as the likelihood of conformations should be roto-translational invariant. We theoretically show that Markov chains evolving with equivariant Markov kernels can induce an invariant distribution by design, and further propose building blocks for the Markov kernels to preserve the desirable equivariance property. The whole framework can be efficiently trained in an end-to-end fashion by optimizing a weighted variational lower bound to the (conditional) likelihood. Experiments on multiple benchmarks show that GeoDiff is superior or comparable to existing state-of-the-art approaches, especially on large molecules.

ICML Conference 2022 Conference Paper

Imitation Learning by Estimating Expertise of Demonstrators

• Mark Beliaev
• Andy Shih
• Stefano Ermon
• Dorsa Sadigh
• Ramtin Pedarsani

Many existing imitation learning datasets are collected from multiple demonstrators, each with different expertise at different parts of the environment. Yet, standard imitation learning algorithms typically treat all demonstrators as homogeneous, regardless of their expertise, absorbing the weaknesses of any suboptimal demonstrators. In this work, we show that unsupervised learning over demonstrator expertise can lead to a consistent boost in the performance of imitation learning algorithms. We develop and optimize a joint model over a learned policy and expertise levels of the demonstrators. This enables our model to learn from the optimal behavior and filter out the suboptimal behavior of each demonstrator. Our model learns a single policy that can outperform even the best demonstrator, and can be used to estimate the expertise of any demonstrator at any state. We illustrate our findings on real-robotic continuous control tasks from Robomimic and discrete environments such as MiniGrid and chess, out-performing competing methods in 21 out of 23 settings, with an average of 7% and up to 60% improvement in terms of the final reward.

NeurIPS Conference 2022 Conference Paper

Improving Self-Supervised Learning by Characterizing Idealized Representations

• Yann Dubois
• Stefano Ermon
• Tatsunori B. Hashimoto
• Percy S. Liang

Despite the empirical successes of self-supervised learning (SSL) methods, it is unclear what characteristics of their representations lead to high downstream accuracies. In this work, we characterize properties that SSL representations should ideally satisfy. Specifically, we prove necessary and sufficient conditions such that for any task invariant to given data augmentations, probes (e. g. , linear or MLP) trained on that representation attain perfect accuracy. These requirements lead to a unifying conceptual framework for improving existing SSL methods and deriving new ones. For contrastive learning, our framework prescribes simple but significant improvements to previous methods such as using asymmetric projection heads. For non-contrastive learning, we use our framework to derive a simple and novel objective. Our resulting SSL algorithms outperform baselines on standard benchmarks, including SwAV+multicrops on linear probing of ImageNet.

EWRL Workshop 2022 Workshop Paper

IQ-Learn: Inverse soft-Q Learning for Imitation

• Divyansh Garg
• Shuvam Chakraborty
• Chris Cundy
• Jiaming Song
• Matthieu Geist
• Stefano Ermon

AAAI Conference 2022 Conference Paper

IS-Count: Large-Scale Object Counting from Satellite Images with Covariate-Based Importance Sampling

• Chenlin Meng
• Enci Liu
• Willie Neiswanger
• Jiaming Song
• Marshall Burke
• David Lobell
• Stefano Ermon

Object detection in high-resolution satellite imagery is emerging as a scalable alternative to on-the-ground survey data collection in many environmental and socioeconomic monitoring applications. However, performing object detection over large geographies can still be prohibitively expensive due to the high cost of purchasing imagery and compute. Inspired by traditional survey data collection strategies, we propose an approach to estimate object count statistics over large geographies through sampling. Given a cost budget, our method selects a small number of representative areas by sampling from a learnable proposal distribution. Using importance sampling, we are able to accurately estimate object counts after processing only a small fraction of the images compared to an exhaustive approach. We show empirically that the proposed framework achieves strong performance on estimating the number of buildings in the United States and Africa, cars in Kenya, brick kilns in Bangladesh, and swimming pools in the U. S. , while requiring as few as 0. 01% of satellite images compared to an exhaustive approach.

NeurIPS Conference 2022 Conference Paper

LISA: Learning Interpretable Skill Abstractions from Language

• Divyansh Garg
• Skanda Vaidyanath
• Kuno Kim
• Jiaming Song
• Stefano Ermon

Learning policies that effectively utilize language instructions in complex, multi-task environments is an important problem in imitation learning. While it is possible to condition on the entire language instruction directly, such an approach could suffer from generalization issues. To encode complex instructions into skills that can generalize to unseen instructions, we propose Learning Interpretable Skill Abstractions (LISA), a hierarchical imitation learning framework that can learn diverse, interpretable skills from language-conditioned demonstrations. LISA uses vector quantization to learn discrete skill codes that are highly correlated with language instructions and the behavior of the learned policy. In navigation and robotic manipulation environments, LISA is able to outperform a strong non-hierarchical baseline in the low data regime and compose learned skills to solve tasks containing unseen long-range instructions. Our method demonstrates a more natural way to condition on language in sequential decision-making problems and achieve interpretable and controllable behavior with the learned skills.

UAI Conference 2022 Conference Paper

Local calibration: metrics and recalibration

• Rachel Luo
• Aadyot Bhatnagar
• Yu Bai 0017
• Shengjia Zhao
• Huan Wang 0016
• Caiming Xiong
• Silvio Savarese
• Stefano Ermon

Probabilistic classifiers output confidence scores along with their predictions, and these confidence scores should be calibrated, i. e. , they should reflect the reliability of the prediction. Confidence scores that minimize standard metrics such as the expected calibration error (ECE) accurately measure the reliability \textit{on average} across the entire population. However, it is in general impossible to measure the reliability of an \textit{individual} prediction. In this work, we propose the local calibration error (LCE) to span the gap between average and individual reliability. For each individual prediction, the LCE measures the average reliability of a set of similar predictions, where similarity is quantified by a kernel function on a pretrained feature space and by a binning scheme over predicted model confidences. We show theoretically that the LCE can be estimated sample-efficiently from data, and empirically find that it reveals miscalibration modes that are more fine-grained than the ECE can detect. Our key result is a novel {\textbf{lo}cal \textbf{re}calibration} method \method{}, to improve confidence scores for individual predictions and decrease the LCE. Experimentally, we show that our recalibration method produces more accurate confidence scores, which improves downstream fairness and decision making on classification tasks with both image and tabular data.

ICML Conference 2022 Conference Paper

Modular Conformal Calibration

• Charles Marx
• Shengjia Zhao
• Willie Neiswanger
• Stefano Ermon

Uncertainty estimates must be calibrated (i. e. , accurate) and sharp (i. e. , informative) in order to be useful. This has motivated a variety of methods for recalibration, which use held-out data to turn an uncalibrated model into a calibrated model. However, the applicability of existing methods is limited due to their assumption that the original model is also a probabilistic model. We introduce a versatile class of algorithms for recalibration in regression that we call modular conformal calibration (MCC). This framework allows one to transform any regression model into a calibrated probabilistic model. The modular design of MCC allows us to make simple adjustments to existing algorithms that enable well-behaved distribution predictions. We also provide finite-sample calibration guarantees for MCC algorithms. Our framework recovers isotonic recalibration, conformal calibration, and conformal interval prediction, implying that our theoretical results apply to those methods as well. Finally, we conduct an empirical study of MCC on 17 regression datasets. Our results show that new algorithms designed in our framework achieve near-perfect calibration and improve sharpness relative to existing methods.

NeurIPS Conference 2022 Conference Paper

SatMAE: Pre-training Transformers for Temporal and Multi-Spectral Satellite Imagery

• Yezhen Cong
• Samar Khanna
• Chenlin Meng
• Patrick Liu
• Erik Rozi
• Yutong He
• Marshall Burke
• David Lobell

Unsupervised pre-training methods for large vision models have shown to enhance performance on downstream supervised tasks. Developing similar techniques for satellite imagery presents significant opportunities as unlabelled data is plentiful and the inherent temporal and multi-spectral structure provides avenues to further improve existing pre-training strategies. In this paper, we present SatMAE, a pre-training framework for temporal or multi-spectral satellite imagery based on Masked Autoencoder (MAE). To leverage temporal information, we include a temporal embedding along with independently masking image patches across time. In addition, we demonstrate that encoding multi-spectral data as groups of bands with distinct spectral positional encodings is beneficial. Our approach yields strong improvements over previous state-of-the-art techniques, both in terms of supervised learning performance on benchmark datasets (up to $\uparrow$ 7%), and transfer learning performance on downstream remote sensing tasks, including land cover classification (up to $\uparrow$ 14%) and semantic segmentation. Code and data are available on the project website: https: //sustainlab-group. github. io/SatMAE/

ICLR Conference 2022 Conference Paper

SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations

• Chenlin Meng
• Yutong He
• Yang Song 0011
• Jiaming Song
• Jiajun Wu 0001
• Jun-Yan Zhu
• Stefano Ermon

Guided image synthesis enables everyday users to create and edit photo-realistic images with minimum effort. The key challenge is balancing faithfulness to the user inputs (e.g., hand-drawn colored strokes) and realism of the synthesized images. Existing GAN-based methods attempt to achieve such balance using either conditional GANs or GAN inversions, which are challenging and often require additional training data or loss functions for individual applications. To address these issues, we introduce a new image synthesis and editing method, Stochastic Differential Editing (SDEdit), based on a diffusion model generative prior, which synthesizes realistic images by iteratively denoising through a stochastic differential equation (SDE). Given an input image with user guide in a form of manipulating RGB pixels, SDEdit first adds noise to the input, then subsequently denoises the resulting image through the SDE prior to increase its realism. SDEdit does not require task-specific training or inversions and can naturally achieve the balance between realism and faithfulness. SDEdit outperforms state-of-the-art GAN-based methods by up to 98.09% on realism and 91.72% on overall satisfaction scores, according to a human perception study, on multiple tasks, including stroke-based image synthesis and editing as well as image compositing.

NeurIPS Conference 2022 Conference Paper

Self-Similarity Priors: Neural Collages as Differentiable Fractal Representations

• Michael Poli
• Winnie Xu
• Stefano Massaroli
• Chenlin Meng
• Kuno Kim
• Stefano Ermon

Many patterns in nature exhibit self-similarity: they can be compactly described via self-referential transformations. Said patterns commonly appear in natural and artificial objects, such as molecules, shorelines, galaxies, and even images. In this work, we investigate the role of learning in the automated discovery of self-similarity and in its utilization for downstream tasks. To this end, we design a novel class of implicit operators, Neural Collages, which (1) represent data as the parameters of a self-referential, structured transformation, and (2) employ hypernetworks to amortize the cost of finding these parameters to a single forward pass. We detail how to leverage the representations produced by Neural Collages in various tasks, including data compression and generation. Neural Collage image compressors are orders of magnitude faster than other self-similarity-based algorithms during encoding and offer compression rates competitive with implicit methods. Finally, we showcase applications of Neural Collages for fractal art and as deep generative models.

ICLR Conference 2022 Conference Paper

Solving Inverse Problems in Medical Imaging with Score-Based Generative Models

• Yang Song 0011
• Liyue Shen
• Lei Xing 0001
• Stefano Ermon

Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.

NeurIPS Conference 2022 Conference Paper

Training and Inference on Any-Order Autoregressive Models the Right Way

• Andy Shih
• Dorsa Sadigh
• Stefano Ermon

Conditional inference on arbitrary subsets of variables is a core problem in probabilistic inference with important applications such as masked language modeling and image inpainting. In recent years, the family of Any-Order Autoregressive Models (AO-ARMs) -- closely related to popular models such as BERT and XLNet -- has shown breakthrough performance in arbitrary conditional tasks across a sweeping range of domains. But, in spite of their success, in this paper we identify significant improvements to be made to previous formulations of AO-ARMs. First, we show that AO-ARMs suffer from redundancy in their probabilistic model, i. e. , they define the same distribution in multiple different ways. We alleviate this redundancy by training on a smaller set of univariate conditionals that still maintains support for efficient arbitrary conditional inference. Second, we upweight the training loss for univariate conditionals that are evaluated more frequently during inference. Our method leads to improved performance with no compromises on tractability, giving state-of-the-art likelihoods in arbitrary conditional modeling on text (Text8), image (CIFAR10, ImageNet32), and continuous tabular data domains.

NeurIPS Conference 2022 Conference Paper

Transform Once: Efficient Operator Learning in Frequency Domain

• Michael Poli
• Stefano Massaroli
• Federico Berto
• Jinkyoo Park
• Tri Dao
• Christopher Ré
• Stefano Ermon

Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i. e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in predictive error across tasks.

ICML Conference 2021 Conference Paper

Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving

• Yang Song 0011
• Chenlin Meng
• Renjie Liao 0001
• Stefano Ermon

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parallelization, we frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point iteration method, as well as hybrid methods of both. Crucially, Jacobi updates operate independently on each equation and can be executed in parallel. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power. Experimentally, we demonstrate the effectiveness of our approach in accelerating (i) backpropagation of RNNs, (ii) evaluation of DenseNets, and (iii) autoregressive sampling of MADE and PixelCNN++, with speedup factors between 2. 1 and 26 under various settings.

ICLR Conference 2021 Conference Paper

Anytime Sampling for Autoregressive Models via Ordered Autoencoding

• Yilun Xu
• Yang Song 0011
• Sahaj Garg
• Linyuan Gong
• Rui Shu
• Aditya Grover
• Stefano Ermon

Autoregressive models are widely used for tasks such as image and audio generation. The sampling process of these models, however, does not allow interruptions and cannot adapt to real-time computational resources. This challenge impedes the deployment of powerful autoregressive models, which involve a slow sampling process that is sequential in nature and typically scales linearly with respect to the data dimension. To address this difficulty, we propose a new family of autoregressive models that enables anytime sampling. Inspired by Principal Component Analysis, we learn a structured representation space where dimensions are ordered based on their importance with respect to reconstruction. Using an autoregressive model in this latent space, we trade off sample quality for computational efficiency by truncating the generation process before decoding into the original data space. Experimentally, we demonstrate in several image and audio generation tasks that sample quality degrades gracefully as we reduce the computational budget for sampling. The approach suffers almost no loss in sample quality (measured by FID) using only 60\% to 80\% of all latent dimensions for image data. Code is available at https://github.com/Newbeeer/Anytime-Auto-Regressive-Model.

ICML Conference 2021 Conference Paper

Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information

• Willie Neiswanger
• Ke Alexander Wang
• Stefano Ermon

In many real world problems, we want to infer some property of an expensive black-box function f, given a budget of T function evaluations. One example is budget constrained global optimization of f, for which Bayesian optimization is a popular method. Other properties of interest include local optima, level sets, integrals, or graph-structured information induced by f. Often, we can find an algorithm A to compute the desired property, but it may require far more than T queries to execute. Given such an A, and a prior distribution over f, we refer to the problem of inferring the output of A using T evaluations as Bayesian Algorithm Execution (BAX). To tackle this problem, we present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm’s output. Applying this to Dijkstra’s algorithm, for instance, we infer shortest paths in synthetic and real-world graphs with black-box edge costs. Using evolution strategies, we yield variants of Bayesian optimization that target local, rather than global, optima. On these problems, InfoBAX uses up to 500 times fewer queries to f than required by the original algorithm. Our method is closely connected to other Bayesian optimal experimental design procedures such as entropy search methods and optimal sensor placement using Gaussian processes.

