Peng Wang
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Peng Wang |
About Me
I am currently a postdoc research fellow advised by Professors Laura Balzano and Qing Qu at University of Michigan. Before that, I got my Ph.D. degree in Systems Engineering and Engineering Management advised by Professor Anthony Man-Cho So at The Chinese University of Hong Kong.
Research Interests
Broadly speaking, my research interest lies in the intersects of optimization, machine learning, and data science. Currently, I am devoted to understanding mathematical foundations of deep learning models, including supervised learning models, diffusion models, and large language models. I mainly study how low-complexity structures (e.g., low-rankness, sparsity, over-parameterization) in practical problems lead to favorable optimization properties and use them to mitigate the challenges caused by worst-case scenarios, enable efficient optimization, and improve our understanding of learning phenomena..
Feel free to email me if you are interested in my research. Remote collaboration is also welcome!
What's New
[May 2025] Our paper on understanding the mechenism of transformers has been accepted by ICML 2025!
[Apr 2025] Our recent works on studying the generalization of diffusion models appears on SIAM News Blog!
[Mar 2025] A tutorial paper on understanding the role of low-rank structures in the training and adaptation of deep learning models is posted!
[Mar 2025] I will attend the Conference on Parsimony and Learning at Stanford University from March 24-27!
[Feb 2025] One paper on the local loss landscape of deep linear networks is posted!
[Jan 2025] One paper on the representation capabilities of diffusion models is posted!
[Jan 2025] One paper is accepted by INFORMS Journal on Computing!
[Jan 2025] One paper on the separation capabilities of shallow nonlinear networks is posted!
[Jan 2025] I will give a presentaion in 1W-MINDS Seminar online at 5PM (Beijing Time) on Jan 9, 2025!
[Jan 2025] I will give a presenation in IMS Young Mathematical Scientists Forum at National University of Singapore!
[Dec 2024] One paper on understanding modality gap in multimodal learning is posted!
[Dec 2024] I will serve as an area chair of CAPL 2025!
[Oct 2024] I will chair a session and give a lecture presentation on diffusion models in Asilomar 2024 at Pacific Grove, CA!
[Oct 2024] Two paper on diffusion models get accepted by NeurIPS Workshop on Mathematics of Modern Machine Learning!
[Sep 2024] I will give a talk on diffusion models in ECE Communications and Signal Processing Seminars at the University of Michigan!
[May 2024] Five papers [paper1, paper2, paper3, paper4, paper5] are accepted by ICML 2024!
Preprints (‘‘*’’ denotes equal contribution, ‘‘\(\dagger\)’’ denotes corresponding author.)
(\(\alpha\)-\(\beta\) order) Laura Balzano\(^\dagger\), Tianjiao Ding\(^\dagger\), Benjamin D. Haeffele, Soo Min Kwon, Qing Qu, Peng Wang\(^\dagger\), Zhangyang Wang, Can Yaras. An Overview of Low-Rank Structures in the Training and Adaptation of Large Models. Under review in IEEE Signal Processing Magazine, 2025. [paper]
(\(\alpha\)-\(\beta\) order) Po Chen, Rujun Jiang, Peng Wang\(^\dagger\). Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks, 2025. [paper]
Peng Wang*, Xiao Li*, Can Yaras, Wei Hu, Zhihui Zhu, Laura Balzano, Wei Hu, Qing Qu. Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination. Minor revision in Journal of Machine Learning Research, 2024. [paper]
Xiao Li*, Zekai Zhang*, Xiang Li, Siyi Chen, Zhihui Zhu, Peng Wang, Qing Qu. Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling, 2025. Under review in NeurIPS 2025. [paper]
Alec S Xu, Can Yaras, Peng Wang, Qing Qu. Understanding How Nonlinear Layers Create Linearly Separable Features for Low-Dimensional Data, 2025. Under review in SIAM Journal on Mathematics of Data Science. [paper]
Peng Wang*, Huijie Zhang*, Zekai Zhang, Siyi Chen, Yi Ma, Qing Qu. Diffusion Models Learn Low-Dimensional Distributions via Subspace Clustering, 2024. [paper]
Accepted by NeurIPS 2024 M3L Workshop & ICLR 2025 DeLTa Workshop.
