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Tailin Wu

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20 papers

2 author rows

ICLR Conference 2025 Conference Paper

CL-DiffPhyCon: Closed-loop Diffusion Control of Complex Physical Systems

Long Wei
Haodong Feng
Yuchen Yang
Ruiqi Feng
Peiyan Hu
Xiang Zheng
Tao Zhang
Dixia Fan

The control problems of complex physical systems have broad applications in science and engineering. Previous studies have shown that generative control methods based on diffusion models offer significant advantages for solving these problems. However, existing generative control approaches face challenges in both performance and efficiency when extended to the closed-loop setting, which is essential for effective control. In this paper, we propose an efficient Closed-Loop Diffusion method for Physical systems Control (CL-DiffPhyCon). By employing an asynchronous denoising framework for different physical time steps, CL-DiffPhyCon generates control signals conditioned on real-time feedback from the system with significantly reduced computational cost during sampling. Additionally, the control process could be further accelerated by incorporating fast sampling techniques, such as DDIM. We evaluate CL-DiffPhyCon on two tasks: 1D Burgers' equation control and 2D incompressible fluid control. The results demonstrate that CL-DiffPhyCon achieves superior control performance with significant improvements in sampling efficiency. The code can be found at https://github.com/AI4Science-WestlakeU/CL_DiffPhyCon.

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ICLR Conference 2025 Conference Paper

EVA: Geometric Inverse Design for Fast Protein Motif-Scaffolding with Coupled Flow

Yufei Huang 0002
Yunshu Liu
Lirong Wu
Haitao Lin
Cheng Tan 0012
Odin Zhang
Zhangyang Gao
Siyuan Li 0002

Motif-scaffolding is a fundamental component of protein design, which aims to construct the scaffold structure that stabilizes motifs conferring desired functions. Recent advances in generative models are promising for designing scaffolds, with two main approaches: training-based and sampling-based methods. Training-based methods are resource-heavy and slow, while training-free sampling-based methods are flexible but require numerous sampling steps and costly, unstable guidance. To speed up and improve sampling-based methods, we analyzed failure cases and found that errors stem from the trade-off between generation and guidance. Thus we proposed to exploit the spatial context and adjust the generative direction to be consistent with guidance to overcome this trade-off. Motivated by this, we formulate motif-scaffolding as a Geometric Inverse Design task inspired by the image inverse problem, and present Evolution-ViA-reconstruction (EVA), a novel sampling-based coupled flow framework on geometric manifolds, which starts with a pretrained flow-based generative model. EVA uses motif-coupled priors to leverage spatial contexts, guiding the generative process along a straighter probability path, with generative directions aligned with guidance in the early sampling steps. EVA is 70× faster than SOTA model RFDiffusion with competitive and even better performance on benchmark tests. Further experiments on real-world cases including vaccine design, multi-motif scaffolding and motif optimal placement searching demonstrate EVA's superior efficiency and effectiveness.

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ICML Conference 2025 Conference Paper

From Uncertain to Safe: Conformal Adaptation of Diffusion Models for Safe PDE Control

Peiyan Hu
Xiaowei Qian 0001
Wenhao Deng 0001
Rui Wang 0017
Haodong Feng
Ruiqi Feng
Tao Zhang 0033
Long Wei

The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this limitation, we propose Safe Diffusion Models for PDE Control (SafeDiffCon), which introduce the uncertainty quantile as model uncertainty quantification to achieve optimal control under safety constraints through both post-training and inference phases. Firstly, our approach post-trains a pre-trained diffusion model to generate control sequences that better satisfy safety constraints while achieving improved control objectives via a reweighted diffusion loss, which incorporates the uncertainty quantile estimated using conformal prediction. Secondly, during inference, the diffusion model dynamically adjusts both its generation process and parameters through iterative guidance and fine-tuning, conditioned on control targets while simultaneously integrating the estimated uncertainty quantile. We evaluate SafeDiffCon on three control tasks: 1D Burgers’ equation, 2D incompressible fluid, and controlled nuclear fusion problem. Results demonstrate that SafeDiffCon is the only method that satisfies all safety constraints, whereas other classical and deep learning baselines fail. Furthermore, while adhering to safety constraints, SafeDiffCon achieves the best control performance. The code can be found at https: //github. com/AI4Science-WestlakeU/safediffcon.