NeurIPS Conference 2021 Conference Paper

BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery

• Chris Cundy
• Aditya Grover
• Stefano Ermon

A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from observational data. However, a point estimate may not accurately capture the uncertainty in inferring the underlying graph in practical scenarios, wherein the true DAG is non-identifiable and/or the observed dataset is limited. We propose Bayesian Causal Discovery Nets (BCD Nets), a variational inference framework for estimating a distribution over DAGs characterizing a linear-Gaussian SEM. Developing a full Bayesian posterior over DAGs is challenging due to the the discrete and combinatorial nature of graphs. We analyse key design choices for scalable VI over DAGs, such as 1) the parametrization of DAGs via an expressive variational family, 2) a continuous relaxation that enables low-variance stochastic optimization, and 3) suitable priors over the latent variables. We provide a series of experiments on real and synthetic data showing that BCD Nets outperform maximum-likelihood methods on standard causal discovery metrics such as structural Hamming distance in low data regimes.

NeurIPS Conference 2021 Conference Paper

Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration

• Shengjia Zhao
• Michael Kim
• Roshni Sahoo
• Tengyu Ma
• Stefano Ermon

When facing uncertainty, decision-makers want predictions they can trust. A machine learning provider can convey confidence to decision-makers by guaranteeing their predictions are distribution calibrated--- amongst the inputs that receive a predicted vector of class probabilities q, the actual distribution over classes is given by q. For multi-class prediction problems, however, directly optimizing predictions under distribution calibration tends to be infeasible, requiring sample complexity that grows exponentially in the number of classes C. In this work, we introduce a new notion---decision calibration---that requires the predicted distribution and true distribution over classes to be ``indistinguishable'' to downstream decision-makers. This perspective gives a new characterization of distribution calibration: a predictor is distribution calibrated if and only if it is decision calibrated with respect to all decision-makers. Our main result shows that under a mild restriction, unlike distribution calibration, decision calibration is actually feasible. We design a recalibration algorithm that provably achieves decision calibration efficiently, provided that the decision-makers have a bounded number of actions (e. g. , polynomial in C). We validate our recalibration algorithm empirically: compared to existing methods, decision calibration improves decision-making on skin lesion and ImageNet classification with modern neural network predictors.

NeurIPS Conference 2021 Conference Paper

CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation

• Yusuke Tashiro
• Jiaming Song
• Yang Song
• Stefano Ermon

The imputation of missing values in time series has many applications in healthcare and finance. While autoregressive models are natural candidates for time series imputation, score-based diffusion models have recently outperformed existing counterparts including autoregressive models in many tasks such as image generation and audio synthesis, and would be promising for time series imputation. In this paper, we propose Conditional Score-based Diffusion model (CSDI), a novel time series imputation method that utilizes score-based diffusion models conditioned on observed data. Unlike existing score-based approaches, the conditional diffusion model is explicitly trained for imputation and can exploit correlations between observed values. On healthcare and environmental data, CSDI improves by 40-65% over existing probabilistic imputation methods on popular performance metrics. In addition, deterministic imputation by CSDI reduces the error by 5-20% compared to the state-of-the-art deterministic imputation methods. Furthermore, CSDI can also be applied to time series interpolation and probabilistic forecasting, and is competitive with existing baselines. The code is available at https: //github. com/ermongroup/CSDI.

NeurIPS Conference 2021 Conference Paper

D2C: Diffusion-Decoding Models for Few-Shot Conditional Generation

• Abhishek Sinha
• Jiaming Song
• Chenlin Meng
• Stefano Ermon

Conditional generative models of high-dimensional images have many applications, but supervision signals from conditions to images can be expensive to acquire. This paper describes Diffusion-Decoding models with Contrastive representations (D2C), a paradigm for training unconditional variational autoencoders (VAE) for few-shot conditional image generation. D2C uses a learned diffusion-based prior over the latent representations to improve generation and contrastive self-supervised learning to improve representation quality. D2C can adapt to novel generation tasks, conditioned on labels or manipulation constraints, by learning from as few as 100 labeled examples. On conditional generation from new labels, D2C achieves superior performance over state-of-the-art VAEs and diffusion models. On conditional image manipulation, D2C generations are two orders of magnitude faster to produce over StyleGAN2 ones and are preferred by 50% - 60% of the human evaluators in a double-blind study. We release our code at https: //github. com/jiamings/d2c.

ICLR Conference 2021 Conference Paper

Denoising Diffusion Implicit Models

• Jiaming Song
• Chenlin Meng
• Stefano Ermon

Denoising diffusion probabilistic models (DDPMs) have achieved high quality image generation without adversarial training, yet they require simulating a Markov chain for many steps in order to produce a sample. To accelerate sampling, we present denoising diffusion implicit models (DDIMs), a more efficient class of iterative implicit probabilistic models with the same training procedure as DDPMs. In DDPMs, the generative process is defined as the reverse of a particular Markovian diffusion process. We generalize DDPMs via a class of non-Markovian diffusion processes that lead to the same training objective. These non-Markovian processes can correspond to generative processes that are deterministic, giving rise to implicit models that produce high quality samples much faster. We empirically demonstrate that DDIMs can produce high quality samples $10 \times$ to $50 \times$ faster in terms of wall-clock time compared to DDPMs, allow us to trade off computation for sample quality, perform semantically meaningful image interpolation directly in the latent space, and reconstruct observations with very low error.

AAAI Conference 2021 Conference Paper

Efficient Poverty Mapping from High Resolution Remote Sensing Images

• Kumar Ayush
• Burak Uzkent
• Kumar Tanmay
• Marshall Burke
• David Lobell
• Stefano Ermon

The combination of high-resolution satellite imagery and machine learning have proven useful in many sustainabilityrelated tasks, including poverty prediction, infrastructure measurement, and forest monitoring. However, the accuracy afforded by high-resolution imagery comes at a cost, as such imagery is extremely expensive to purchase at scale. This creates a substantial hurdle to the efficient scaling and widespread adoption of high-resolution-based approaches. To reduce acquisition costs while maintaining accuracy, we propose a reinforcement learning approach in which free lowresolution imagery is used to dynamically identify where to acquire costly high-resolution images, prior to performing a deep learning task on the high-resolution images. We apply this approach to the task of poverty prediction in Uganda, building on an earlier approach that used object detection to count objects and use these counts to predict poverty. Our approach exceeds previous performance benchmarks on this task while using 80% fewer high-resolution images, and could be useful in many domains that require high-resolution imagery.

NeurIPS Conference 2021 Conference Paper

Estimating High Order Gradients of the Data Distribution by Denoising

• Chenlin Meng
• Yang Song
• Wenzhe Li
• Stefano Ermon

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives provide additional local information about the data distribution and enable new applications. Although they can be estimated via automatic differentiation of a learned density model, this can amplify estimation errors and is expensive in high dimensional settings. To overcome these limitations, we propose a method to directly estimate high order derivatives (scores) of a data density from samples. We first show that denoising score matching can be interpreted as a particular case of Tweedie’s formula. By leveraging Tweedie’s formula on higher order moments, we generalize denoising score matching to estimate higher order derivatives. We demonstrate empirically that models trained with the proposed method can approximate second order derivatives more efficiently and accurately than via automatic differentiation. We show that our models can be used to quantify uncertainty in denoising and to improve the mixing speed of Langevin dynamics via Ozaki discretization for sampling synthetic data and natural images.

ICLR Conference 2021 Conference Paper

Evaluating the Disentanglement of Deep Generative Models through Manifold Topology

• Sharon Zhou
• Eric Zelikman
• Fred Lu
• Andrew Y. Ng
• Gunnar E. Carlsson
• Stefano Ermon

Learning disentangled representations is regarded as a fundamental task for improving the generalization, robustness, and interpretability of generative models. However, measuring disentanglement has been challenging and inconsistent, often dependent on an ad-hoc external model or specific to a certain dataset. To address this, we present a method for quantifying disentanglement that only uses the generative model, by measuring the topological similarity of conditional submanifolds in the learned representation. This method showcases both unsupervised and supervised variants. To illustrate the effectiveness and applicability of our method, we empirically evaluate several state-of-the-art models across multiple datasets. We find that our method ranks models similarly to existing methods. We make our code publicly available at https://github.com/stanfordmlgroup/disentanglement.

UAI Conference 2021 Conference Paper

Featurized density ratio estimation

• Kristy Choi
• Madeline Liao
• Stefano Ermon

Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are sufficiently different. In our work, we propose to leverage an invertible generative model to map the two distributions into a common feature space prior to estimation. This featurization brings the densities closer together in latent space, sidestepping pathological scenarios where the learned density ratios in input space can be arbitrarily inaccurate. At the same time, the invertibility of our feature map guarantees that the ratios computed in feature space are equivalent to those in input space. Empirically, we demonstrate the efficacy of our approach in a variety of downstream tasks that require access to accurate density ratios such as mutual information estimation, targeted sampling in deep generative models, and classification with data augmentation.

NeurIPS Conference 2021 Conference Paper

HyperSPNs: Compact and Expressive Probabilistic Circuits

• Andy Shih
• Dorsa Sadigh
• Stefano Ermon

Probabilistic circuits (PCs) are a family of generative models which allows for the computation of exact likelihoods and marginals of its probability distributions. PCs are both expressive and tractable, and serve as popular choices for discrete density estimation tasks. However, large PCs are susceptible to overfitting, and only a few regularization strategies (e. g. , dropout, weight-decay) have been explored. We propose HyperSPNs: a new paradigm of generating the mixture weights of large PCs using a small-scale neural network. Our framework can be viewed as a soft weight-sharing strategy, which combines the greater expressiveness of large models with the better generalization and memory-footprint properties of small models. We show the merits of our regularization strategy on two state-of-the-art PC families introduced in recent literature -- RAT-SPNs and EiNETs -- and demonstrate generalization improvements in both models on a suite of density estimation benchmarks in both discrete and continuous domains.

NeurIPS Conference 2021 Conference Paper

Imitation with Neural Density Models

• Kuno Kim
• Akshat Jindal
• Yang Song
• Jiaming Song
• Yanan Sui
• Stefano Ermon

We propose a new framework for Imitation Learning (IL) via density estimation of the expert's occupancy measure followed by Maximum Occupancy Entropy Reinforcement Learning (RL) using the density as a reward. Our approach maximizes a non-adversarial model-free RL objective that provably lower bounds reverse Kullback–Leibler divergence between occupancy measures of the expert and imitator. We present a practical IL algorithm, Neural Density Imitation (NDI), which obtains state-of-the-art demonstration efficiency on benchmark control tasks.

ICLR Conference 2021 Conference Paper

Improved Autoregressive Modeling with Distribution Smoothing

• Chenlin Meng
• Jiaming Song
• Yang Song 0011
• Shengjia Zhao
• Stefano Ermon

While autoregressive models excel at image compression, their sample quality is often lacking. Although not realistic, generated images often have high likelihood according to the model, resembling the case of adversarial examples. Inspired by a successful adversarial defense method, we incorporate randomized smoothing into autoregressive generative modeling. We first model a smoothed version of the data distribution, and then reverse the smoothing process to recover the original data distribution. This procedure drastically improves the sample quality of existing autoregressive models on several synthetic and real-world image datasets while obtaining competitive likelihoods on synthetic datasets.

NeurIPS Conference 2021 Conference Paper

Improving Compositionality of Neural Networks by Decoding Representations to Inputs

• Mike Wu
• Noah Goodman
• Stefano Ermon

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated strong performance on novel applications, they sacrifice many of the functionalities of traditional software programs. With this as motivation, we take a modest first step towards improving deep learning programs by jointly training a generative model to constrain neural network activations to "decode" back to inputs. We call this design a Decodable Neural Network, or DecNN. Doing so enables a form of compositionality in neural networks, where one can recursively compose DecNN with itself to create an ensemble-like model with uncertainty. In our experiments, we demonstrate applications of this uncertainty to out-of-distribution detection, adversarial example detection, and calibration --- while matching standard neural networks in accuracy. We further explore this compositionality by combining DecNN with pretrained models, where we show promising results that neural networks can be regularized from using protected features.

NeurIPS Conference 2021 Conference Paper

IQ-Learn: Inverse soft-Q Learning for Imitation

• Divyansh Garg
• Shuvam Chakraborty
• Chris Cundy
• Jiaming Song
• Stefano Ermon

In many sequential decision-making problems (e. g. , robotics control, game playing, sequential prediction), human or expert data is available containing useful information about the task. However, imitation learning (IL) from a small amount of expert data can be challenging in high-dimensional environments with complex dynamics. Behavioral cloning is a simple method that is widely used due to its simplicity of implementation and stable convergence but doesn't utilize any information involving the environment’s dynamics. Many existing methods that exploit dynamics information are difficult to train in practice due to an adversarial optimization process over reward and policy approximators or biased, high variance gradient estimators. We introduce a method for dynamics-aware IL which avoids adversarial training by learning a single Q-function, implicitly representing both reward and policy. On standard benchmarks, the implicitly learned rewards show a high positive correlation with the ground-truth rewards, illustrating our method can also be used for inverse reinforcement learning (IRL). Our method, Inverse soft-Q learning (IQ-Learn) obtains state-of-the-art results in offline and online imitation learning settings, significantly outperforming existing methods both in the number of required environment interactions and scalability in high-dimensional spaces, often by more than 3x.

NeurIPS Conference 2021 Conference Paper

Maximum Likelihood Training of Score-Based Diffusion Models

• Yang Song
• Conor Durkan
• Iain Murray
• Stefano Ermon

Score-based diffusion models synthesize samples by reversing a stochastic process that diffuses data to noise, and are trained by minimizing a weighted combination of score matching losses. The log-likelihood of score-based diffusion models can be tractably computed through a connection to continuous normalizing flows, but log-likelihood is not directly optimized by the weighted combination of score matching losses. We show that for a specific weighting scheme, the objective upper bounds the negative log-likelihood, thus enabling approximate maximum likelihood training of score-based diffusion models. We empirically observe that maximum likelihood training consistently improves the likelihood of score-based diffusion models across multiple datasets, stochastic processes, and model architectures. Our best models achieve negative log-likelihoods of 2. 83 and 3. 76 bits/dim on CIFAR-10 and ImageNet $32\times 32$ without any data augmentation, on a par with state-of-the-art autoregressive models on these tasks.

ICLR Conference 2021 Conference Paper

Negative Data Augmentation

• Abhishek Sinha
• Kumar Ayush
• Jiaming Song
• Burak Uzkent
• Hongxia Jin
• Stefano Ermon

Data augmentation is often used to enlarge datasets with synthetic samples generated in accordance with the underlying data distribution. To enable a wider range of augmentations, we explore negative data augmentation strategies (NDA) that intentionally create out-of-distribution samples. We show that such negative out-of-distribution samples provide information on the support of the data distribution, and can be leveraged for generative modeling and representation learning. We introduce a new GAN training objective where we use NDA as an additional source of synthetic data for the discriminator. We prove that under suitable conditions, optimizing the resulting objective still recovers the true data distribution but can directly bias the generator towards avoiding samples that lack the desired structure. Empirically, models trained with our method achieve improved conditional/unconditional image generation along with improved anomaly detection capabilities. Further, we incorporate the same negative data augmentation strategy in a contrastive learning framework for self-supervised representation learning on images and videos, achieving improved performance on downstream image classification, object detection, and action recognition tasks. These results suggest that prior knowledge on what does not constitute valid data is an effective form of weak supervision across a range of unsupervised learning tasks.

