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Ziming Liu

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21 papers

2 author rows

IROS Conference 2025 Conference Paper

Delving into Mapping Uncertainty for Mapless Trajectory Prediction

Zongzheng Zhang
Xuchong Qiu
Boran Zhang
Guantian Zheng
Xunjiang Gu
Guoxuan Chi
Huan-ang Gao
Leichen Wang

Recent advances in autonomous driving are moving towards mapless approaches, where High-Definition (HD) maps are generated online directly from sensor data, reducing the need for expensive labeling and maintenance. However, the reliability of these online-generated maps remains uncertain. While incorporating map uncertainty into downstream trajectory prediction tasks has shown potential for performance improvements, current strategies provide limited insights into the specific scenarios where this uncertainty is beneficial. In this work, we first analyze the driving scenarios in which mapping uncertainty has the greatest positive impact on trajectory prediction and identify a critical, previously overlooked factor: the agent’s kinematic state. Building on these insights, we propose a novel Proprioceptive Scenario Gating that adaptively integrates map uncertainty into trajectory prediction based on forecasts of the ego vehicle’s future kinematics. This lightweight, self-supervised approach enhances the synergy between online mapping and trajectory prediction, providing interpretability around where uncertainty is advantageous and outperforming previous integration methods. Additionally, we introduce a Covariance-based Map Uncertainty approach that better aligns with map geometry, further improving trajectory prediction. Extensive ablation studies confirm the effectiveness of our approach, achieving up to 23. 6% improvement in mapless trajectory prediction performance over the state-of-the-art method using the real-world nuScenes driving dataset. Our code, data, and models are publicly available at https://github.com/Ethan-Zheng136/Map-Uncertainty-for-Trajectory-Prediction.

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ICML Conference 2025 Conference Paper

DSP: Dynamic Sequence Parallelism for Multi-Dimensional Transformers

Xuanlei Zhao
Shenggan Cheng
Chang Chen
Zangwei Zheng
Ziming Liu
Zheming Yang
Yang You 0001

Scaling multi-dimensional transformers to long sequences is indispensable across various domains. However, the challenges of large memory requirements and slow speeds of such sequences necessitate sequence parallelism. All existing approaches fall under the category of embedded sequence parallelism, which are limited to shard along a single sequence dimension, thereby introducing significant communication overhead. However, the nature of multi-dimensional transformers involves independent calculations across multiple sequence dimensions. To this end, we propose Dynamic Sequence Parallelism (DSP) as a novel abstraction of sequence parallelism. DSP dynamically switches the parallel dimension among all sequences according to the computation stage with efficient resharding strategy. DSP offers significant reductions in communication costs, adaptability across modules, and ease of implementation with minimal constraints. Experimental evaluations demonstrate DSP’s superiority over state-of-the-art embedded sequence parallelism methods by remarkable throughput improvements ranging from 32. 2% to 10x, with less than 25% communication volume.

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AAAI Conference 2025 Conference Paper

Epsilon: Exploring Comprehensive Visual-Semantic Projection for Multi-Label Zero-Shot Learning

Ziming Liu
Jingcai Guo
Song Guo
Xiaocheng Lu

This paper investigates a challenging problem of zero-shot learning in the multi-label scenario (MLZSL), wherein the model is trained to recognize multiple unseen classes within a sample (e.g., an image) based on seen classes and auxiliary knowledge, e.g., semantic information. Existing methods usually resort to analyzing the relationship of various seen classes residing in a sample from the dimension of spatial or semantic characteristics and transferring the learned model to unseen ones. However, they neglect the integrity of local and global features. Although the use of the attention structure will accurately locate local features, especially objects, it will significantly lose its integrity, and the relationship between classes will also be affected. Rough processing of global features will also directly affect comprehensiveness. This neglect will make the model lose its grasp of the main components of the image. Relying only on the local existence of seen classes during the inference stage introduces unavoidable bias. In this paper, we propose a novel and comprehensive visual-semantic framework for MLZSL, dubbed Epsilon, to fully make use of such properties and enable a more accurate and robust visual-semantic projection. In terms of spatial information, we achieve effective refinement by group aggregating image features into several semantic prompts. It can aggregate semantic information rather than class information, preserving the correlation between semantics. In terms of global semantics, we use global forward propagation to collect as much information as possible to ensure that semantics are not omitted. Experiments on large-scale MLZSL benchmark datasets NUS-Wide and Open-Images-v4 demonstrate that the proposed Epsilon outperforms other state-of-the-art methods with large margins.