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ICML Conference 2025 Conference Paper

M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation

Tao Zhang 0102
Zhenhai Liu
Feipeng Qi
Yongjun Jiao
Tailin Wu

Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling–where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at github. com/AI4Science-WestlakeU/M2PDE.

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ICML Conference 2025 Conference Paper

On the Guidance of Flow Matching

Ruiqi Feng
Chenglei Yu
Wenhao Deng 0001
Peiyan Hu
Tailin Wu

Flow matching has shown state-of-the-art performance in various generative tasks, ranging from image generation to decision-making, where generation under energy guidance (abbreviated as guidance in the following) is pivotal. However, the guidance of flow matching is more general than and thus substantially different from that of its predecessor, diffusion models. Therefore, the challenge in guidance for general flow matching remains largely underexplored. In this paper, we propose the first framework of general guidance for flow matching. From this framework, we derive a family of guidance techniques that can be applied to general flow matching. These include a new training-free asymptotically exact guidance, novel training losses for training-based guidance, and two classes of approximate guidance that cover classical gradient guidance methods as special cases. We theoretically investigate these different methods to give a practical guideline for choosing suitable methods in different scenarios. Experiments on synthetic datasets, image inverse problems, and offline reinforcement learning demonstrate the effectiveness of our proposed guidance methods and verify the correctness of our flow matching guidance framework. Code to reproduce the experiments can be found at https: //github. com/AI4Science-WestlakeU/flow_guidance.

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ICLR Conference 2025 Conference Paper

Re-Evaluating the Impact of Unseen-Class Unlabeled Data on Semi-Supervised Learning Model

Rundong He
Yicong Dong
Lanzhe Guo
Yilong Yin
Tailin Wu

Semi-supervised learning (SSL) effectively leverages unlabeled data and has been proven successful across various fields. Current safe SSL methods believe that unseen classes in unlabeled data harm the performance of SSL models. However, previous methods for assessing the impact of unseen classes on SSL model performance are flawed. They fix the size of the unlabeled dataset and adjust the proportion of unseen classes within the unlabeled data to assess the impact. This process contravenes the principle of controlling variables. Adjusting the proportion of unseen classes in unlabeled data alters the proportion of seen classes, meaning the decreased classification performance of seen classes may not be due to an increase in unseen class samples in the unlabeled data, but rather a decrease in seen class samples. Thus, the prior flawed assessment standard that "unseen classes in unlabeled data can damage SSL model performance" may not always hold true. This paper strictly adheres to the principle of controlling variables, maintaining the proportion of seen classes in unlabeled data while only changing the unseen classes across five critical dimensions, to investigate their impact on SSL models from global robustness and local robustness. Experiments demonstrate that unseen classes in unlabeled data do not necessarily impair the performance of SSL models; in fact, under certain conditions, unseen classes may even enhance them.

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AAAI Conference 2025 Conference Paper

Relation-Aware Equivariant Graph Networks for Epitope-Unknown Antibody Design and Specificity Optimization

Lirong Wu
Haitao Lin
Yufei Huang
Zhangyang Gao
Cheng Tan
Yunfan Liu
Tailin Wu
Stan Z. Li

Antibodies are Y-shaped proteins that protect the host by binding to specific antigens, and their binding is mainly determined by the Complementary Determining Regions (CDRs) in the antibody. Despite the great progress made in CDR design, existing computational methods still encounter several challenges: 1) poor capability of modeling complex CDRs with long sequences due to insufficient contextual information; 2) conditioned on pre-given antigenic epitopes and their static interaction with the target antibody; 3) neglect of specificity during antibody optimization leads to non-specific antibodies. In this paper, we take into account a variety of node features, edge features, and edge relations to include more contextual and geometric information. We propose a novel Relation-Aware Antibody Design (RAAD) framework, which dynamically models antigen-antibody interactions for co-designing the sequences and structures of antigen-specific CDRs. Furthermore, we propose a new evaluation metric to better measure antibody specificity and develop a contrasting specificity-enhancing constraint to optimize the specificity of antibodies. Extensive experiments have demonstrated the superior capability of RAAD in terms of antibody modeling, generation, and optimization across different CDR types, sequence lengths, pre-training strategies, and input contexts.