ICLR Conference 2021 Conference Paper

On the Critical Role of Conventions in Adaptive Human-AI Collaboration

• Andy Shih
• Arjun Sawhney
• Jovana Kondic
• Stefano Ermon
• Dorsa Sadigh

Humans can quickly adapt to new partners in collaborative tasks (e.g. playing basketball), because they understand which fundamental skills of the task (e.g. how to dribble, how to shoot) carry over across new partners. Humans can also quickly adapt to similar tasks with the same partners by carrying over conventions that they have developed (e.g. raising hand signals pass the ball), without learning to coordinate from scratch. To collaborate seamlessly with humans, AI agents should adapt quickly to new partners and new tasks as well. However, current approaches have not attempted to distinguish between the complexities intrinsic to a task and the conventions used by a partner, and more generally there has been little focus on leveraging conventions for adapting to new settings. In this work, we propose a learning framework that teases apart rule-dependent representation from convention-dependent representation in a principled way. We show that, under some assumptions, our rule-dependent representation is a sufficient statistic of the distribution over best-response strategies across partners. Using this separation of representations, our agents are able to adapt quickly to new partners, and to coordinate with old partners on new tasks in a zero-shot manner. We experimentally validate our approach on three collaborative tasks varying in complexity: a contextual multi-armed bandit, a block placing task, and the card game Hanabi.

NeurIPS Conference 2021 Conference Paper

PiRank: Scalable Learning To Rank via Differentiable Sorting

• Robin Swezey
• Aditya Grover
• Bruno Charron
• Stefano Ermon

A key challenge with machine learning approaches for ranking is the gap between the performance metrics of interest and the surrogate loss functions that can be optimized with gradient-based methods. This gap arises because ranking metrics typically involve a sorting operation which is not differentiable w. r. t. the model parameters. Prior works have proposed surrogates that are loosely related to ranking metrics or simple smoothed versions thereof, and often fail to scale to real-world applications. We propose PiRank, a new class of differentiable surrogates for ranking, which employ a continuous, temperature-controlled relaxation to the sorting operator based on NeuralSort [1]. We show that PiRank exactly recovers the desired metrics in the limit of zero temperature and further propose a divide-and-conquer extension that scales favorably to large list sizes, both in theory and practice. Empirically, we demonstrate the role of larger list sizes during training and show that PiRank significantly improves over comparable approaches on publicly available Internet-scale learning-to-rank benchmarks.

AAAI Conference 2021 Conference Paper

Predicting Livelihood Indicators from Community-Generated Street-Level Imagery

• Jihyeon Lee
• Dylan Grosz
• Burak Uzkent
• Sicheng Zeng
• Marshall Burke
• David Lobell
• Stefano Ermon

Major decisions from governments and other large organizations rely on measurements of the populace’s well-being, but making such measurements at a broad scale is expensive and thus infrequent in much of the developing world. We propose an inexpensive, scalable, and interpretable approach to predict key livelihood indicators from public crowd-sourced street-level imagery. Such imagery can be cheaply collected and more frequently updated compared to traditional surveying methods, while containing plausibly relevant information for a range of livelihood indicators. We propose two approaches to learn from the street-level imagery: (1) a method that creates multi-household cluster representations by detecting informative objects and (2) a graph-based approach that captures the relationships between images. By visualizing what features are important to a model and how they are used, we can help end-user organizations understand the models and offer an alternate approach for index estimation that uses cheaply obtained roadway features. By comparing our results against ground data collected in nationallyrepresentative household surveys, we demonstrate the performance of our approach in accurately predicting indicators of poverty, population, and health and its scalability by testing in two different countries, India and Kenya. Our code is available at https: //github. com/sustainlab-group/mapillarygcn.

NeurIPS Conference 2021 Conference Paper

Pseudo-Spherical Contrastive Divergence

• Lantao Yu
• Jiaming Song
• Yang Song
• Stefano Ermon

Energy-based models (EBMs) offer flexible distribution parametrization. However, due to the intractable partition function, they are typically trained via contrastive divergence for maximum likelihood estimation. In this paper, we propose pseudo-spherical contrastive divergence (PS-CD) to generalize maximum likelihood learning of EBMs. PS-CD is derived from the maximization of a family of strictly proper homogeneous scoring rules, which avoids the computation of the intractable partition function and provides a generalized family of learning objectives that include contrastive divergence as a special case. Moreover, PS-CD allows us to flexibly choose various learning objectives to train EBMs without additional computational cost or variational minimax optimization. Theoretical analysis on the proposed method and extensive experiments on both synthetic data and commonly used image datasets demonstrate the effectiveness and modeling flexibility of PS-CD, as well as its robustness to data contamination, thus showing its superiority over maximum likelihood and $f$-EBMs.

NeurIPS Conference 2021 Conference Paper

Reliable Decisions with Threshold Calibration

• Roshni Sahoo
• Shengjia Zhao
• Alyssa Chen
• Stefano Ermon

Decision makers rely on probabilistic forecasts to predict the loss of different decision rules before deployment. When the forecasted probabilities match the true frequencies, predicted losses will be accurate. Although perfect forecasts are typically impossible, probabilities can be calibrated to match the true frequencies on average. However, we find that this \textit{average} notion of calibration, which is typically used in practice, does not necessarily guarantee accurate decision loss prediction. Specifically in the regression setting, the loss of threshold decisions, which are decisions based on whether the forecasted outcome falls above or below a cutoff, might not be predicted accurately. We propose a stronger notion of calibration called threshold calibration, which is exactly the condition required to ensure that decision loss is predicted accurately for threshold decisions. We provide an efficient algorithm which takes an uncalibrated forecaster as input and provably outputs a threshold-calibrated forecaster. Our procedure allows downstream decision makers to confidently estimate the loss of any threshold decision under any threshold loss function. Empirically, threshold calibration improves decision loss prediction without compromising on the quality of the decisions in two real-world settings: hospital scheduling decisions and resource allocation decisions.

ICML Conference 2021 Conference Paper

Reward Identification in Inverse Reinforcement Learning

• Kuno Kim
• Shivam Garg 0001
• Kirankumar Shiragur
• Stefano Ermon

We study the problem of reward identifiability in the context of Inverse Reinforcement Learning (IRL). The reward identifiability question is critical to answer when reasoning about the effectiveness of using Markov Decision Processes (MDPs) as computational models of real world decision makers in order to understand complex decision making behavior and perform counterfactual reasoning. While identifiability has been acknowledged as a fundamental theoretical question in IRL, little is known about the types of MDPs for which rewards are identifiable, or even if there exist such MDPs. In this work, we formalize the reward identification problem in IRL and study how identifiability relates to properties of the MDP model. For deterministic MDP models with the MaxEntRL objective, we prove necessary and sufficient conditions for identifiability. Building on these results, we present efficient algorithms for testing whether or not an MDP model is identifiable.

ICLR Conference 2021 Conference Paper

Score-Based Generative Modeling through Stochastic Differential Equations

• Yang Song 0011
• Jascha Sohl-Dickstein
• Diederik P. Kingma
• Abhishek Kumar
• Stefano Ermon
• Ben Poole

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (a.k.a., score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of $1024\times 1024$ images for the first time from a score-based generative model.

NeurIPS Conference 2021 Conference Paper

Spatial-Temporal Super-Resolution of Satellite Imagery via Conditional Pixel Synthesis

• Yutong He
• Dingjie Wang
• Nicholas Lai
• William Zhang
• Chenlin Meng
• Marshall Burke
• David Lobell
• Stefano Ermon

High-resolution satellite imagery has proven useful for a broad range of tasks, including measurement of global human population, local economic livelihoods, and biodiversity, among many others. Unfortunately, high-resolution imagery is both infrequently collected and expensive to purchase, making it hard to efficiently and effectively scale these downstream tasks over both time and space. We propose a new conditional pixel synthesis model that uses abundant, low-cost, low-resolution imagery to generate accurate high-resolution imagery at locations and times in which it is unavailable. We show that our model attains photo-realistic sample quality and outperforms competing baselines on a key downstream task – object counting – particularly in geographic locations where conditions on the ground are changing rapidly.

NeurIPS Conference 2021 Conference Paper

SustainBench: Benchmarks for Monitoring the Sustainable Development Goals with Machine Learning

• Christopher Yeh
• Chenlin Meng
• Sherrie Wang
• Anne Driscoll
• Erik Rozi
• Patrick Liu
• Jihyeon Lee
• Marshall Burke

Progress toward the United Nations Sustainable Development Goals (SDGs) has been hindered by a lack of data on key environmental and socioeconomic indicators, which historically have come from ground surveys with sparse temporal and spatial coverage. Recent advances in machine learning have made it possible to utilize abundant, frequently-updated, and globally available data, such as from satellites or social media, to provide insights into progress toward SDGs. Despite promising early results, approaches to using such data for SDG measurement thus far have largely evaluated on different datasets or used inconsistent evaluation metrics, making it hard to understand whether performance is improving and where additional research would be most fruitful. Furthermore, processing satellite and ground survey data requires domain knowledge that many in the machine learning community lack. In this paper, we introduce SustainBench, a collection of 15 benchmark tasks across 7 SDGs, including tasks related to economic development, agriculture, health, education, water and sanitation, climate action, and life on land. Datasets for 11 of the 15 tasks are released publicly for the first time. Our goals for SustainBench are to (1) lower the barriers to entry for the machine learning community to contribute to measuring and achieving the SDGs; (2) provide standard benchmarks for evaluating machine learning models on tasks across a variety of SDGs; and (3) encourage the development of novel machine learning methods where improved model performance facilitates progress towards the SDGs.

ICML Conference 2021 Conference Paper

Temporal Predictive Coding For Model-Based Planning In Latent Space

• Tung D. Nguyen
• Rui Shu
• Tuan Pham
• Hung Bui
• Stefano Ermon

High-dimensional observations are a major challenge in the application of model-based reinforcement learning (MBRL) to real-world environments. To handle high-dimensional sensory inputs, existing approaches use representation learning to map high-dimensional observations into a lower-dimensional latent space that is more amenable to dynamics estimation and planning. In this work, we present an information-theoretic approach that employs temporal predictive coding to encode elements in the environment that can be predicted across time. Since this approach focuses on encoding temporally-predictable information, we implicitly prioritize the encoding of task-relevant components over nuisance information within the environment that are provably task-irrelevant. By learning this representation in conjunction with a recurrent state space model, we can then perform planning in latent space. We evaluate our model on a challenging modification of standard DMControl tasks where the background is replaced with natural videos that contain complex but irrelevant information to the planning task. Our experiments show that our model is superior to existing methods in the challenging complex-background setting while remaining competitive with current state-of-the-art models in the standard setting.

ICLR Conference 2020 Conference Paper

A Theory of Usable Information under Computational Constraints

• Yilun Xu
• Shengjia Zhao
• Jiaming Song
• Russell Stewart
• Stefano Ermon

We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon’s information theory that takes into account the modeling power and computational constraints of the observer. The resulting predictive V-information encompasses mutual information and other notions of informativeness such as the coefficient of determination. Unlike Shannon’s mutual information and in violation of the data processing inequality, V-information can be created through computation. This is consistent with deep neural networks extracting hierarchies of progressively more informative features in representation learning. Additionally, we show that by incorporating computational constraints, V-information can be reliably estimated from data even in high dimensions with PAC-style guarantees. Empirically, we demonstrate predictive V-information is more effective than mutual information for structure learning and fair representation learning. Codes are available at https://github.com/Newbeeer/V-information .

AAAI Conference 2020 Conference Paper

AlignFlow: Cycle Consistent Learning from Multiple Domains via Normalizing Flows

• Aditya Grover
• Christopher Chute
• Rui Shu
• Zhangjie Cao
• Stefano Ermon

Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain adaptation. We propose AlignFlow, a generative modeling framework that models each domain via a normalizing flow. The use of normalizing flows allows for a) flexibility in specifying learning objectives via adversarial training, maximum likelihood estimation, or a hybrid of the two methods; and b) learning and exact inference of a shared representation in the latent space of the generative model. We derive a uniform set of conditions under which AlignFlow is marginally-consistent for the different learning objectives. Furthermore, we show that AlignFlow guarantees exact cycle consistency in mapping datapoints from a source domain to target and back to the source domain. Empirically, AlignFlow outperforms relevant baselines on image-to-image translation and unsupervised domain adaptation and can be used to simultaneously interpolate across the various domains using the learned representation.

NeurIPS Conference 2020 Conference Paper

Autoregressive Score Matching

• Chenlin Meng
• Lantao Yu
• Yang Song
• Jiaming Song
• Stefano Ermon

Autoregressive models use chain rule to define a joint probability distribution as a product of conditionals. These conditionals need to be normalized, imposing constraints on the functional families that can be used. To increase flexibility, we propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariate log-conditionals (scores), which need not be normalized. To train AR-CSM, we introduce a new divergence between distributions named Composite Score Matching (CSM). For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. Compared to previous score matching algorithms, our method is more scalable to high dimensional data and more stable to optimize. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.

NeurIPS Conference 2020 Conference Paper

Belief Propagation Neural Networks

• Jonathan Kuck
• Shuvam Chakraborty
• Hao Tang
• Rachel Luo
• Jiaming Song
• Ashish Sabharwal
• Stefano Ermon

Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap, we introduce belief propagation neural networks (BPNNs), a class of parameterized operators that operate on factor graphs and generalize Belief Propagation (BP). In its strictest form, a BPNN layer (BPNN-D) is a learned iterative operator that provably maintains many of the desirable properties of BP for any choice of the parameters. Empirically, we show that by training BPNN-D learns to perform the task better than the original BP: it converges 1. 7x faster on Ising models while providing tighter bounds. On challenging model counting problems, BPNNs compute estimates 100's of times faster than state-of-the-art handcrafted methods, while returning an estimate of comparable quality.

ICML Conference 2020 Conference Paper

Bridging the Gap Between f-GANs and Wasserstein GANs

• Jiaming Song
• Stefano Ermon

Generative adversarial networks (GANs) variants approximately minimize divergences between the model and the data distribution using a discriminator. Wasserstein GANs (WGANs) enjoy superior empirical performance, however, unlike in f-GANs, the discriminator does not provide an estimate for the ratio between model and data densities, which is useful in applications such as inverse reinforcement learning. To overcome this limitation, we propose an new training objective where we additionally optimize over a set of importance weights over the generated samples. By suitably constraining the feasible set of importance weights, we obtain a family of objectives which includes and generalizes the original f-GAN and WGAN objectives. We show that a natural extension outperforms WGANs while providing density ratios as in f-GAN, and demonstrate empirical success on distribution modeling, density ratio estimation and image generation.

NeurIPS Conference 2020 Conference Paper

Diversity can be Transferred: Output Diversification for White- and Black-box Attacks

• Yusuke Tashiro
• Yang Song
• Stefano Ermon

Adversarial attacks often involve random perturbations of the inputs drawn from uniform or Gaussian distributions, e. g. to initialize optimization-based white-box attacks or generate update directions in black-box attacks. These simple perturbations, however, could be sub-optimal as they are agnostic to the model being attacked. To improve the efficiency of these attacks, we propose Output Diversified Sampling (ODS), a novel sampling strategy that attempts to maximize diversity in the target model's outputs among the generated samples. While ODS is a gradient-based strategy, the diversity offered by ODS is transferable and can be helpful for both white-box and black-box attacks via surrogate models. Empirically, we demonstrate that ODS significantly improves the performance of existing white-box and black-box attacks. In particular, ODS reduces the number of queries needed for state-of-the-art black-box attacks on ImageNet by a factor of two.