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TMLR Journal 2025 Journal Article

Harmonic Loss Trains Interpretable AI Models

David D. Baek
Ziming Liu
Riya Tyagi
Max Tegmark

In this paper, we introduce harmonic loss as an alternative supervisory signal for training neural networks and large language models (LLMs). Harmonic loss differs from standard cross-entropy loss by (a) replacing the usual SoftMax normalization with a scale-invariant HarMax function and (b) computing logits via Euclidean distance rather than a dot product. Harmonic loss enables improved interpretability and faster convergence, owing to its scale invariance and finite convergence point by design, which can be interpreted as a class center. We first validate the performance of harmonic models across algorithmic, vision, and language datasets. Through extensive experiments, we demonstrate that models trained with harmonic loss perform better than standard models by: (a) enhancing interpretability (i.e. geometry of representations), (b) requiring less data for generalization, and (c) reducing grokking. Moreover, we compare a GPT-2 model trained with harmonic loss to the standard GPT-2, illustrating that the harmonic model develops more interpretable representations. We hope our work will inspire future research exploring various methods to improve the geometry of representations, paving the way toward building more interpretable AI models.

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NeurIPS Conference 2025 Conference Paper

Impromptu VLA: Open Weights and Open Data for Driving Vision-Language-Action Models

Haohan Chi
Huan-ang Gao
Ziming Liu
Jianing Liu
Chenyu Liu
Jinwei Li
Kaisen Yang
Yangcheng Yu

Vision-Language-Action (VLA) models for autonomous driving show promise but falter in unstructured corner case scenarios, largely due to a scarcity of targeted benchmarks. To address this, we introduce Impromptu VLA. Our core contribution is the Impromptu VLA Dataset: over 80, 000 meticulously curated video clips, distilled from over 2M source clips sourced from 8 open-source large-scale datasets. This dataset is built upon our novel taxonomy of four challenging unstructured categories and features rich, planning-oriented question-answering annotations and action trajectories. Crucially, experiments demonstrate that VLAs trained with our dataset achieve substantial performance gains on established benchmarks—improving closed-loop NeuroNCAP scores and collision rates, and reaching near state-of-the-art L2 accuracy in open-loop nuScenes trajectory prediction. Furthermore, our Q&A suite serves as an effective diagnostic, revealing clear VLM improvements in perception, prediction, and planning. Our code, data and models are available at https: //github. com/ahydchh/Impromptu-VLA

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IROS Conference 2025 Conference Paper

IMVPR: Implicit BEV-Enhanced Multi-View Aggregation for Visual Place Recognition

Xu Cao
Caibo Zhang
Ziming Liu
Xuchang Zhong
Hao Fang

Visual Place Recognition (VPR) is essential for robotics and autonomous driving, enabling localization by matching current observations with a database of known places. While monocular VPR methods rely on visual features, they are sensitive to environmental changes, and multimodal approaches using LiDAR or radar incur high costs and complexity. Multi-view camera configurations offer a cost-effective alternative by expanding perception range and providing richer structural information. In this work, we propose IMVPR, an implicit BEV-enhanced multi-view place recognition network that achieves consistent and parallel multi-view feature fusion and place descriptors aggregation. Unlike methods that explicitly construct BEV features, we introduce descriptor queries to implicitly represent 3D spatial locations, facilitating spatial point projection-based fusion. A cross-attention mechanism further enables end-to-end multi-view feature aggregation. We evaluate IMVPR on four scenes from the nuScenes dataset, including both in-domain and out-of-domain scenarios, demonstrating its superior accuracy and generalization compared to state-of-the-art methods, including multimodal approaches. Our results highlight the potential of multi-view vision-based methods as a scalable and robust solution for VPR.

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IROS Conference 2025 Conference Paper

Reusing Attention for One-stage Lane Topology Understanding

Yang Li 0178
Zongzheng Zhang
Xuchong Qiu
Xinrun Li
Ziming Liu
Leichen Wang
Ruikai Li
Zhenxin Zhu

Understanding lane topology relationships accurately is critical for safe autonomous driving. However, existing two-stage methods suffer from inefficiencies due to error propagations and increased computational overheads. To address these challenges, we propose a one-stage architecture that simultaneously predicts traffic elements, lane centerlines and topology relationship, improving both the accuracy and inference speed of lane topology understanding for autonomous driving. Our key innovation lies in reusing intermediate attention resources within distinct transformer decoders. This approach effectively leverages the inherent relational knowledge within the element detection module to enable the modeling of topology relationships among traffic elements and lanes without requiring additional computationally expensive graph networks. Furthermore, we are the first to demonstrate that knowledge can be distilled from models that utilize standard definition (SD) maps to those operates without using SD maps, enabling superior performance even in the absence of SD maps. Extensive experiments on the OpenLane-V2 dataset show that our approach outperforms baseline methods in both accuracy and efficiency, achieving superior results in lane detection, traffic element identification, and topology reasoning. Our code is available at https://github.com/Yang-Li-2000/one-stage.git.