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ICLR Conference 2025 Conference Paper

Wavelet Diffusion Neural Operator

Peiyan Hu
Rui Wang 0017
Xiang Zheng
Tao Zhang 0033
Haodong Feng
Ruiqi Feng
Long Wei
Yue Wang 0017

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 78% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

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ICLR Conference 2024 Conference Paper

BENO: Boundary-embedded Neural Operators for Elliptic PDEs

Haixin Wang 0003
Jiaxin Li
Anubhav Dwivedi
Kentaro Hara
Tailin Wu

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically neglect complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model and strong baselines extensively in elliptic PDEs with complex boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96%.

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ICLR Conference 2024 Conference Paper

Compositional Generative Inverse Design

Tailin Wu
Takashi Maruyama
Long Wei
Tao Zhang 0102
Yilun Du
Gianluca Iaccarino
Jure Leskovec

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.

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NeurIPS Conference 2024 Conference Paper

DiffPhyCon: A Generative Approach to Control Complex Physical Systems

Long Wei
Peiyan Hu
Ruiqi Feng
Haodong Feng
Yixuan Du
Tao Zhang
Rui Wang
Yue Wang

Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs. On the other hand, recent deep learning and reinforcement learning-based approaches often struggle to optimize long-term control sequences under the constraints of system dynamics. In this work, we introduce Diffusion Physical systems Control (DiffPhyCon), a new class of method to address the physical systems control problem. DiffPhyCon excels by simultaneously minimizing both the learned generative energy function and the predefined control objectives across the entire trajectory and control sequence. Thus, it can explore globally and plan near-optimal control sequences. Moreover, we enhance DiffPhyCon with prior reweighting, enabling the discovery of control sequences that significantly deviate from the training distribution. We test our method on three tasks: 1D Burgers' equation, 2D jellyfish movement control, and 2D high-dimensional smoke control, where our generated jellyfish dataset is released as a benchmark for complex physical system control research. Our method outperforms widely applied classical approaches and state-of-the-art deep learning and reinforcement learning methods. Notably, DiffPhyCon unveils an intriguing fast-close-slow-open pattern observed in the jellyfish, aligning with established findings in the field of fluid dynamics. The project website, jellyfish dataset, and code can be found at https: //github. com/AI4Science-WestlakeU/diffphycon.

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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.

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ICLR Conference 2023 Conference Paper

Learning Controllable Adaptive Simulation for Multi-resolution Physics

Tailin Wu
Takashi Maruyama
Qingqing Zhao
Gordon Wetzstein
Jure Leskovec

Simulating the time evolution of physical systems is pivotal in many scientific and engineering problems. An open challenge in simulating such systems is their multi-resolution dynamics: a small fraction of the system is extremely dynamic, and requires very fine-grained resolution, while a majority of the system is changing slowly and can be modeled by coarser spatial scales. Typical learning-based surrogate models use a uniform spatial scale, which needs to resolve to the finest required scale and can waste a huge compute to achieve required accuracy. In this work, we introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model that jointly learns the evolution model and optimizes appropriate spatial resolutions that devote more compute to the highly dynamic regions. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We introduce learning techniques that optimizes LAMP with weighted sum of error and computational cost as objective, allowing LAMP to adapt to varying relative importance of error vs. computation tradeoff at inference time. We evaluate our method in a 1D benchmark of nonlinear PDEs and a challenging 2D mesh-based simulation. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error: it achieves an average of 33.7% error reduction for 1D nonlinear PDEs, and outperforms MeshGraphNets + classical Adaptive Mesh Refinement (AMR) in 2D mesh-based simulations. Project website with data and code can be found at: http://snap.stanford.edu/lamp.