ICML Conference 2020 Conference Paper

Domain Adaptive Imitation Learning

• Kuno Kim
• Yihong Gu
• Jiaming Song
• Shengjia Zhao
• Stefano Ermon

We study the question of how to imitate tasks across domains with discrepancies such as embodiment, viewpoint, and dynamics mismatch. Many prior works require paired, aligned demonstrations and an additional RL step that requires environment interactions. However, paired, aligned demonstrations are seldom obtainable and RL procedures are expensive. In this work, we formalize the Domain Adaptive Imitation Learning (DAIL) problem - a unified framework for imitation learning in the presence of viewpoint, embodiment, and/or dynamics mismatch. Informally, DAIL is the process of learning how to perform a task optimally, given demonstrations of the task in a distinct domain. We propose a two step approach to DAIL: alignment followed by adaptation. In the alignment step we execute a novel unsupervised MDP alignment algorithm, Generative Adversarial MDP Alignment (GAMA), to learn state and action correspondences from \emph{unpaired, unaligned} demonstrations. In the adaptation step we leverage the correspondences to zero-shot imitate tasks across domains. To describe when DAIL is feasible via alignment and adaptation, we introduce a theory of MDP alignability. We experimentally evaluate GAMA against baselines in embodiment, viewpoint, and dynamics mismatch scenarios where aligned demonstrations don’t exist and show the effectiveness of our approach

NeurIPS Conference 2020 Conference Paper

Efficient Learning of Generative Models via Finite-Difference Score Matching

• Tianyu Pang
• Kun Xu
• Chongxuan Li
• Yang Song
• Stefano Ermon
• Jun Zhu

Several machine learning applications involve the optimization of higher-order derivatives (e. g. , gradients of gradients) during training, which can be expensive with respect to memory and computation even with automatic differentiation. As a typical example in generative modeling, score matching~(SM) involves the optimization of the trace of a Hessian. To improve computing efficiency, we rewrite the SM objective and its variants in terms of directional derivatives, and present a generic strategy to efficiently approximate any-order directional derivative with finite difference~(FD). Our approximation only involves function evaluations, which can be executed in parallel, and no gradient computations. Thus, it reduces the total computational cost while also improving numerical stability. We provide two instantiations by reformulating variants of SM objectives into the FD forms. Empirically, we demonstrate that our methods produce results comparable to the gradient-based counterparts while being much more computationally efficient.

ICML Conference 2020 Conference Paper

Fair Generative Modeling via Weak Supervision

• Kristy Choi
• Aditya Grover
• Trisha Singh
• Rui Shu
• Stefano Ermon

Real-world datasets are often biased with respect to key demographic factors such as race and gender. Due to the latent nature of the underlying factors, detecting and mitigating bias is especially challenging for unsupervised machine learning. We present a weakly supervised algorithm for overcoming dataset bias for deep generative models. Our approach requires access to an additional small, unlabeled reference dataset as the supervision signal, thus sidestepping the need for explicit labels on the underlying bias factors. Using this supplementary dataset, we detect the bias in existing datasets via a density ratio technique and learn generative models which efficiently achieve the twin goals of: 1) data efficiency by using training examples from both biased and reference datasets for learning; and 2) data generation close in distribution to the reference dataset at test time. Empirically, we demonstrate the efficacy of our approach which reduces bias w. r. t. latent factors by an average of up to 34. 6% over baselines for comparable image generation using generative adversarial networks.

UAI Conference 2020 Conference Paper

Flexible Approximate Inference via Stratified Normalizing Flows

• Chris Cundy
• Stefano Ermon

A major obstacle to forming posterior distributions in machine learning is the difficulty of evaluating partition functions. Monte-Carlo approaches are unbiased, but can suffer from high variance. Variational methods are biased, but tend to have lower variance. We develop an approximate inference procedure that allows explicit control of the bias/variance tradeoff, interpolating between the sampling and the variational regime. We use a normalizing flow to map the integrand onto a uniform distribution. We then randomly sample regions from a partition of this uniform distribution and fit simpler, local variational approximations in the image of these regions through the flow. When a partition with only one region is used, we recover standard variational inference, and in the limit of an infinitely fine partition we recover Monte-Carlo sampling. We show experiments validating the effectiveness of our approach.

IJCAI Conference 2020 Conference Paper

Generating Interpretable Poverty Maps using Object Detection in Satellite Images

• Kumar Ayush
• Burak Uzkent
• Marshall Burke
• David Lobell
• Stefano Ermon

Accurate local-level poverty measurement is an essential task for governments and humanitarian organizations to track the progress towards improving livelihoods and distribute scarce resources. Recent computer vision advances in using satellite imagery to predict poverty have shown increasing accuracy, but they do not generate features that are interpretable to policymakers, inhibiting adoption by practitioners. Here we demonstrate an interpretable computational framework to accurately predict poverty at a local level by applying object detectors to high resolution (30cm) satellite images. Using the weighted counts of objects as features, we achieve 0. 539 Pearson's r^2 in predicting village-level poverty in Uganda, a 31% improvement over existing (and less interpretable) benchmarks. Feature importance and ablation analysis reveal intuitive relationships between object counts and poverty predictions. Our results suggest that interpretability does not have to come at the cost of performance, at least in this important domain.

NeurIPS Conference 2020 Conference Paper

HiPPO: Recurrent Memory with Optimal Polynomial Projections

• Albert Gu
• Tri Dao
• Stefano Ermon
• Atri Rudra
• Christopher Ré

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98. 3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

NeurIPS Conference 2020 Conference Paper

Improved Techniques for Training Score-Based Generative Models

• Yang Song
• Stefano Ermon

Score-based generative models can produce high quality image samples comparable to GANs, without requiring adversarial optimization. However, existing training procedures are limited to images of low resolution (typically below 32 x 32), and can be unstable under some settings. We provide a new theoretical analysis of learning and sampling from score models in high dimensional spaces, explaining existing failure modes and motivating new solutions that generalize across datasets. To enhance stability, we also propose to maintain an exponential moving average of model weights. With these improvements, we can effortlessly scale score-based generative models to images with unprecedented resolutions ranging from 64 x 64 to 256 x 256. Our score-based models can generate high-fidelity samples that rival best-in-class GANs on various image datasets, including CelebA, FFHQ, and multiple LSUN categories.

ICML Conference 2020 Conference Paper

Individual Calibration with Randomized Forecasting

• Shengjia Zhao
• Tengyu Ma 0001
• Stefano Ermon

Machine learning applications often require calibrated predictions, e. g. a 90% credible interval should contain the true outcome 90% of the times. However, typical definitions of calibration only require this to hold on average, and offer no guarantees on predictions made on individual samples. Thus, predictions can be systematically over or under confident on certain subgroups, leading to issues of fairness and potential vulnerabilities. We show that calibration for individual samples is possible in the regression setup if and only if the predictions are randomized, i. e. outputting randomized credible intervals. Randomization removes systematic bias by trading off bias with variance. We design a training objective to enforce individual calibration and use it to train randomized regression functions. The resulting models are more calibrated for arbitrarily chosen subgroups of the data, and can achieve higher utility in decision making against adversaries that exploit miscalibrated predictions.

AAAI Conference 2020 Conference Paper

Meta-Amortized Variational Inference and Learning

• Mike Wu
• Kristy Choi
• Noah Goodman
• Stefano Ermon

Despite the recent success in probabilistic modeling and their applications, generative models trained using traditional inference techniques struggle to adapt to new distributions, even when the target distribution may be closely related to the ones seen during training. In this work, we present a doublyamortized variational inference procedure as a way to address this challenge. By sharing computation across not only a set of query inputs, but also a set of different, related probabilistic models, we learn transferable latent representations that generalize across several related distributions. In particular, given a set of distributions over images, we find the learned representations to transfer to different data transformations. We empirically demonstrate the effectiveness of our method by introducing the MetaVAE, and show that it significantly outperforms baselines on downstream image classification tasks on MNIST (10-50%) and NORB (10-35%).

NeurIPS Conference 2020 Conference Paper

MOPO: Model-based Offline Policy Optimization

• Tianhe Yu
• Garrett Thomas
• Lantao Yu
• Stefano Ermon
• James Y. Zou
• Sergey Levine
• Chelsea Finn
• Tengyu Ma

Offline reinforcement learning (RL) refers to the problem of learning policies entirely from a batch of previously collected data. This problem setting is compelling, because it offers the promise of utilizing large, diverse, previously collected datasets to acquire policies without any costly or dangerous active exploration, but it is also exceptionally difficult, due to the distributional shift between the offline training data and the learned policy. While there has been significant progress in model-free offline RL, the most successful prior methods constrain the policy to the support of the data, precluding generalization to new states. In this paper, we observe that an existing model-based RL algorithm on its own already produces significant gains in the offline setting, as compared to model-free approaches, despite not being designed for this setting. However, although many standard model-based RL methods already estimate the uncertainty of their model, they do not by themselves provide a mechanism to avoid the issues associated with distributional shift in the offline setting. We therefore propose to modify existing model-based RL methods to address these issues by casting offline model-based RL into a penalized MDP framework. We theoretically show that, by using this penalized MDP, we are maximizing a lower bound of the return in the true MDP. Based on our theoretical results, we propose a new model-based offline RL algorithm that applies the variance of a Lipschitz-regularized model as a penalty to the reward function. We find that this algorithm outperforms both standard model-based RL methods and existing state-of-the-art model-free offline RL approaches on existing offline RL benchmarks, as well as two challenging continuous control tasks that require generalizing from data collected for a different task.

NeurIPS Conference 2020 Conference Paper

Multi-label Contrastive Predictive Coding

• Jiaming Song
• Stefano Ermon

Variational mutual information (MI) estimators are widely used in unsupervised representation learning methods such as contrastive predictive coding (CPC). A lower bound on MI can be obtained from a multi-class classification problem, where a critic attempts to distinguish a positive sample drawn from the underlying joint distribution from (m-1) negative samples drawn from a suitable proposal distribution. Using this approach, MI estimates are bounded above by \log m, and could thus severely underestimate unless m is very large. To overcome this limitation, we introduce a novel estimator based on a multi-label classification problem, where the critic needs to jointly identify \emph{multiple} positive samples at the same time. We show that using the same amount of negative samples, multi-label CPC is able to exceed the \log m bound, while still being a valid lower bound of mutual information. We demonstrate that the proposed approach is able to lead to better mutual information estimation, gain empirical improvements in unsupervised representation learning, and beat the current state-of-the-art in knowledge distillation over 10 out of 13 tasks.

ICML Conference 2020 Conference Paper

Predictive Coding for Locally-Linear Control

• Rui Shu
• Tung Nguyen
• Yinlam Chow
• Tuan Pham
• Khoat Than
• Mohammad Ghavamzadeh
• Stefano Ermon
• Hung H. Bui

High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the observations into a lower dimensional latent space, estimating the latent dynamics, and then performing control directly in the latent space. To ensure the learned latent dynamics are predictive of next-observations, all existing LCE approaches decode back into the observation space and explicitly perform next-observation prediction—a challenging high-dimensional task that furthermore introduces a large number of nuisance parameters (i. e. , the decoder) which are discarded during control. In this paper, we propose a novel information-theoretic LCE approach and show theoretically that explicit next-observation prediction can be replaced with predictive coding. We then use predictive coding to develop a decoder-free LCE model whose latent dynamics are amenable to locally-linear control. Extensive experiments on benchmark tasks show that our model reliably learns a controllable latent space that leads to superior performance when compared with state-of-the-art LCE baselines.

NeurIPS Conference 2020 Conference Paper

Probabilistic Circuits for Variational Inference in Discrete Graphical Models

• Andy Shih
• Stefano Ermon

Inference in discrete graphical models with variational methods is difficult because of the inability to re-parameterize gradients of the Evidence Lower Bound (ELBO). Many sampling-based methods have been proposed for estimating these gradients, but they suffer from high bias or variance. In this paper, we propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN), to compute ELBO gradients exactly (without sampling) for a certain class of densities. In particular, we show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is a polynomial the corresponding ELBO can be computed analytically. To scale to graphical models with thousands of variables, we develop an efficient and effective construction of selective-SPNs with size (O(kn)), where (n) is the number of variables and (k) is an adjustable hyperparameter. We demonstrate our approach on three types of graphical models -- Ising models, Latent Dirichlet Allocation, and factor graphs from the UAI Inference Competition. Selective-SPNs give a better lower bound than mean-field and structured mean-field, and is competitive with approximations that do not provide a lower bound, such as Loopy Belief Propagation and Tree-Reweighted Belief Propagation. Our results show that probabilistic circuits are promising tools for variational inference in discrete graphical models as they combine tractability and expressivity.

ICML Conference 2020 Conference Paper

Training Deep Energy-Based Models with f-Divergence Minimization

• Lantao Yu
• Yang Song 0011
• Jiaming Song
• Stefano Ermon

Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence to approximate the gradient of the KL divergence between data and model distribution. While KL divergence has many desirable properties, other f-divergences have shown advantages in training implicit density generative models such as generative adversarial networks. In this paper, we propose a general variational framework termed f-EBM to train EBMs using any desired f-divergence. We introduce a corresponding optimization algorithm and prove its local convergence property with non-linear dynamical systems theory. Experimental results demonstrate the superiority of f-EBM over contrastive divergence, as well as the benefits of training EBMs using f-divergences other than KL.

ICLR Conference 2020 Conference Paper

Understanding the Limitations of Variational Mutual Information Estimators

• Jiaming Song
• Stefano Ermon

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

ICLR Conference 2020 Conference Paper

Weakly Supervised Disentanglement with Guarantees

• Rui Shu
• Yining Chen
• Abhishek Kumar
• Stefano Ermon
• Ben Poole

Learning disentangled representations that correspond to factors of variation in real-world data is critical to interpretable and human-controllable machine learning. Recently, concerns about the viability of learning disentangled representations in a purely unsupervised manner has spurred a shift toward the incorporation of weak supervision. However, there is currently no formalism that identifies when and how weak supervision will guarantee disentanglement. To address this issue, we provide a theoretical framework to assist in analyzing the disentanglement guarantees (or lack thereof) conferred by weak supervision when coupled with learning algorithms based on distribution matching. We empirically verify the guarantees and limitations of several weak supervision methods (restricted labeling, match-pairing, and rank-pairing), demonstrating the predictive power and usefulness of our theoretical framework.

ICML Conference 2019 Conference Paper

Adaptive Antithetic Sampling for Variance Reduction

• Hongyu Ren
• Shengjia Zhao
• Stefano Ermon

Variance reduction is crucial in stochastic estimation and optimization problems. Antithetic sampling reduces the variance of a Monte Carlo estimator by drawing correlated, rather than independent, samples. However, designing an effective correlation structure is challenging and application specific, thus limiting the practical applicability of these methods. In this paper, we propose a general-purpose adaptive antithetic sampling framework. We provide gradient-based and gradient-free methods to train the samplers such that they reduce variance while ensuring that the underlying Monte Carlo estimator is provably unbiased. We demonstrate the effectiveness of our approach on Bayesian inference and generative model training, where it reduces variance and improves task performance with little computational overhead.