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NeurIPS Conference 2025 Conference Paper

StarTrail: Concentric Ring Sequence Parallelism for Efficient Near-Infinite-Context Transformer Model Training

Ziming Liu
Shaoyu Wang
Shenggan Cheng
Zhongkai Zhao
Kai Wang
Xuanlei Zhao
James Demmel
Yang You

Training Transformer models on long sequences in a distributed setting poses significant challenges in terms of efficiency and scalability. Current methods are either constrained by the number of attention heads or excessive communication overheads. To address this problem, we propose StarTrail, a multi-dimensional concentric distributed training system for long sequences, fostering an efficient communication paradigm and providing additional tuning flexibility for communication arrangements. Specifically, StarTrail introduces an extra parallel dimension and divides the peer-to-peer communication into sub-rings to substantially reduce communication volume and avoid bandwidth bottlenecks. Through comprehensive experiments across diverse hardware environments and on both Natural Language Processing (NLP) and Computer Vision (CV) tasks, we demonstrate that our approach significantly surpasses state-of-the-art methods that support Long sequence lengths, achieving performance improvements of up to 77. 12% on GPT-style models and up to 114. 33% on DiT (Diffusion Transformer) models without affecting the computations results.

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NeurIPS Conference 2025 Conference Paper

Superposition Yields Robust Neural Scaling

Yizhou Liu
Ziming Liu
Jeff Gore

The success of today's large language models (LLMs) depends on the observation that larger models perform better. However, the origin of this neural scaling law, that loss decreases as a power law with model size, remains unclear. We propose that representation superposition, meaning that LLMs represent more features than they have dimensions, can be a key contributor to loss and cause neural scaling. Based on Anthropic's toy model, we use weight decay to control the degree of superposition, allowing us to systematically study how loss scales with model size. When superposition is weak, the loss follows a power law only if data feature frequencies are power-law distributed. In contrast, under strong superposition, the loss generically scales inversely with model dimension across a broad class of frequency distributions, due to geometric overlaps between representation vectors. We confirmed that open-sourced LLMs operate in the strong superposition regime and have loss scaling inversely with model dimension, and that the Chinchilla scaling laws are also consistent with this behavior. Our results identify representation superposition as a central driver of neural scaling laws, providing insights into questions like when neural scaling laws can be improved and when they will break down.

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ICML Conference 2024 Conference Paper

Easing Concept Bleeding in Diffusion via Entity Localization and Anchoring

Jiewei Zhang
Song Guo 0001
Peiran Dong
Jie Zhang 0076
Ziming Liu
Yue Yu 0001
Xiaoming Wu

Recent diffusion models have manifested extraordinary capabilities in generating high-quality, diverse, and innovative images guided by textual prompts. Nevertheless, these state-of-the-art models may encounter the challenge of concept bleeding when generating images with multiple entities or attributes in the prompt, leading to the unanticipated merging or overlapping of distinct objects in the synthesized result. The current work exploits auxiliary networks to produce mask-constrained regions for entities, necessitating the training of an object detection network. In this paper, we investigate the bleeding reason and find that the cross-attention map associated with a specific entity or attribute tends to extend beyond its intended focus, encompassing the background or other unrelated objects and thereby acting as the primary source of concept bleeding. Motivated by this, we propose Entity Localization and Anchoring (ELA) to drive the entity to concentrate on the expected region accurately during inference, eliminating the necessity for training. Specifically, we initially identify the region corresponding to each entity and subsequently employ a tailored loss function to anchor entities within their designated positioning areas. Extensive experiments demonstrate its superior capability in precisely generating multiple objects as specified in the textual prompts.