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NeurIPS Conference 2022 Conference Paper

Learning to Accelerate Partial Differential Equations via Latent Global Evolution

Tailin Wu
Takashi Maruyama
Jure Leskovec

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems. However, both classical solvers and recent deep learning-based surrogate models are typically extremely computationally intensive, because of their local evolution: they need to update the state of each discretized cell at each time step during inference. Here we develop Latent Evolution of PDEs (LE-PDE), a simple, fast and scalable method to accelerate the simulation and inverse optimization of PDEs. LE-PDE learns a compact, global representation of the system and efficiently evolves it fully in the latent space with learned latent evolution models. LE-PDE achieves speedup by having a much smaller latent dimension to update during long rollout as compared to updating in the input space. We introduce new learning objectives to effectively learn such latent dynamics to ensure long-term stability. We further introduce techniques for speeding-up inverse optimization of boundary conditions for PDEs via backpropagation through time in latent space, and an annealing technique to address the non-differentiability and sparse interaction of boundary conditions. We test our method in a 1D benchmark of nonlinear PDEs, 2D Navier-Stokes flows into turbulent phase and an inverse optimization of boundary conditions in 2D Navier-Stokes flow. Compared to state-of-the-art deep learning-based surrogate models and other strong baselines, we demonstrate up to 128x reduction in the dimensions to update, and up to 15x improvement in speed, while achieving competitive accuracy.

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NeurIPS Conference 2022 Conference Paper

ZeroC: A Neuro-Symbolic Model for Zero-shot Concept Recognition and Acquisition at Inference Time

Tailin Wu
Megan Tjandrasuwita
Zhengxuan Wu
Xuelin Yang
Kevin Liu
Rok Sosic
Jure Leskovec

Humans have the remarkable ability to recognize and acquire novel visual concepts in a zero-shot manner. Given a high-level, symbolic description of a novel concept in terms of previously learned visual concepts and their relations, humans can recognize novel concepts without seeing any examples. Moreover, they can acquire new concepts by parsing and communicating symbolic structures using learned visual concepts and relations. Endowing these capabilities in machines is pivotal in improving their generalization capability at inference time. In this work, we introduce Zero-shot Concept Recognition and Acquisition (ZeroC), a neuro-symbolic architecture that can recognize and acquire novel concepts in a zero-shot way. ZeroC represents concepts as graphs of constituent concept models (as nodes) and their relations (as edges). To allow inference time composition, we employ energy-based models (EBMs) to model concepts and relations. We design ZeroC architecture so that it allows a one-to-one mapping between a symbolic graph structure of a concept and its corresponding EBM, which for the first time, allows acquiring new concepts, communicating its graph structure, and applying it to classification and detection tasks (even across domains) at inference time. We introduce algorithms for learning and inference with ZeroC. We evaluate ZeroC on a challenging grid-world dataset which is designed to probe zero-shot concept recognition and acquisition, and demonstrate its capability.

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NeurIPS Conference 2020 Conference Paper

AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity

Silviu-Marian Udrescu
Andrew Tan
Jiahai Feng
Orisvaldo Neto
Tailin Wu
Max Tegmark

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically being orders of magnitude more robust toward noise and bad data, and also by discovering many formulas that stumped previous methods. We develop a method for discovering generalized symmetries (arbitrary modularity in the computational graph of a formula) from gradient properties of a neural network fit. We use normalizing flows to generalize our symbolic regression method to probability distributions from which we only have samples, and employ statistical hypothesis testing to accelerate robust brute-force search.

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NeurIPS Conference 2020 Conference Paper

Graph Information Bottleneck

Tailin Wu
Hongyu Ren
Pan Li
Jure Leskovec

Representation learning of graph-structured data is challenging because both graph structure and node features carry important information. Graph Neural Networks (GNNs) provide an expressive way to fuse information from network structure and node features. However, GNNs are prone to adversarial attacks. Here we introduce Graph Information Bottleneck (GIB), an information-theoretic principle that optimally balances expressiveness and robustness of the learned representation of graph-structured data. Inheriting from the general Information Bottleneck (IB), GIB aims to learn the minimal sufficient representation for a given task by maximizing the mutual information between the representation and the target, and simultaneously constraining the mutual information between the representation and the input data. Different from the general IB, GIB regularizes the structural as well as the feature information. We design two sampling algorithms for structural regularization and instantiate the GIB principle with two new models: GIB-Cat and GIB-Bern, and demonstrate the benefits by evaluating the resilience to adversarial attacks. We show that our proposed models are more robust than state-of-the-art graph defense models. GIB-based models empirically achieve up to 31% improvement with adversarial perturbation of the graph structure as well as node features.