UAI Conference 2019 Conference Paper

Adaptive Hashing for Model Counting

• Jonathan Kuck
• Tri Dao
• Shenjia Zhao
• Burak Bartan
• Ashish Sabharwal
• Stefano Ermon

Randomized hashing algorithms have seen recent success in providing bounds on the model count of a propositional formula. These methods repeatedly check the satisfiability of a formula subject to increasingly stringent random constraints. Key to these approaches is the choice of a fixed family of hash functions that strikes a good balance between computational efficiency and statistical guarantees for a hypothetical worst case formula. In this paper we propose a scheme where the family of hash functions is chosen adaptively, based on properties of the specific input formula. Akin to adaptive importance sampling, we use solutions to the formula (found during the bounding procedure of current methods) to estimate properties of the solution set, which guides the construction of random constraints. Additionally, we introduce an orthogonal variance reduction technique that is broadly applicable to hashing based methods. We empirically show that, when combined, these approaches lead to better lower bounds on existing benchmarks, with a median improvement factor of 2^13 over 1, 198 propositional formulas.

NeurIPS Conference 2019 Conference Paper

Approximating the Permanent by Sampling from Adaptive Partitions

• Jonathan Kuck
• Tri Dao
• Hamid Rezatofighi
• Ashish Sabharwal
• Stefano Ermon

Computing the permanent of a non-negative matrix is a core problem with practical applications ranging from target tracking to statistical thermodynamics. However, this problem is also #P-complete, which leaves little hope for finding an exact solution that can be computed efficiently. While the problem admits a fully polynomial randomized approximation scheme, this method has seen little use because it is both inefficient in practice and difficult to implement. We present ADAPART, a simple and efficient method for exact sampling of permutations, each associated with a weight as determined by a matrix. ADAPART uses an adaptive, iterative partitioning strategy over permutations to convert any upper bounding method for the permanent into one that satisfies a desirable `nesting' property over the partition used. These samples are then used to construct tight bounds on the permanent which hold with a high probability. Empirically, ADAPART provides significant speedups (sometimes exceeding 50x) over prior work. We also empirically observe polynomial scaling in some cases. In the context of multi-target tracking, ADAPART allows us to use the optimal proposal distribution during particle filtering, leading to orders of magnitude fewer samples and improved tracking performance.

NeurIPS Conference 2019 Conference Paper

Bias Correction of Learned Generative Models using Likelihood-Free Importance Weighting

• Aditya Grover
• Jiaming Song
• Ashish Kapoor
• Kenneth Tran
• Alekh Agarwal
• Eric Horvitz
• Stefano Ermon

A learned generative model often produces biased statistics relative to the underlying data distribution. A standard technique to correct this bias is importance sampling, where samples from the model are weighted by the likelihood ratio under model and true distributions. When the likelihood ratio is unknown, it can be estimated by training a probabilistic classifier to distinguish samples from the two distributions. We employ this likelihood-free importance weighting method to correct for the bias in generative models. We find that this technique consistently improves standard goodness-of-fit metrics for evaluating the sample quality of state-of-the-art deep generative models, suggesting reduced bias. Finally, we demonstrate its utility on representative applications in a) data augmentation for classification using generative adversarial networks, and b) model-based policy evaluation using off-policy data.

ICML Conference 2019 Conference Paper

Calibrated Model-Based Deep Reinforcement Learning

• Ali Malik
• Volodymyr Kuleshov
• Jiaming Song
• Danny Nemer
• Harlan Seymour
• Stefano Ermon

Estimates of predictive uncertainty are important for accurate model-based planning and reinforcement learning. However, predictive uncertainties — especially ones derived from modern deep learning systems — can be inaccurate and impose a bottleneck on performance. This paper explores which uncertainties are needed for model-based reinforcement learning and argues that ideal uncertainties should be calibrated, i. e. their probabilities should match empirical frequencies of predicted events. We describe a simple way to augment any model-based reinforcement learning agent with a calibrated model and show that doing so consistently improves planning, sample complexity, and exploration. On the \textsc{HalfCheetah} MuJoCo task, our system achieves state-of-the-art performance using 50% fewer samples than the current leading approach. Our findings suggest that calibration can improve the performance of model-based reinforcement learning with minimal computational and implementation overhead.

NeurIPS Conference 2019 Conference Paper

Generative Modeling by Estimating Gradients of the Data Distribution

• Yang Song
• Stefano Ermon

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on low-dimensional manifolds, we perturb the data with different levels of Gaussian noise, and jointly estimate the corresponding scores, i. e. , the vector fields of gradients of the perturbed data distribution for all noise levels. For sampling, we propose an annealed Langevin dynamics where we use gradients corresponding to gradually decreasing noise levels as the sampling process gets closer to the data manifold. Our framework allows flexible model architectures, requires no sampling during training or the use of adversarial methods, and provides a learning objective that can be used for principled model comparisons. Our models produce samples comparable to GANs on MNIST, CelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score of 8. 87 on CIFAR-10. Additionally, we demonstrate that our models learn effective representations via image inpainting experiments.

ICML Conference 2019 Conference Paper

Graphite: Iterative Generative Modeling of Graphs

• Aditya Grover
• Aaron Zweig
• Stefano Ermon

Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In this work, we propose Graphite, an algorithmic framework for unsupervised learning of representations over nodes in large graphs using deep latent variable generative models. Our model parameterizes variational autoencoders (VAE) with graph neural networks, and uses a novel iterative graph refinement strategy inspired by low-rank approximations for decoding. On a wide variety of synthetic and benchmark datasets, Graphite outperforms competing approaches for the tasks of density estimation, link prediction, and node classification. Finally, we derive a theoretical connection between message passing in graph neural networks and mean-field variational inference.

AAAI Conference 2019 Conference Paper

InfoVAE: Balancing Learning and Inference in Variational Autoencoders

• Shengjia Zhao
• Jiaming Song
• Stefano Ermon

A key advance in learning generative models is the use of amortized inference distributions that are jointly trained with the models. We find that existing training objectives for variational autoencoders can lead to inaccurate amortized inference distributions and, in some cases, improving the objective provably degrades the inference quality. In addition, it has been observed that variational autoencoders tend to ignore the latent variables when combined with a decoding distribution that is too flexible. We again identify the cause in existing training criteria and propose a new class of objectives (Info- VAE) that mitigate these problems. We show that our model can significantly improve the quality of the variational posterior and can make effective use of the latent features regardless of the flexibility of the decoding distribution. Through extensive qualitative and quantitative analyses, we demonstrate that our models outperform competing approaches on multiple performance metrics.

IJCAI Conference 2019 Conference Paper

Learning to Interpret Satellite Images using Wikipedia

• Burak Uzkent
• Evan Sheehan
• Chenlin Meng
• Zhongyi Tang
• Marshall Burke
• David Lobell
• Stefano Ermon

Despite recent progress in computer vision, fine-grained interpretation of satellite images remains challenging because of a lack of labeled training data. To overcome this limitation, we construct a novel dataset called WikiSatNet by pairing geo-referenced Wikipedia articles with satellite imagery of their corresponding locations. We then propose two strategies to learn representations of satellite images by predicting properties of the corresponding articles from the images. Leveraging this new multi-modal dataset, we can drastically reduce the quantity of human-annotated labels and time required for downstream tasks. On the recently released fMoW dataset, our pre-training strategies can boost the performance of a model pre-trained on ImageNet by up to 4. 5% in F1 score.

NeurIPS Conference 2019 Conference Paper

Meta-Inverse Reinforcement Learning with Probabilistic Context Variables

• Lantao Yu
• Tianhe Yu
• Chelsea Finn
• Stefano Ermon

Reinforcement learning demands a reward function, which is often difficult to provide or design in real world applications. While inverse reinforcement learning (IRL) holds promise for automatically learning reward functions from demonstrations, several major challenges remain. First, existing IRL methods learn reward functions from scratch, requiring large numbers of demonstrations to correctly infer the reward for each task the agent may need to perform. Second, and more subtly, existing methods typically assume demonstrations for one, isolated behavior or task, while in practice, it is significantly more natural and scalable to provide datasets of heterogeneous behaviors. To this end, we propose a deep latent variable model that is capable of learning rewards from unstructured, multi-task demonstration data, and critically, use this experience to infer robust rewards for new, structurally-similar tasks from a single demonstration. Our experiments on multiple continuous control tasks demonstrate the effectiveness of our approach compared to state-of-the-art imitation and inverse reinforcement learning methods.

NeurIPS Conference 2019 Conference Paper

MintNet: Building Invertible Neural Networks with Masked Convolutions

• Yang Song
• Chenlin Meng
• Stefano Ermon

We propose a new way of constructing invertible neural networks by combining simple building blocks with a novel set of composition rules. This leads to a rich set of invertible architectures, including those similar to ResNets. Inversion is achieved with a locally convergent iterative procedure that is parallelizable and very fast in practice. Additionally, the determinant of the Jacobian can be computed analytically and efficiently, enabling their generative use as flow models. To demonstrate their flexibility, we show that our invertible neural networks are competitive with ResNets on MNIST and CIFAR-10 classification. When trained as generative models, our invertible networks achieve competitive likelihoods on MNIST, CIFAR-10 and ImageNet 32x32, with bits per dimension of 0. 98, 3. 32 and 4. 06 respectively.

ICML Conference 2019 Conference Paper

Multi-Agent Adversarial Inverse Reinforcement Learning

• Lantao Yu
• Jiaming Song
• Stefano Ermon

Reinforcement learning agents are prone to undesired behaviors due to reward mis-specification. Finding a set of reward functions to properly guide agent behaviors is particularly challenging in multi-agent scenarios. Inverse reinforcement learning provides a framework to automatically acquire suitable reward functions from expert demonstrations. Its extension to multi-agent settings, however, is difficult due to the more complex notions of rational behaviors. In this paper, we propose MA-AIRL, a new framework for multi-agent inverse reinforcement learning, which is effective and scalable for Markov games with high-dimensional state-action space and unknown dynamics. We derive our algorithm based on a new solution concept and maximum pseudolikelihood estimation within an adversarial reward learning framework. In the experiments, we demonstrate that MA-AIRL can recover reward functions that are highly correlated with the ground truth rewards, while significantly outperforms prior methods in terms of policy imitation.

ICML Conference 2019 Conference Paper

Neural Joint Source-Channel Coding

• Kristy Choi
• Kedar Tatwawadi
• Aditya Grover
• Tsachy Weissman
• Stefano Ermon

For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall short in the finite bit-length regime, as it requires non-trivial tuning of hand-crafted codes and assumes infinite computational power for decoding. In this work, we propose to jointly learn the encoding and decoding processes using a new discrete variational autoencoder model. By adding noise into the latent codes to simulate the channel during training, we learn to both compress and error-correct given a fixed bit-length and computational budget. We obtain codes that are not only competitive against several separation schemes, but also learn useful robust representations of the data for downstream tasks such as classification. Finally, inference amortization yields an extremely fast neural decoder, almost an order of magnitude faster compared to standard decoding methods based on iterative belief propagation.

IJCAI Conference 2019 Conference Paper

Reparameterizable Subset Sampling via Continuous Relaxations

• Sang Michael Xie
• Stefano Ermon

Many machine learning tasks require sampling a subset of items from a collection based on a parameterized distribution. The Gumbel-softmax trick can be used to sample a single item, and allows for low-variance reparameterized gradients with respect to the parameters of the underlying distribution. However, stochastic optimization involving subset sampling is typically not reparameterizable. To overcome this limitation, we define a continuous relaxation of subset sampling that provides reparameterization gradients by generalizing the Gumbel-max trick. We use this approach to sample subsets of features in an instance-wise feature selection task for model interpretability, subsets of neighbors to implement a deep stochastic k-nearest neighbors model, and sub-sequences of neighbors to implement parametric t-SNE by directly comparing the identities of local neighbors. We improve performance in all these tasks by incorporating subset sampling in end-to-end training.

UAI Conference 2019 Conference Paper

Sliced Score Matching: A Scalable Approach to Density and Score Estimation

• Yang Song 0011
• Sahaj Garg
• Jiaxin Shi
• Stefano Ermon

Score matching is a popular method for estimating unnormalized statistical models. However, it has been so far limited to simple, shallow models or low-dimensional data, due to the difficulty of computing the Hessian of log-density functions. We show this difficulty can be mitigated by projecting the scores onto random vectors before comparing them. This objective, called sliced score matching, only involves Hessian-vector products, which can be easily implemented using reverse-mode automatic differentiation. Therefore, sliced score matching is amenable to more complex models and higher dimensional data compared to score matching. Theoretically, we prove the consistency and asymptotic normality of sliced score matching estimators. Moreover, we demonstrate that sliced score matching can be used to learn deep score estimators for implicit distributions. In our experiments, we show sliced score matching can learn deep energy-based models effectively, and can produce accurate score estimates for applications such as variational inference with implicit distributions and training Wasserstein Auto-Encoders.

NeurIPS Conference 2019 Conference Paper

Temporal FiLM: Capturing Long-Range Sequence Dependencies with Feature-Wise Modulations.

• Sawyer Birnbaum
• Volodymyr Kuleshov
• Zayd Enam
• Pang Wei Koh
• Stefano Ermon

Learning representations that accurately capture long-range dependencies in sequential inputs --- including text, audio, and genomic data --- is a key problem in deep learning. Feed-forward convolutional models capture only feature interactions within finite receptive fields while recurrent architectures can be slow and difficult to train due to vanishing gradients. Here, we propose Temporal Feature-Wise Linear Modulation (TFiLM) --- a novel architectural component inspired by adaptive batch normalization and its extensions --- that uses a recurrent neural network to alter the activations of a convolutional model. This approach expands the receptive field of convolutional sequence models with minimal computational overhead. Empirically, we find that TFiLM significantly improves the learning speed and accuracy of feed-forward neural networks on a range of generative and discriminative learning tasks, including text classification and audio super-resolution.

AAAI Conference 2019 Conference Paper

Tile2Vec: Unsupervised Representation Learning for Spatially Distributed Data

• Neal Jean
• Sherrie Wang
• Anshul Samar
• George Azzari
• David Lobell
• Stefano Ermon

Geospatial analysis lacks methods like the word vector representations and pre-trained networks that significantly boost performance across a wide range of natural language and computer vision tasks. To fill this gap, we introduce Tile2Vec, an unsupervised representation learning algorithm that extends the distributional hypothesis from natural language — words appearing in similar contexts tend to have similar meanings — to spatially distributed data. We demonstrate empirically that Tile2Vec learns semantically meaningful representations for both image and non-image datasets. Our learned representations significantly improve performance in downstream classification tasks and, similarly to word vectors, allow visual analogies to be obtained via simple arithmetic in the latent space.

UAI Conference 2018 Conference Paper

A Lagrangian Perspective on Latent Variable Generative Models

• Shengjia Zhao
• Jiaming Song
• Stefano Ermon

A large number of objectives have been proposed to train latent variable generative models. We show that many of them are Lagrangian dual functions of the same primal optimization problem. The primal problem optimizes the mutual information between latent and visible variables, subject to the constraints of accurately modeling the data distribution and performing correct amortized inference. By choosing to maximize or minimize mutual information, and choosing different Lagrange multipliers, we obtain different objectives including InfoGAN, ALI/BiGAN, ALICE, CycleGAN, beta-VAE, adversarial autoencoders, AVB, AS-VAE and InfoVAE. Based on this observation, we provide an exhaustive characterization of the statistical and computational trade-offs made by all the training objectives in this class of Lagrangian duals. Next, we propose a dual optimization method where we optimize model parameters as well as the Lagrange multipliers. This method achieves Pareto optimal solutions in terms of optimizing information and satisfying the constraints.