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NeurIPS Conference 2024 Conference Paper

How Diffusion Models Learn to Factorize and Compose

Qiyao Liang
Ziming Liu
Mitchell Ostrow
Ila Fiete

Diffusion models are capable of generating photo-realistic images that combine elements which do not appear together in natural images, demonstrating their ability to compositionally generalize. Nonetheless, the precise mechanism of compositionality and how it is acquired through training remains elusive. Here, we consider a highly reduced setting to examine whether diffusion models learn semantically meaningful and fully factorized representations of composable features. We performed extensive controlled experiments on conditional DDPMs trained to generate various forms of 2D Gaussian data. We demonstrate that the models learn factorized, semi-continuous manifold representations that are orthogonal in underlying continuous latent features of independent variations but are not aligned for different values of the same feature. With such representations, models demonstrate superior compositionality but have limited ability to interpolate over unseen values of a given feature. Our experimental results further demonstrate that diffusion models can attain compositionality with a small amount of compositional examples, suggesting a novel way to train DDPMs. Finally, we connect manifold formation in diffusion models to percolation theory in physics, thereby offering insights into the sudden onset of factorized representation learning. Our thorough toy experiments thus contribute a deeper understanding of how diffusion models capture compositional structure in data, paving the way for future research aimed at enhancing factorization and compositional generalization in generative models for real-world applications.

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IJCAI Conference 2024 Conference Paper

ParsNets: A Parsimonious Composition of Orthogonal and Low-Rank Linear Networks for Zero-Shot Learning

Jingcai Guo
Qihua Zhou
Xiaocheng Lu
Ruibin Li
Ziming Liu
Jie Zhang
Bo Han
Junyang Chen

This paper provides a novel parsimonious yet efficient design for zero-shot learning (ZSL), dubbed ParsNets, in which we are interested in learning a composition of on-device friendly linear networks, each with orthogonality and low-rankness properties, to achieve equivalent or better performance against deep models. Concretely, we first refactor the core module of ZSL, i. e. , the visual-semantics mapping function, into several base linear networks that correspond to diverse components of the semantic space, wherein the complex nonlinearity can be collapsed into simple local linearities. Then, to facilitate the generalization of local linearities, we construct a maximal margin geometry on the learned features by enforcing low-rank constraints on intra-class samples and high-rank constraints on inter-class samples, resulting in orthogonal subspaces for different classes. To enhance the model's adaptability and counterbalance the over-/under-fittings, a set of sample-wise indicators is employed to select a sparse subset from these base linear networks to form a composite semantic predictor for each sample. Notably, maximal margin geometry can guarantee the diversity of features and, meanwhile, local linearities guarantee efficiency. Thus, our ParsNets can generalize better to unseen classes and can be deployed flexibly on resource-constrained devices.

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AAAI Conference 2024 Conference Paper

ProCC: Progressive Cross-Primitive Compatibility for Open-World Compositional Zero-Shot Learning

Fushuo Huo
Wenchao Xu
Song Guo
Jingcai Guo
Haozhao Wang
Ziming Liu
Xiaocheng Lu

Open-World Compositional Zero-shot Learning (OW-CZSL) aims to recognize novel compositions of state and object primitives in images with no priors on the compositional space, which induces a tremendously large output space containing all possible state-object compositions. Existing works either learn the joint compositional state-object embedding or predict simple primitives with separate classifiers. However, the former method heavily relies on external word embedding methods, and the latter ignores the interactions of interdependent primitives, respectively. In this paper, we revisit the primitive prediction approach and propose a novel method, termed Progressive Cross-primitive Compatibility (ProCC), to mimic the human learning process for OW-CZSL tasks. Specifically, the cross-primitive compatibility module explicitly learns to model the interactions of state and object features with the trainable memory units, which efficiently acquires cross-primitive visual attention to reason high-feasibility compositions, without the aid of external knowledge. Moreover, to alleviate the invalid cross-primitive interactions, especially for partial-supervision conditions (pCZSL), we design a progressive training paradigm to optimize the primitive classifiers conditioned on pre-trained features in an easy-to-hard manner. Extensive experiments on three widely used benchmark datasets demonstrate that our method outperforms other representative methods on both OW-CZSL and pCZSL settings by large margins.