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ICLR Conference 2020 Conference Paper

Phase Transitions for the Information Bottleneck in Representation Learning

Tailin Wu
Ian S. Fischer

In the Information Bottleneck (IB), when tuning the relative strength between compression and prediction terms, how do the two terms behave, and what's their relationship with the dataset and the learned representation? In this paper, we set out to answer these questions by studying multiple phase transitions in the IB objective: IB_β[p(z|x)] = I(X; Z) − βI(Y; Z) defined on the encoding distribution p(z|x) for input X, target Y and representation Z, where sudden jumps of dI(Y; Z)/dβ and prediction accuracy are observed with increasing β. We introduce a definition for IB phase transitions as a qualitative change of the IB loss landscape, and show that the transitions correspond to the onset of learning new classes. Using second-order calculus of variations, we derive a formula that provides a practical condition for IB phase transitions, and draw its connection with the Fisher information matrix for parameterized models. We provide two perspectives to understand the formula, revealing that each IB phase transition is finding a component of maximum (nonlinear) correlation between X and Y orthogonal to the learned representation, in close analogy with canonical-correlation analysis (CCA) in linear settings. Based on the theory, we present an algorithm for discovering phase transition points. Finally, we verify that our theory and algorithm accurately predict phase transitions in categorical datasets, predict the onset of learning new classes and class difficulty in MNIST, and predict prominent phase transitions in CIFAR10.

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UAI Conference 2019 Conference Paper

Learnability for the Information Bottleneck

Tailin Wu
Ian S. Fischer
Isaac L. Chuang
Max Tegmark

The Information Bottleneck (IB) method (Tishby et al. (2000)) provides an insightful and principled approach for balancing compression and prediction for representation learning. The IB objective I (X; Z ) − βI(Y; Z) employs a Lagrange multiplier β to tune this trade-off. However, in practice, not only is β chosen empirically without theoretical guidance, there is also a lack of theoretical understanding between β, learnability, the intrinsic nature of the dataset and model capacity. In this paper, we show that if β is improperly chosen, learning cannot happen – the trivial representation P(Z|X) = P(Z) becomes the global minimum of the IB objective. We show how this can be avoided, by identifying a sharp phase transition between the unlearnable and the learnable which arises as β is varied. This phase transition defines the concept of IB-Learnability. We prove several sufficient conditions for IB-Learnability, which provides theoretical guidance for choosing a good β. We further show that IB-learnability is determined by the largest confident, typical, and imbalanced subset of the examples (the conspicuous subset), and discuss its relation with model capacity. We give practical algorithms to estimate the minimum β for a given dataset. We also empirically demonstrate our theoretical conditions with analyses of synthetic datasets, MNIST, and CIFAR10.

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UAI Conference 2017 Conference Paper

Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels

Curtis G. Northcutt
Tailin Wu
Isaac L. Chuang

P̃ Ñ learning is the problem of binary classification when training examples may be mislabeled (flipped) uniformly with noise rate ρ1 for positive examples and ρ0 for negative examples. We propose Rank Pruning (RP) to solve P̃ Ñ learning and the open problem of estimating the noise rates. Unlike prior solutions, RP is efficient and general, requiring O(T ) for any unrestricted choice of probabilistic classifier with T fitting time. We prove RP achieves consistent noise estimation and equivalent expected risk as learning with uncorrupted labels in ideal conditions, and derive closed-form solutions when conditions are non-ideal. RP achieves state-of-the-art noise estimation and F1, error, and AUC-PR for both MNIST and CIFAR datasets, regardless of the amount of noise. To highlight, RP with a CNN classifier can predict if an MNIST digit is a one or not with only 0. 25% error, and 0. 46% error across all digits, even when 50% of positive examples are mislabeled and 50% of observed positive labels are mislabeled negative examples.

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