ICML Conference 2018 Conference Paper

Accelerating Natural Gradient with Higher-Order Invariance

• Yang Song 0011
• Jiaming Song
• Stefano Ermon

An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with small but finite step sizes. In this paper, we study invariance properties from a combined perspective of Riemannian geometry and numerical differential equation solving. We define the order of invariance of a numerical method to be its convergence order to an invariant solution. We propose to use higher-order integrators and geodesic corrections to obtain more invariant optimization trajectories. We prove the numerical convergence properties of geodesic corrected updates and show that they can be as computational efficient as plain natural gradient. Experimentally, we demonstrate that invariance leads to faster optimization and our techniques improve on traditional natural gradient in deep neural network training and natural policy gradient for reinforcement learning.

ICML Conference 2018 Conference Paper

Accurate Uncertainties for Deep Learning Using Calibrated Regression

• Volodymyr Kuleshov
• Nathan Fenner
• Stefano Ermon

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use of approximate inference, Bayesian uncertainty estimates are often inaccurate {—} for example, a 90% credible interval may not contain the true outcome 90% of the time. Here, we propose a simple procedure for calibrating any regression algorithm; when applied to Bayesian and probabilistic models, it is guaranteed to produce calibrated uncertainty estimates given enough data. Our procedure is inspired by Platt scaling and extends previous work on classification. We evaluate this approach on Bayesian linear regression, feedforward, and recurrent neural networks, and find that it consistently outputs well-calibrated credible intervals while improving performance on time series forecasting and model-based reinforcement learning tasks.

IJCAI Conference 2018 Conference Paper

Adversarial Constraint Learning for Structured Prediction

• Hongyu Ren
• Russell Stewart
• Jiaming Song
• Volodymyr Kuleshov
• Stefano Ermon

Constraint-based learning reduces the burden of collecting labels by having users specify general properties of structured outputs, such as constraints imposed by physical laws. We propose a novel framework for simultaneously learning these constraints and using them for supervision, bypassing the difficulty of using domain expertise to manually specify constraints. Learning requires a black-box simulator of structured outputs, which generates valid labels, but need not model their corresponding inputs or the input-label relationship. At training time, we constrain the model to produce outputs that cannot be distinguished from simulated labels by adversarial training. Providing our framework with a small number of labeled inputs gives rise to a new semi-supervised structured prediction model; we evaluate this model on multiple tasks --- tracking, pose estimation and time series prediction --- and find that it achieves high accuracy with only a small number of labeled inputs. In some cases, no labels are required at all.

NeurIPS Conference 2018 Conference Paper

Amortized Inference Regularization

• Rui Shu
• Hung Bui
• Shengjia Zhao
• Mykel Kochenderfer
• Stefano Ermon

The variational autoencoder (VAE) is a popular model for density estimation and representation learning. Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is accurate. However, it is often overlooked that an overly-expressive inference model can be detrimental to the test set performance of both the amortized posterior approximator and, more importantly, the generative density estimator. In this paper, we leverage the fact that VAEs rely on amortized inference and propose techniques for amortized inference regularization (AIR) that control the smoothness of the inference model. We demonstrate that, by applying AIR, it is possible to improve VAE generalization on both inference and generative performance. Our paper challenges the belief that amortized inference is simply a mechanism for approximating maximum likelihood training and illustrates that regularization of the amortization family provides a new direction for understanding and improving generalization in VAEs.

AAAI Conference 2018 Conference Paper

Approximate Inference via Weighted Rademacher Complexity

• Jonathan Kuck
• Ashish Sabharwal
• Stefano Ermon

Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary weighted set, defined as the sum of weights of all elements in the set. Our technique provides upper and lower bounds on a novel generalization of Rademacher complexity to the weighted setting in terms of the weighted set size. This generalizes Massart’s Lemma, a known upper bound on the Rademacher complexity in terms of the unweighted set size. We show that the weighted Rademacher complexity can be estimated by solving a randomly perturbed optimization problem, allowing us to derive high-probability bounds on the size of any weighted set. We apply our method to the problems of calculating the partition function of an Ising model and computing propositional model counts (#SAT). Our experiments demonstrate that we can produce tighter bounds than competing methods in both the weighted and unweighted settings.

UAI Conference 2018 Conference Paper

Bayesian optimization and attribute adjustment

• Stephan Eismann
• Daniel Levy 0002
• Rui Shu
• Stefan Bartzsch
• Stefano Ermon

Automatic design via Bayesian optimization holds great promise given the constant increase of available data across domains. However, it faces difficulties from high-dimensional, potentially discrete, search spaces. We propose to probabilistically embed inputs into a lower dimensional, continuous latent space, where we perform gradient-based optimization guided by a Gaussian process. Building on variational autoncoders, we use both labeled and unlabeled data to guide the encoding and increase its accuracy. In addition, we propose an adversarial extension to render the latent representation invariant with respect to specific design attributes, which allows us to transfer these attributes across structures. We apply the framework both to a functional-protein dataset and to perform optimization of drag coefficients directly over high-dimensional shapes without incorporating domain knowledge or handcrafted features.

NeurIPS Conference 2018 Conference Paper

Bias and Generalization in Deep Generative Models: An Empirical Study

• Shengjia Zhao
• Hongyu Ren
• Arianna Yuan
• Jiaming Song
• Noah Goodman
• Stefano Ermon

In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework to systematically investigate bias and generalization in deep generative models of images by probing the learning algorithm with carefully designed training datasets. By measuring properties of the learned distribution, we are able to find interesting patterns of generalization. We verify that these patterns are consistent across datasets, common models and architectures.

AAAI Conference 2018 Conference Paper

Boosted Generative Models

• Aditya Grover
• Stefano Ermon

We propose a novel approach for using unsupervised boosting to create an ensemble of generative models, where models are trained in sequence to correct earlier mistakes. Our metaalgorithmic framework can leverage any existing base learner that permits likelihood evaluation, including recent deep expressive models. Further, our approach allows the ensemble to include discriminative models trained to distinguish real data from model-generated data. We show theoretical conditions under which incorporating a new model in the ensemble will improve the fit and empirically demonstrate the effectiveness of our black-box boosting algorithms on density estimation, classification, and sample generation on benchmark datasets for a wide range of generative models.

NeurIPS Conference 2018 Conference Paper

Constructing Unrestricted Adversarial Examples with Generative Models

• Yang Song
• Rui Shu
• Nate Kushman
• Stefano Ermon

Adversarial examples are typically constructed by perturbing an existing data point within a small matrix norm, and current defense methods are focused on guarding against this type of attack. In this paper, we propose a new class of adversarial examples that are synthesized entirely from scratch using a conditional generative model, without being restricted to norm-bounded perturbations. We first train an Auxiliary Classifier Generative Adversarial Network (AC-GAN) to model the class-conditional distribution over data samples. Then, conditioned on a desired class, we search over the AC-GAN latent space to find images that are likely under the generative model and are misclassified by a target classifier. We demonstrate through human evaluation that these new kind of adversarial images, which we call Generative Adversarial Examples, are legitimate and belong to the desired class. Our empirical results on the MNIST, SVHN, and CelebA datasets show that generative adversarial examples can bypass strong adversarial training and certified defense methods designed for traditional adversarial attacks.

AAAI Conference 2018 Conference Paper

Deterministic Policy Optimization by Combining Pathwise and Score Function Estimators for Discrete Action Spaces

• Daniel Levy
• Stefano Ermon

Policy optimization methods have shown great promise in solving complex reinforcement and imitation learning tasks. While model-free methods are broadly applicable, they often require many samples to optimize complex policies. Modelbased methods greatly improve sample-efficiency but at the cost of poor generalization, requiring a carefully handcrafted model of the system dynamics for each task. Recently, hybrid methods have been successful in trading off applicability for improved sample-complexity. However, these have been limited to continuous action spaces. In this work, we present a new hybrid method based on an approximation of the dynamics as an expectation over the next state under the current policy. This relaxation allows us to derive a novel hybrid policy gradient estimator, combining score function and pathwise derivative estimators, that is applicable to discrete action spaces. We show significant gains in sample complexity, ranging between 1. 7 and 25×, when learning parameterized policies on Cart Pole, Acrobot, Mountain Car and Hand Mass. Our method is applicable to both discrete and continuous action spaces, when competing pathwise methods are limited to the latter.

AAAI Conference 2018 Conference Paper

Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models

• Aditya Grover
• Manik Dhar
• Stefano Ermon

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explicit density which makes quantitative evaluations challenging. To bridge this gap, we propose Flow-GANs, a generative adversarial network for which we can perform exact likelihood evaluation, thus supporting both adversarial and maximum likelihood training. When trained adversarially, Flow-GANs generate high-quality samples but attain extremely poor log-likelihood scores, inferior even to a mixture model memorizing the training data; the opposite is true when trained by maximum likelihood. Results on MNIST and CIFAR-10 demonstrate that hybrid training can attain high held-out likelihoods while retaining visual fidelity in the generated samples.

ICML Conference 2018 Conference Paper

Modeling Sparse Deviations for Compressed Sensing using Generative Models

• Manik Dhar
• Aditya Grover
• Stefano Ermon

In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative model. A domain-specific generative model can provide a stronger prior and thus allow for recovery with far fewer measurements. However, unlike sparsity-based approaches, existing methods based on generative models guarantee exact recovery only over their support, which is typically only a small subset of the space on which the signals are defined. We propose Sparse-Gen, a framework that allows for sparse deviations from the support set, thereby achieving the best of both worlds by using a domain specific prior and allowing reconstruction over the full space of signals. Theoretically, our framework provides a new class of signals that can be acquired using compressed sensing, reducing classic sparse vector recovery to a special case and avoiding the restrictive support due to a generative model prior. Empirically, we observe consistent improvements in reconstruction accuracy over competing approaches, especially in the more practical setting of transfer compressed sensing where a generative model for a data-rich, source domain aids sensing on a data-scarce, target domain.

NeurIPS Conference 2018 Conference Paper

Multi-Agent Generative Adversarial Imitation Learning

• Jiaming Song
• Hongyu Ren
• Dorsa Sadigh
• Stefano Ermon

Imitation learning algorithms can be used to learn a policy from expert demonstrations without access to a reward signal. However, most existing approaches are not applicable in multi-agent settings due to the existence of multiple (Nash) equilibria and non-stationary environments. We propose a new framework for multi-agent imitation learning for general Markov games, where we build upon a generalized notion of inverse reinforcement learning. We further introduce a practical multi-agent actor-critic algorithm with good empirical performance. Our method can be used to imitate complex behaviors in high-dimensional environments with multiple cooperative or competing agents.

NeurIPS Conference 2018 Conference Paper

Semi-supervised Deep Kernel Learning: Regression with Unlabeled Data by Minimizing Predictive Variance

• Neal Jean
• Sang Michael Xie
• Stefano Ermon

Large amounts of labeled data are typically required to train deep learning models. For many real-world problems, however, acquiring additional data can be expensive or even impossible. We present semi-supervised deep kernel learning (SSDKL), a semi-supervised regression model based on minimizing predictive variance in the posterior regularization framework. SSDKL combines the hierarchical representation learning of neural networks with the probabilistic modeling capabilities of Gaussian processes. By leveraging unlabeled data, we show improvements on a diverse set of real-world regression tasks over supervised deep kernel learning and semi-supervised methods such as VAT and mean teacher adapted for regression.

NeurIPS Conference 2018 Conference Paper

Streamlining Variational Inference for Constraint Satisfaction Problems

• Aditya Grover
• Tudor Achim
• Stefano Ermon

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16. 3% on average for k = 3, 4, 5, 6.

NeurIPS Conference 2017 Conference Paper

A-NICE-MC: Adversarial Training for MCMC

• Jiaming Song
• Shengjia Zhao
• Stefano Ermon

Existing Markov Chain Monte Carlo (MCMC) methods are either based on general-purpose and domain-agnostic schemes, which can lead to slow convergence, or require hand-crafting of problem-specific proposals by an expert. We propose A-NICE-MC, a novel method to train flexible parametric Markov chain kernels to produce samples with desired properties. First, we propose an efficient likelihood-free adversarial training method to train a Markov chain and mimic a given data distribution. Then, we leverage flexible volume preserving flows to obtain parametric kernels for MCMC. Using a bootstrap approach, we show how to train efficient Markov Chains to sample from a prescribed posterior distribution by iteratively improving the quality of both the model and the samples. A-NICE-MC provides the first framework to automatically design efficient domain-specific MCMC proposals. Empirical results demonstrate that A-NICE-MC combines the strong guarantees of MCMC with the expressiveness of deep neural networks, and is able to significantly outperform competing methods such as Hamiltonian Monte Carlo.

AAAI Conference 2017 Conference Paper

Deep Gaussian Process for Crop Yield Prediction Based on Remote Sensing Data

• Jiaxuan You
• Xiaocheng Li
• Melvin Low
• David Lobell
• Stefano Ermon

Agricultural monitoring, especially in developing countries, can help prevent famine and support humanitarian efforts. A central challenge is yield estimation, i. e. , predicting crop yields before harvest. We introduce a scalable, accurate, and inexpensive method to predict crop yields using publicly available remote sensing data. Our approach improves existing techniques in three ways. First, we forego hand-crafted features traditionally used in the remote sensing community and propose an approach based on modern representation learning ideas. We also introduce a novel dimensionality reduction technique that allows us to train a Convolutional Neural Network or Long-short Term Memory network and automatically learn useful features even when labeled training data are scarce. Finally, we incorporate a Gaussian Process component to explicitly model the spatio-temporal structure of the data and further improve accuracy. We evaluate our approach on county-level soybean yield prediction in the U. S. and show that it outperforms competing techniques.

AAAI Conference 2017 Conference Paper

Estimating Uncertainty Online Against an Adversary

• Volodymyr Kuleshov
• Stefano Ermon

Assessing uncertainty is an important step towards ensuring the safety and reliability of machine learning systems. Existing uncertainty estimation techniques may fail when their modeling assumptions are not met, e. g. when the data distribution differs from the one seen at training time. Here, we propose techniques that assess a classification algorithm’s uncertainty via calibrated probabilities (i. e. probabilities that match empirical outcome frequencies in the long run) and which are guaranteed to be reliable (i. e. accurate and calibrated) on out-of-distribution input, including input generated by an adversary. This represents an extension of classical online learning that handles uncertainty in addition to guaranteeing accuracy under adversarial assumptions. We establish formal guarantees for our methods, and we validate them on two real-world problems: question answering and medical diagnosis from genomic data.

UAI Conference 2017 Conference Paper

Fast Amortized Inference and Learning in Log-linear Models with Randomly Perturbed Nearest Neighbor Search

• Stephen Mussmann
• Daniel Levy 0002
• Stefano Ermon

Inference in log-linear models scales linearly in the size of output space in the worst-case. This is often a bottleneck in natural language processing and computer vision tasks when the output space is feasibly enumerable but very large. We propose a method to perform inference in log-linear models with sublinear amortized cost. Our idea hinges on using Gumbel random variable perturbations and a pre-computed Maximum Inner Product Search data structure to access the most-likely elements in sublinear amortized time. Our method yields provable runtime and accuracy guarantees. Further, we present empirical experiments on ImageNet and Word Embeddings showing significant speedups for sampling, inference, and learning in log-linear models.