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ICML Conference 2023 Conference Paper

Anchor Sampling for Federated Learning with Partial Client Participation

Feijie Wu
Song Guo 0001
Zhihao Qu
Shiqi He
Ziming Liu
Jing Gao 0004

Compared with full client participation, partial client participation is a more practical scenario in federated learning, but it may amplify some challenges in federated learning, such as data heterogeneity. The lack of inactive clients’ updates in partial client participation makes it more likely for the model aggregation to deviate from the aggregation based on full client participation. Training with large batches on individual clients is proposed to address data heterogeneity in general, but their effectiveness under partial client participation is not clear. Motivated by these challenges, we propose to develop a novel federated learning framework, referred to as FedAMD, for partial client participation. The core idea is anchor sampling, which separates partial participants into anchor and miner groups. Each client in the anchor group aims at the local bullseye with the gradient computation using a large batch. Guided by the bullseyes, clients in the miner group steer multiple near-optimal local updates using small batches and update the global model. By integrating the results of the two groups, FedAMD is able to accelerate the training process and improve the model performance. Measured by $\epsilon$-approximation and compared to the state-of-the-art methods, FedAMD achieves the convergence by up to $O(1/\epsilon)$ fewer communication rounds under non-convex objectives. Empirical studies on real-world datasets validate the effectiveness of FedAMD and demonstrate the superiority of the proposed algorithm: Not only does it considerably save computation and communication costs, but also the test accuracy significantly improves.

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AAAI Conference 2023 Conference Paper

Graph Knows Unknowns: Reformulate Zero-Shot Learning as Sample-Level Graph Recognition

Jingcai Guo
Song Guo
Qihua Zhou
Ziming Liu
Xiaocheng Lu
Fushuo Huo

Zero-shot learning (ZSL) is an extreme case of transfer learning that aims to recognize samples (e.g., images) of unseen classes relying on a train-set covering only seen classes and a set of auxiliary knowledge (e.g., semantic descriptors). Existing methods usually resort to constructing a visual-to-semantics mapping based on features extracted from each whole sample. However, since the visual and semantic spaces are inherently independent and may exist in different manifolds, these methods may easily suffer from the domain bias problem due to the knowledge transfer from seen to unseen classes. Unlike existing works, this paper investigates the fine-grained ZSL from a novel perspective of sample-level graph. Specifically, we decompose an input into several fine-grained elements and construct a graph structure per sample to measure and utilize element-granularity relations within each sample. Taking advantage of recently developed graph neural networks (GNNs), we formulate the ZSL problem to a graph-to-semantics mapping task, which can better exploit element-semantics correlation and local sub-structural information in samples. Experimental results on the widely used benchmark datasets demonstrate that the proposed method can mitigate the domain bias problem and achieve competitive performance against other representative methods.

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NeurIPS Conference 2023 Conference Paper

Restart Sampling for Improving Generative Processes

Yilun Xu
Mingyang Deng
Xiang Cheng
Yonglong Tian
Ziming Liu
Tommi Jaakkola

Generative processes that involve solving differential equations, such as diffusion models, frequently necessitate balancing speed and quality. ODE-based samplers are fast but plateau in performance while SDE-based samplers deliver higher sample quality at the cost of increased sampling time. We attribute this difference to sampling errors: ODE-samplers involve smaller discretization errors while stochasticity in SDE contracts accumulated errors. Based on these findings, we propose a novel sampling algorithm called \textit{Restart} in order to better balance discretization errors and contraction. The sampling method alternates between adding substantial noise in additional forward steps and strictly following a backward ODE. Empirically, Restart sampler surpasses previous SDE and ODE samplers in both speed and accuracy. Restart not only outperforms the previous best SDE results, but also accelerates the sampling speed by 10-fold / 2-fold on CIFAR-10 / ImageNet $64{\times} 64$. In addition, it attains significantly better sample quality than ODE samplers within comparable sampling times. Moreover, Restart better balances text-image alignment/visual quality versus diversity than previous samplers in the large-scale text-to-image Stable Diffusion model pre-trained on LAION $512{\times} 512$. Code is available at https: //github. com/Newbeeer/diffusion_restart_sampling

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NeurIPS Conference 2023 Conference Paper

The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks

Ziqian Zhong
Ziming Liu
Max Tegmark
Jacob Andreas

Do neural networks, trained on well-understood algorithmic tasks, reliably rediscover known algorithms? Several recent studies, on tasks ranging from group operations to in-context linear regression, have suggested that the answer is yes. Using modular addition as a prototypical problem, we show that algorithm discovery in neural networks is sometimes more complex: small changes to model hyperparameters and initializations can induce discovery of qualitatively different algorithms from a fixed training set, and even learning of multiple different solutions in parallel. In modular addition, we specifically show that models learn a known Clock algorithm, a previously undescribed, less intuitive, but comprehensible procedure we term the Pizza algorithm, and a variety of even more complex procedures. Our results show that even simple learning problems can admit a surprising diversity of solutions, motivating the development of new tools for mechanistically characterizing the behavior of neural networks across the algorithmic phase space.