Can Yaras*, Peng Wang*, Wei Hu, Zhihui Zhu, Laura Balzano, Qing Qu. The Law of Parsimony in Gradient Descent for Learning Deep Linear Networks, 2023. To be submitted. [paper]
Taoli Zheng, Peng Wang, Anthony Man-Cho So. A Linearly Convergent Algorithm for Rotationally Invariant L1-Norm Principal Component Analysis, 2022. [paper]
Journal Papers
Peng Wang, Rujun Jiang, Qingyuan Kong, Laura Balzano. A Proximal Difference-of-Convex Algorithm for Sample Average Approximation of Chance Constrained Programming. Accepted for publication in INFORMS Journal on Computing, 2025. [paper, code]
Peng Wang, Huikang Liu, Anthony Man-Cho So. Linear Convergence of Proximal Alternating Minimization Method with Extrapolation for L1-Norm Principal Component Analysis. SIAM Journal on Optimization (2023) 33(2):684-712. [paper]
Peng Wang, Zirui Zhou, Anthony Man-Cho So. Non-Convex Exact Community Recovery in Stochastic Block Model. Mathematical Programming, Series A (2022) 195(1-2):793-829. [paper]
Conference Papers
Peng Wang, Yifu Lu, Yaodong Yu, Druv Pai, Qing Qu, Yi Ma. Attention-Only Transformers via Unrolled Subspace Denoising. Accepted by ICML 2025.
Can Yaras*, Siyi Chen*, Peng Wang, Qing Qu. Explaining and Mitigating the Modality Gap in Contrastive Multimodal Learning. CAPL 2025. [paper]
Siyi Chen*, Huijie Zhang*, Minzhe Guo, Yifu Lu, Peng Wang, Qing Qu. Exploring Low-Dimensional Subspaces in Diffusion Models for Controllable Image Editing. NeurIPS 2024. [paper]
Peng Wang, Huikang Liu, Druv Pai, Yaodong Yu, Zhihui Zhu, Qing Qu, Yi Ma. A Global Geometric Analysis of Maximal Coding Rate Reduction. ICML 2024. [paper]
Can Yaras, Peng Wang, Laura Balzano, Qing Qu. Compressible Dynamics in Deep Overparameterized Low-Rank Learning & Adaptation. ICML 2024 (Oral, acceptance rate: 1.52%). [paper]
Huikang Liu*, Peng Wang*, Longxiu Huang, Qing Qu, Laura Balzano. Matrix Completion with ReLU Sampling. ICML 2024. [paper]
Jiachen Jiang, Jinxin Zhou, Peng Wang, Qing Qu, Dustin Mixon, Chong You, Zhihui Zhu. Generalized Neural Collapse for a Large Number of Classes. ICML 2024. [paper]
Huijie Zhang, Jinfan Zhou, Yifu Lu, Minzhe Guo, Peng Wang, Liyue Shen, and Qing Qu. The Emergence of Reproducibility and Consistency in Diffusion Models. ICML 2024. [paper]
Can Yaras*, Peng Wang*, Wei Hu, Zhihui Zhu, Laura Balzano, Qing Qu. Invariant Low-Dimensional Subspaces in Gradient Descent for Learning Deep Matrix Factorizations. NeurIPS M3L Workshop 2023. [paper]
Jinxin Wang, Yuen-Man Pun, Xiaolu Wang, Peng Wang, Anthony Man-Cho So. Projected Tensor Power Method for Hypergraph Community Recovery. ICML 2023. [paper]
Peng Wang*, Huikang Liu*, Can Yaras*, Laura Balzano, Qing Qu. Linear Convergence Analysis of Neural Collapse with Unconstrained Features. NeurIPS Workshop on Optimization for Machine Learning, NeurIPS OPT Workshop 2022. [paper]
Can Yaras*, Peng Wang*, Zhihui Zhu, Laura Balzano, Qing Qu. Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifold. NeurIPS 2022. [paper]
Peng Wang, Huikang Liu, Anthony Man-Cho So, Laura Balzano. Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering. ICML 2022. [paper]
Xiaolu Wang, Peng Wang, Anthony Man-Cho So. Exact Community Recovery over Signed Graphs. AISTATS 2022. [paper]
Peng Wang, Huikang Liu, Zirui Zhou, Anthony Man-Cho So. Optimal Non-Convex Exact Recovery in Stochastic Block Model via Projected Power Method. ICML 2021. [paper]
Peng Wang*, Zirui Zhou*, Anthony Man-Cho So. A Nearly-Linear Time Algorithm for Exact Community Recovery in Stochastic Block Model. ICML 2020. [paper]
Peng Wang, Huikang Liu, Anthony Man-Cho So. Globally Convergent Accelerated Proximal Alternating Maximization Method for L1-Principal Component Analysis. ICASSP 2019 (IEEE SPS Student Travel Award). [paper]
Huikang Liu, Peng Wang, Anthony Man-Cho So. Fast First-Order Methods for the Massive Robust Multicast Beamforming Problem with Interference Temperature Constraints. ICASSP 2019. [paper]