AAAI Conference 2017 Conference Paper

General Bounds on Satisfiability Thresholds for Random CSPs via Fourier Analysis

• Colin Wei
• Stefano Ermon

Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to variables passes certain thresholds, they transition from being almost certainly satisfiable to unsatisfiable. The exact location of this threshold has been thoroughly investigated, but only for certain common classes of constraints. In this paper, we present new bounds for the location of these thresholds in boolean CSPs. Our main contribution is that our bounds are fully general, and apply to any fixed constraint function that could be used to generate an ensemble of random CSPs. These bounds rely on a novel Fourier analysis and can be easily computed from the Fourier spectrum of a constraint function. Our bounds are within a constant factor of the exact threshold location for many well-studied random CSPs. We demonstrate that our bounds can be easily instantiated to obtain thresholds for many constraint functions that had not been previously studied, and evaluate them experimentally.

UAI Conference 2017 Conference Paper

Hybrid Deep Discriminative/Generative Models for Semi-Supervised Learning

• Volodymyr Kuleshov
• Stefano Ermon

Most methods in machine learning are described as either discriminative or generative. The former often attain higher predictive accuracy, while the latter are more strongly regularized and can deal with missing data. Here, we propose a new framework to combine a broad class of discriminative and generative models, interpolating between the two extremes with a multiconditional likelihood objective. Unlike previous approaches, we couple the two components through shared latent variables, and train using recent advances in variational inference. Instantiating our framework with modern deep architectures gives rise to deep hybrid models, a highly flexible family that generalizes several existing models and is effective in the semi-supervised setting, where it results in improvements over the state of the art on the SVHN dataset.

NeurIPS Conference 2017 Conference Paper

InfoGAIL: Interpretable Imitation Learning from Visual Demonstrations

• Yunzhu Li
• Jiaming Song
• Stefano Ermon

The goal of imitation learning is to mimic expert behavior without access to an explicit reward signal. Expert demonstrations provided by humans, however, often show significant variability due to latent factors that are typically not explicitly modeled. In this paper, we propose a new algorithm that can infer the latent structure of expert demonstrations in an unsupervised way. Our method, built on top of Generative Adversarial Imitation Learning, can not only imitate complex behaviors, but also learn interpretable and meaningful representations of complex behavioral data, including visual demonstrations. In the driving domain, we show that a model learned from human demonstrations is able to both accurately reproduce a variety of behaviors and accurately anticipate human actions using raw visual inputs. Compared with various baselines, our method can better capture the latent structure underlying expert demonstrations, often recovering semantically meaningful factors of variation in the data.

AAAI Conference 2017 Conference Paper

Label-Free Supervision of Neural Networks with Physics and Domain Knowledge

• Russell Stewart
• Stefano Ermon

In many machine learning applications, labeled data is scarce and obtaining more labels is expensive. We introduce a new approach to supervising neural networks by specifying constraints that should hold over the output space, rather than direct examples of input-output pairs. These constraints are derived from prior domain knowledge, e. g. , from known laws of physics. We demonstrate the effectiveness of this approach on real world and simulated computer vision tasks. We are able to train a convolutional neural network to detect and track objects without any labeled examples. Our approach can significantly reduce the need for labeled training data, but introduces new challenges for encoding prior knowledge into appropriate loss functions.

ICML Conference 2017 Conference Paper

Learning Hierarchical Features from Deep Generative Models

• Shengjia Zhao
• Jiaming Song
• Stefano Ermon

Deep neural networks have been shown to be very successful at learning feature hierarchies in supervised learning tasks. Generative models, on the other hand, have benefited less from hierarchical models with multiple layers of latent variables. In this paper, we prove that hierarchical latent variable models do not take advantage of the hierarchical structure when trained with existing variational methods, and provide some limitations on the kind of features existing models can learn. Finally we propose an alternative architecture that do not suffer from these limitations. Our model is able to learn highly interpretable and disentangled hierarchical features on several natural image datasets with no task specific regularization or prior knowledge.

NeurIPS Conference 2017 Conference Paper

Neural Variational Inference and Learning in Undirected Graphical Models

• Volodymyr Kuleshov
• Stefano Ermon

Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the log-likelihood of the model. Central to our approach is an upper bound on the log-partition function parametrized by a function q that we express as a flexible neural network. Our bound makes it possible to track the partition function during learning, to speed-up sampling, and to train a broad class of hybrid directed/undirected models via a unified variational inference framework. We empirically demonstrate the effectiveness of our method on several popular generative modeling datasets.

NeurIPS Conference 2016 Conference Paper

Adaptive Concentration Inequalities for Sequential Decision Problems

• Shengjia Zhao
• Enze Zhou
• Ashish Sabharwal
• Stefano Ermon

A key challenge in sequential decision problems is to determine how many samples are needed for an agent to make reliable decisions with good probabilistic guarantees. We introduce Hoeffding-like concentration inequalities that hold for a random, adaptively chosen number of samples. Our inequalities are tight under natural assumptions and can greatly simplify the analysis of common sequential decision problems. In particular, we apply them to sequential hypothesis testing, best arm identification, and sorting. The resulting algorithms rival or exceed the state of the art both theoretically and empirically.

ICML Conference 2016 Conference Paper

Beyond Parity Constraints: Fourier Analysis of Hash Functions for Inference

• Tudor Achim
• Ashish Sabharwal
• Stefano Ermon

Random projections have played an important role in scaling up machine learning and data mining algorithms. Recently they have also been applied to probabilistic inference to estimate properties of high-dimensional distributions; however, they all rely on the same class of projections based on universal hashing. We provide a general framework to analyze random projections which relates their statistical properties to their Fourier spectrum, which is a well-studied area of theoretical computer science. Using this framework we introduce two new classes of hash functions for probabilistic inference and model counting that show promising performance on synthetic and real-world benchmarks.

AAAI Conference 2016 Conference Paper

Closing the Gap Between Short and Long XORs for Model Counting

• Shengjia Zhao
• Sorathan Chaturapruek
• Ashish Sabharwal
• Stefano Ermon

Many recent algorithms for approximate model counting are based on a reduction to combinatorial searches over random subsets of the space defined by parity or XOR constraints. Long parity constraints (involving many variables) provide strong theoretical guarantees but are computationally difficult. Short parity constraints are easier to solve but have weaker statistical properties. It is currently not known how long these parity constraints need to be. We close the gap by providing matching necessary and sufficient conditions on the required asymptotic length of the parity constraints. Further, we provide a new family of lower bounds and the first non-trivial upper bounds on the model count that are valid for arbitrarily short XORs. We empirically demonstrate the effectiveness of these bounds on model counting benchmarks and in a Satisfiability Modulo Theory (SMT) application motivated by the analysis of contingency tables in statistics.

AAAI Conference 2016 Conference Paper

Exact Sampling with Integer Linear Programs and Random Perturbations

• Carolyn Kim
• Ashish Sabharwal
• Stefano Ermon

We consider the problem of sampling from a discrete probability distribution specified by a graphical model. Exact samples can, in principle, be obtained by computing the mode of the original model perturbed with an exponentially many i. i. d. random variables. We propose a novel algorithm that views this as a combinatorial optimization problem and searches for the extreme state using a standard integer linear programming (ILP) solver, appropriately extended to account for the random perturbation. Our technique, GumbelMIP, leverages linear programming (LP) relaxations to evaluate the quality of samples and prune large portions of the search space, and can thus scale to large tree-width models beyond the reach of current exact inference methods. Further, when the optimization problem is not solved to optimality, our method yields a novel approximate sampling technique. We empirically demonstrate that our approach parallelizes well, our exact sampler scales better than alternative approaches, and our approximate sampler yields better quality samples than a Gibbs sampler and a low-dimensional perturbation method.

NeurIPS Conference 2016 Conference Paper

Generative Adversarial Imitation Learning

• Jonathan Ho
• Stefano Ermon

Consider learning a policy from example expert behavior, without interaction with the expert or access to a reinforcement signal. One approach is to recover the expert's cost function with inverse reinforcement learning, then extract a policy from that cost function with reinforcement learning. This approach is indirect and can be slow. We propose a new general framework for directly extracting a policy from data as if it were obtained by reinforcement learning following inverse reinforcement learning. We show that a certain instantiation of our framework draws an analogy between imitation learning and generative adversarial networks, from which we derive a model-free imitation learning algorithm that obtains significant performance gains over existing model-free methods in imitating complex behaviors in large, high-dimensional environments.

ICML Conference 2016 Conference Paper

Learning and Inference via Maximum Inner Product Search

• Stephen Mussmann
• Stefano Ermon

A large class of commonly used probabilistic models known as log-linear models are defined up to a normalization constant. Typical learning algorithms for such models require solving a sequence of probabilistic inference queries. These inferences are typically intractable, and are a major bottleneck for learning models with large output spaces. In this paper, we provide a new approach for amortizing the cost of a sequence of related inference queries, such as the ones arising during learning. Our technique relies on a surprising connection with algorithms developed in the past two decades for similarity search in large data bases. Our approach achieves improved running times with provable approximation guarantees. We show that it performs well both on synthetic data and neural language models with large output spaces.

ICML Conference 2016 Conference Paper

Model-Free Imitation Learning with Policy Optimization

• Jonathan Ho
• Jayesh K. Gupta
• Stefano Ermon

In imitation learning, an agent learns how to behave in an environment with an unknown cost function by mimicking expert demonstrations. Existing imitation learning algorithms typically involve solving a sequence of planning or reinforcement learning problems. Such algorithms are therefore not directly applicable to large, high-dimensional environments, and their performance can significantly degrade if the planning problems are not solved to optimality. Under the apprenticeship learning formalism, we develop alternative model-free algorithms for finding a parameterized stochastic policy that performs at least as well as an expert policy on an unknown cost function, based on sample trajectories from the expert. Our approach, based on policy gradients, scales to large continuous environments with guaranteed convergence to local minima.

NeurIPS Conference 2016 Conference Paper

Solving Marginal MAP Problems with NP Oracles and Parity Constraints

• Yexiang Xue
• Zhiyuan Li
• Stefano Ermon
• Carla Gomes
• Bart Selman

Arising from many applications at the intersection of decision-making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) problems unify the two main classes of inference, namely maximization (optimization) and marginal inference (counting), and are believed to have higher complexity than both of them. We propose XOR MMAP, a novel approach to solve the Marginal MAP problem, which represents the intractable counting subproblem with queries to NP oracles, subject to additional parity constraints. XOR MMAP provides a constant factor approximation to the Marginal MAP problem, by encoding it as a single optimization in a polynomial size of the original problem. We evaluate our approach in several machine learning and decision-making applications, and show that our approach outperforms several state-of-the-art Marginal MAP solvers.

UAI Conference 2016 Conference Paper

Sparse Gaussian Processes for Bayesian Optimization

• Mitchell McIntire
• Daniel Ratner
• Stefano Ermon

Bayesian optimization schemes often rely on Gaussian processes (GP). GP models are very flexible, but are known to scale poorly with the number of training points. While several efficient sparse GP models are known, they have limitations when applied in optimization settings. We propose a novel Bayesian optimization framework that uses sparse online Gaussian processes. We introduce a new updating scheme for the online GP that accounts for our preference during optimization for regions with better performance. We apply this method to optimize the performance of a free-electron laser, and demonstrate empirically that the weighted updating scheme leads to substantial improvements to performance in optimization.

AAAI Conference 2016 Conference Paper

Transfer Learning from Deep Features for Remote Sensing and Poverty Mapping

• Michael Xie
• Neal Jean
• Marshall Burke
• David Lobell
• Stefano Ermon

The lack of reliable data in developing countries is a major obstacle to sustainable development, food security, and disaster relief. Poverty data, for example, is typically scarce, sparse in coverage, and labor-intensive to obtain. Remote sensing data such as high-resolution satellite imagery, on the other hand, is becoming increasingly available and inexpensive. Unfortunately, such data is highly unstructured and currently no techniques exist to automatically extract useful insights to inform policy decisions and help direct humanitarian efforts. We propose a novel machine learning approach to extract large-scale socioeconomic indicators from highresolution satellite imagery. The main challenge is that training data is very scarce, making it difficult to apply modern techniques such as Convolutional Neural Networks (CNN). We therefore propose a transfer learning approach where nighttime light intensities are used as a data-rich proxy. We train a fully convolutional CNN model to predict nighttime lights from daytime imagery, simultaneously learning features that are useful for poverty prediction. The model learns filters identifying different terrains and man-made structures, including roads, buildings, and farmlands, without any supervision beyond nighttime lights. We demonstrate that these learned features are highly informative for poverty mapping, even approaching the predictive performance of survey data collected in the field.

ICML Conference 2016 Conference Paper

Variable Elimination in the Fourier Domain

• Yexiang Xue
• Stefano Ermon
• Ronan LeBras
• Carla P. Gomes
• Bart Selman

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major computational advantages. We explore a different type of compact representation based on discrete Fourier representations, complementing the classical approach based on conditional independencies. We show that a large class of probabilistic graphical models have a compact Fourier representation. This theoretical result opens up an entirely new way of approximating a probability distribution. We demonstrate the significance of this approach by applying it to the variable elimination algorithm. Compared with the traditional bucket representation and other approximate inference algorithms, we obtain significant improvements.

NeurIPS Conference 2016 Conference Paper

Variational Bayes on Monte Carlo Steroids

• Aditya Grover
• Stefano Ermon

Variational approaches are often used to approximate intractable posteriors or normalization constants in hierarchical latent variable models. While often effective in practice, it is known that the approximation error can be arbitrarily large. We propose a new class of bounds on the marginal log-likelihood of directed latent variable models. Our approach relies on random projections to simplify the posterior. In contrast to standard variational methods, our bounds are guaranteed to be tight with high probability. We provide a new approach for learning latent variable models based on optimizing our new bounds on the log-likelihood. We demonstrate empirical improvements on benchmark datasets in vision and language for sigmoid belief networks, where a neural network is used to approximate the posterior.

ICML Conference 2015 Conference Paper

A Hybrid Approach for Probabilistic Inference using Random Projections

• Michael Zhu
• Stefano Ermon

We introduce a new meta-algorithm for probabilistic inference in graphical models based on random projections. The key idea is to use approximate inference algorithms for an (exponentially) large number of samples, obtained by randomly projecting the original statistical model using universal hash functions. In the case where the approximate inference algorithm is a variational approximation, this approach can be viewed as interpolating between sampling-based and variational techniques. The number of samples used controls the trade-off between the accuracy of the approximate inference algorithm and the variance of the estimator. We show empirically that by using random projections, we can improve the accuracy of common approximate inference algorithms.

UAI Conference 2015 Conference Paper

Importance Sampling over Sets: A New Probabilistic Inference Scheme

• Stefan Hadjis
• Stefano Ermon

Computing expectations in high-dimensional spaces is a key challenge in probabilistic inference and machine learning. Monte Carlo sampling, and importance sampling in particular, is one of the leading approaches. We propose a generalized importance sampling scheme based on randomly selecting (exponentially large) subsets of states rather than individual ones. By collecting a small number of extreme states in the sampled sets, we obtain estimates of statistics of interest, such as the partition function of an undirected graphical model. We incorporate this idea into a novel maximum likelihood learning algorithm based on cutting planes. We demonstrate empirically that our scheme provides accurate answers and scales to problems with up to a million variables.