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NeurIPS Conference 2023 Conference Paper

The Quantization Model of Neural Scaling

Eric Michaud
Ziming Liu
Uzay Girit
Max Tegmark

We propose the Quantization Model of neural scaling laws, explaining both the observed power law dropoff of loss with model and data size, and also the sudden emergence of new capabilities with scale. We derive this model from what we call the Quantization Hypothesis, where network knowledge and skills are "quantized" into discrete chunks (quanta). We show that when quanta are learned in order of decreasing use frequency, then a power law in use frequencies explains observed power law scaling of loss. We validate this prediction on toy datasets, then study how scaling curves decompose for large language models. Using language model gradients, we automatically decompose model behavior into a diverse set of skills (quanta). We tentatively find that the frequency at which these quanta are used in the training distribution roughly follows a power law corresponding with the empirical scaling exponent for language models, a prediction of our theory.

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NeurIPS Conference 2023 Conference Paper

Towards Test-Time Refusals via Concept Negation

Peiran Dong
Song Guo
Junxiao Wang
Bingjie Wang
Jiewei Zhang
Ziming Liu

Generative models produce unbounded outputs, necessitating the use of refusal techniques to confine their output space. Employing generative refusals is crucial in upholding the ethical and copyright integrity of synthesized content, particularly when working with widely adopted diffusion models. "Concept negation'' presents a promising paradigm to achieve generative refusals, as it effectively defines and governs the model's output space based on concepts, utilizing natural language interfaces that are readily comprehensible to humans. However, despite the valuable contributions of prior research to the field of concept negation, it still suffers from significant limitations. The existing concept negation methods, which operate based on the composition of score or noise predictions from the diffusion process, are limited to independent concepts (e. g. , ``a blonde girl`` without ``glasses``) and fail to consider the interconnected nature of concepts in reality (e. g. , ``Mickey mouse eats ice cream`` without ``Disney characters``). Keeping the limitations in mind, we propose a novel framework, called $ProtoRe$, to improve the flexibility of concept negation via test-time negative concept identification along with purification in the feature space. $ProtoRe$ works by incorporating CLIP's language-contrastive knowledge to identify the prototype of negative concepts, extract the negative features from outputs using the prototype as a prompt, and further refine the attention maps by retrieving negative features. Our evaluation on multiple benchmarks shows that $ProtoRe$ outperforms state-of-the-art methods under various settings, in terms of the effectiveness of purification and the fidelity of generative images.

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NeurIPS Conference 2022 Conference Paper

Poisson Flow Generative Models

Yilun Xu
Ziming Liu
Max Tegmark
Tommi Jaakkola

We propose a new "Poisson flow" generative model~(PFGM) that maps a uniform distribution on a high-dimensional hemisphere into any data distribution. We interpret the data points as electrical charges on the $z=0$ hyperplane in a space augmented with an additional dimension $z$, generating a high-dimensional electric field (the gradient of the solution to Poisson equation). We prove that if these charges flow upward along electric field lines, their initial distribution in the $z=0$ plane transforms into a distribution on the hemisphere of radius $r$ that becomes uniform in the $r \to\infty$ limit. To learn the bijective transformation, we estimate the normalized field in the augmented space. For sampling, we devise a backward ODE that is anchored by the physically meaningful additional dimension: the samples hit the (unaugmented) data manifold when the $z$ reaches zero. Experimentally, PFGM achieves current state-of-the-art performance among the normalizing flow models on CIFAR-10, with an Inception score of $9. 68$ and a FID score of $2. 35$. It also performs on par with the state-of-the-art SDE approaches while offering $10\times $ to $20 \times$ acceleration on image generation tasks. Additionally, PFGM appears more tolerant of estimation errors on a weaker network architecture and robust to the step size in the Euler method. The code is available at https: //github. com/Newbeeer/poisson_flow.

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NeurIPS Conference 2022 Conference Paper

Towards Understanding Grokking: An Effective Theory of Representation Learning

Ziming Liu
Ouail Kitouni
Niklas S Nolte
Eric Michaud
Max Tegmark
Mike Williams

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations, whose training dynamics and dependence on training set size can be predicted by our effective theory (in a toy setting). We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. Compared to the comprehension phase, the grokking phase stays closer to the memorization phase, leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e. g. , effective theories and phase diagrams, for understanding deep learning.

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