AAAI Conference 2015 Conference Paper

Learning Large-Scale Dynamic Discrete Choice Models of Spatio-Temporal Preferences with Application to Migratory Pastoralism in East Africa

• Stefano Ermon
• Yexiang Xue
• Russell Toth
• Bistra Dilkina
• Richard Bernstein
• Theodoros Damoulas
• Patrick Clark
• Steve DeGloria

Understanding spatio-temporal resource preferences is paramount in the design of policies for sustainable development. Unfortunately, resource preferences are often unknown to policy-makers and have to be inferred from data. In this paper we consider the problem of inferring agents’ preferences from observed movement trajectories, and formulate it as an Inverse Reinforcement Learning (IRL) problem. With the goal of informing policy-making, we take a probabilistic approach and consider generative models that can be used to simulate behavior under new circumstances such as changes in resource availability, access policies, or climate. We study the Dynamic Discrete Choice (DDC) models from econometrics and prove that they generalize the Max-Entropy IRL model, a widely used probabilistic approach from the machine learning literature. Furthermore, we develop SPL-GD, a new learning algorithm for DDC models that is considerably faster than the state of the art and scales to very large datasets. We consider an application in the context of pastoralism in the arid and semi-arid regions of Africa, where migratory pastoralists face regular risks due to resource availability, droughts, and resource degradation from climate change and development. We show how our approach based on satellite and survey data can accurately model migratory pastoralism in East Africa and that it considerably outperforms other approaches on a largescale real-world dataset of pastoralists’ movements in Ethiopia collected over 3 years.

AAAI Conference 2015 Conference Paper

Pattern Decomposition with Complex Combinatorial Constraints: Application to Materials Discovery

• Stefano Ermon
• Ronan Le Bras
• Santosh Suram
• John Gregoire
• Carla Gomes
• Bart Selman
• Robert van Dover

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e. g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

IJCAI Conference 2015 Conference Paper

Uncovering Hidden Structure through Parallel Problem Decomposition for the Set Basis Problem: Application to Materials Discovery

• Yexiang Xue
• Stefano Ermon
• Carla P. Gomes
• Bart Selman

Exploiting parallelism is a key strategy for speeding up computation. However, on hard combinatorial problems, such a strategy has been surprisingly challenging due to the intricate variable interactions. We introduce a novel way in which parallelism can be used to exploit hidden structure of hard combinatorial problems. Our approach complements divide-and-conquer and portfolio approaches. We evaluate our approach on the minimum set basis problem: a core combinatorial problem with a range of applications in optimization, machine learning, and system security. We also highlight a novel sustainability related application, concerning the discovery of new materials for renewable energy sources such as improved fuel cell catalysts. In our approach, a large number of smaller sub-problems are identified and solved concurrently. We then aggregate the information from those solutions, and use this information to initialize the search of a global, complete solver. We show that this strategy leads to a substantial speed-up over a sequential approach, since the aggregated sub-problem solution information often provides key structural insights to the complete solver. Our approach also greatly outperforms state-of-the-art incomplete solvers in terms of solution quality. Our work opens up a novel angle for using parallelism to solve hard combinatorial problems.

AAAI Conference 2014 Conference Paper

Designing Fast Absorbing Markov Chains

• Stefano Ermon
• Carla Gomes
• Ashish Sabharwal
• Bart Selman

Markov Chains are a fundamental tool for the analysis of real world phenomena and randomized algorithms. Given a graph with some specified sink nodes and an initial probability distribution, we consider the problem of designing an absorbing Markov Chain that minimizes the time required to reach a sink node, by selecting transition probabilities subject to some natural regularity constraints. By exploiting the Markovian structure, we obtain closed form expressions for the objective function as well as its gradient, which can be thus evaluated efficiently without any simulation of the underlying process and fed to a gradient-based optimization package. For the special case of designing reversible Markov Chains, we show that global optimum can be efficiently computed by exploiting convexity. We demonstrate how our method can be used for the evaluation and design of local search methods tailored for certain domains.

ICML Conference 2014 Conference Paper

Low-density Parity Constraints for Hashing-Based Discrete Integration

• Stefano Ermon
• Carla P. Gomes
• Ashish Sabharwal
• Bart Selman

In recent years, a number of probabilistic inference and counting techniques have been proposed that exploit pairwise independent hash functions to infer properties of succinctly defined high-dimensional sets. While providing desirable statistical guarantees, typical constructions of such hash functions are themselves not amenable to efficient inference. Inspired by the success of LDPC codes, we propose the use of low-density parity constraints to make inference more tractable in practice. While not strongly universal, we show that such sparse constraints belong to a new class of hash functions that we call Average Universal. These weaker hash functions retain the desirable statistical guarantees needed by most such probabilistic inference methods. Thus, they continue to provide provable accuracy guarantees while at the same time making a number of algorithms significantly more scalable in practice. Using this technique, we provide new, tighter bounds for challenging discrete integration and model counting problems.

AAAI Conference 2014 Conference Paper

Uncovering Hidden Structure through Parallel Problem Decomposition

• Yexiang Xue
• Stefano Ermon
• Carla Gomes
• Bart Selman

A key strategy for speeding up computation is to run in parallel on multiple cores. However, on hard combinatorial problems, exploiting parallelism has been surprisingly challenging. It appears that traditional divide-and-conquer strategies do not work well, due to the intricate non-local nature of the interactions between the problem variables. In this paper, we introduce a novel way in which parallelism can be used to exploit hidden structure of hard combinatorial problems. We demonstrate the success of this approach on minimal set basis problem, which has a wide range of applications in machine learning and system security, etc. We also show the effectiveness on a related application problem from materials discovery. In our approach, a large number of smaller sub-problems are identified and solved concurrently. We then aggregate the information from those solutions, and use this to initialize the search of a global, complete solver. We show that this strategy leads to a significant speed-up over a sequential approach. The strategy also greatly outperforms state-of-the-art incomplete solvers in terms of solution quality. Our work opens up a novel angle for using parallelism to solve hard combinatorial problems.

NeurIPS Conference 2013 Conference Paper

Embed and Project: Discrete Sampling with Universal Hashing

• Stefano Ermon
• Carla Gomes
• Ashish Sabharwal
• Bart Selman

We consider the problem of sampling from a probability distribution defined over a high-dimensional discrete set, specified for instance by a graphical model. We propose a sampling algorithm, called PAWS, based on embedding the set into a higher-dimensional space which is then randomly projected using universal hash functions to a lower-dimensional subspace and explored using combinatorial search methods. Our scheme can leverage fast combinatorial optimization tools as a blackbox and, unlike MCMC methods, samples produced are guaranteed to be within an (arbitrarily small) constant factor of the true probability distribution. We demonstrate that by using state-of-the-art combinatorial search tools, PAWS can efficiently sample from Ising grids with strong interactions and from software verification instances, while MCMC and variational methods fail in both cases.

UAI Conference 2013 Conference Paper

Optimization With Parity Constraints: From Binary Codes to Discrete Integration

• Stefano Ermon
• Carla P. Gomes
• Ashish Sabharwal
• Bart Selman

Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly generated parity constraints. By exploiting a connection with max-likelihood decoding of binary codes, we show that these optimizations are computationally hard. Inspired by iterative message passing decoding algorithms, we propose an Integer Linear Programming (ILP) formulation for the problem, enhanced with new sparsification techniques to improve decoding performance. By solving the ILP through a sequence of LP relaxations, we get both lower and upper bounds on the partition function, which hold with high probability and are much tighter than those obtained with variational methods.

ICML Conference 2013 Conference Paper

Taming the Curse of Dimensionality: Discrete Integration by Hashing and Optimization

• Stefano Ermon
• Carla P. Gomes
• Ashish Sabharwal
• Bart Selman

Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a general discrete integral defined over an exponentially large set. This algorithm relies on solving only a small number of instances of a discrete combinatorial optimization problem subject to randomly generated parity constraints used as a hash function. As an application, we demonstrate that with a small number of MAP queries we can efficiently approximate the partition function of discrete graphical models, which can in turn be used, for instance, for marginal computation or model selection.

NeurIPS Conference 2012 Conference Paper

Density Propagation and Improved Bounds on the Partition Function

• Stefano Ermon
• Ashish Sabharwal
• Bart Selman
• Carla Gomes

Given a probabilistic graphical model, its density of states is a function that, for any likelihood value, gives the number of configurations with that probability. We introduce a novel message-passing algorithm called Density Propagation (DP) for estimating this function. We show that DP is exact for tree-structured graphical models and is, in general, a strict generalization of both sum-product and max-product algorithms. Further, we use density of states and tree decomposition to introduce a new family of upper and lower bounds on the partition function. For any tree decompostion, the new upper bound based on finer-grained density of state information is provably at least as tight as previously known bounds based on convexity of the log-partition function, and strictly stronger if a general condition holds. We conclude with empirical evidence of improvement over convex relaxations and mean-field based bounds.

AAMAS Conference 2012 Conference Paper

Probabilistic Planning with Non-Linear Utility Functions and Worst-Case Guarantees

• Stefano Ermon
• Carla Gomes
• Bart Selman
• Alexander Vladimirsky

Markov Decision Processes are one of the most widely used frameworks to formulate probabilistic planning problems. Since planners are often risk-sensitive in high-stake situations, non-linear utility functions are often introduced to describe their preferences among all possible outcomes. Alternatively, risk-sensitive decision makers often require their plans to satisfy certain worst-case guarantees. We show how to combine these two approaches by considering problems where we maximize the expected utility of the total reward subject to worst-case constraints. We generalize several existing results on the structure of optimal policies to the constrained case, both for finite and infinite horizon problems. We provide a Dynamic Programming algorithm to compute the optimal policy, and we introduce an admissible heuristic to effectively prune the search space. Finally, we use a stochastic shortest path problem on large real-world road networks to demonstrate the practical applicability of our method.

SAT Conference 2012 Conference Paper

SMT-Aided Combinatorial Materials Discovery

• Stefano Ermon
• Ronan LeBras
• Carla P. Gomes
• Bart Selman
• R. Bruce van Dover

Abstract In combinatorial materials discovery, one searches for new materials with desirable properties by obtaining measurements on hundreds of samples in a single high-throughput batch experiment. As manual data analysis is becoming more and more impractical, there is a growing need to develop new techniques to automatically analyze and interpret such data. We describe a novel approach to the phase map identification problem where we integrate domain-specific scientific background knowledge about the physical and chemical properties of the materials into an SMT reasoning framework. We evaluate the performance of our method on realistic synthetic measurements, and we show that it provides accurate and physically meaningful interpretations of the data, even in the presence of artificially added noise.

UAI Conference 2012 Conference Paper

Uniform Solution Sampling Using a Constraint Solver As an Oracle

• Stefano Ermon
• Carla P. Gomes
• Bart Selman

We consider the problem of sampling from solutions defined by a set of hard constraints on a combinatorial space. We propose a new sampling technique that, while enforcing a uniform exploration of the search space, leverages the reasoning power of a systematic constraint solver in a black-box scheme. We present a series of challenging domains, such as energy barriers and highly asymmetric spaces, that reveal the difficulties introduced by hard constraints. We demonstrate that standard approaches such as Simulated Annealing and Gibbs Sampling are greatly affected, while our new technique can overcome many of these difficulties. Finally, we show that our sampling scheme naturally defines a new approximate model counting technique, which we empirically show to be very accurate on a range of benchmark problems.

IJCAI Conference 2011 Conference Paper

A Flat Histogram Method for Computing the Density of States of Combinatorial Problems

• Stefano Ermon
• Carla Gomes
• Bart Selman

Consider a combinatorial state space S, such as the set of all truth assignments to N Boolean variables. Given a partition of S, we consider the problem of estimating the size of all the subsets in which S is divided. This problem, also known as computing the density of states, is quite general and has many applications. For instance, if we consider a Boolean formula in CNF and we partition according to the number of violated constraints, computing the density of states is a generalization of both SAT, MAXSAT and model counting. We propose a novel Markov Chain Monte Carlo algorithm to compute the density of states of Boolean formulas that is based on a flat histogram approach. Our method represents a new approach to a variety of inference, learning, and counting problems. We demonstrate its practical effectiveness by showing that the method converges quickly to an accurate solution on a range of synthetic and real-world instances.

AAMAS Conference 2011 Conference Paper

A Message Passing Approach To Multiagent Gaussian Inference for Dynamic Processes

• Stefano Ermon
• Carla Gomes
• Bart Selman

In [1], we introduced a novel distributed inference algorithm for the multiagent Gaussian inference problem, based on the framework of graphical models and message passing algorithms. We compare it to current state of the art techniques and we demonstrate that it is the most efficient one in terms of communication resources used. Moreover, we show experimentally that it outperforms the other methods in terms of estimation error on a general class of problems, even in presence of data loss.

NeurIPS Conference 2011 Conference Paper

Accelerated Adaptive Markov Chain for Partition Function Computation

• Stefano Ermon
• Carla Gomes
• Ashish Sabharwal
• Bart Selman

We propose a novel Adaptive Markov Chain Monte Carlo algorithm to compute the partition function. In particular, we show how to accelerate a flat histogram sampling technique by significantly reducing the number of ``null moves'' in the chain, while maintaining asymptotic convergence properties. Our experiments show that our method converges quickly to highly accurate solutions on a range of benchmark instances, outperforming other state-of-the-art methods such as IJGP, TRW, and Gibbs sampling both in run-time and accuracy. We also show how obtaining a so-called density of states distribution allows for efficient weight learning in Markov Logic theories.

IJCAI Conference 2011 Conference Paper

Risk-Sensitive Policies for Sustainable Renewable Resource Allocation

• Stefano Ermon
• Jon Conrad
• Carla Gomes
• Bart Selman

Markov Decision Processes arise as a natural model for many renewable resources allocation problems. In many such problems, high stakes decisions with potentially catastrophic outcomes (such as the collapse of an entire ecosystem) need to be taken by carefully balancing social, economic, and ecologic goals. We introduce a broad class of such MDP models with a risk averse attitude of the decision maker, in order to obtain policies that are more balanced with respect to the welfare of future generations. We prove that they admit a closed form solution that can be efficiently computed. We show an application of the proposed framework to the Pacific Halibut marine fishery, obtaining new and more cautious policies. Our results strengthen findings of related policies from the literature by providing new evidence that a policy based on periodic closures of the fishery should be employed, in place of the one traditionally used that harvests a constant proportion of the stock every year.

AAMAS Conference 2010 Conference Paper

Collaborative Multiagent Gaussian Inference in a Dynamic Environment Using Belief Propagation

• Stefano Ermon
• Carla Gomes
• Bart Selman

The problem of multiagent Gaussian inference in a dynamicenvironment, also known as distributed Kalman filtering, is formulated into the framework of message passing algorithms. Upon generalizing the derivation of the standardKalman filter to the distributed case, we propose novel solutions that outperform current state of the art techniques.

UAI Conference 2010 Conference Paper

Playing games against nature: optimal policies for renewable resource allocation

• Stefano Ermon
• Jon Conrad
• Carla P. Gomes
• Bart Selman

In this paper we introduce a class of Markov decision processes that arise as a natural model for many renewable resource allocation problems. Upon extending results from the inventory control literature, we prove that they admit a closed form solution and we show how to exploit this structure to speed up its computation. We consider the application of the proposed framework to several problems arising in very different domains, and as part of the ongoing effort in the emerging field of Computational Sustainability we discuss in detail its application to the Northern Pacific Halibut marine fishery. Our approach is applied to a model based on real world data, obtaining a policy with a guaranteed lower bound on the utility function that is structurally very different from the one currently employed.