Lei Wu (吴磊)

Assistant Professor School of Mathematical Sciences Center for Machine Learning Research Peking University Office: 静园6院 205 Email: leiwu (at) math (dot) pku (dot) edu (dot) cn Google Scholar     Github      CV

About Me

I am currently an Assistant Professor in the School of Mathematical Sciences and Center for Machine Learning Research at Peking University.

Previously, I was a postdoc in PACM at Princeton University and in the Wharton Statistics and Data Science Department at the University of Pennsylvania. I completed my Ph.D. in computational mathematics at Peking University in 2018, advised by Prof. Weinan E. I received my B.S. degree in mathematics from Nankai University in 2012.

My research aims to understand the mechanisms behind the success of deep learning, with a particular focus on:

• The approximation and representation power of neural networks

• The dynamical behavior of popular optimization algorithms such as SGD and Adam

• Emergent phenomena in the training of large language models (LLMs)

Recruiting

We are actively seeking self-motivated postdocs, PhD students, and undergraduate interns to join our team. If you are interested in collaborating with me, please email me your CV, transcript, and a brief description of your research interests.

Research Highlights

(See also: Full publication list)

• Understanding scaling laws.

  • Functional scaling laws (FSL) for kernel regression and LLM pre-training (NeurIPS 2025, Spotlight)

  • Optimal batch-size scheduling under FSL (ICLR 2026)

  • Optimal learning-rate scheduling under FSL (arXiv 2026)

• LLM pre-training.

  • Accelerate training via the sharpness disparity in transformer

• Implicit regularization, dynamical stability, and flatness bias.
  

  • A dynamical stability perspective of implicit regularization (NeurIPS 2018) (Discover the edge of stability (EoS) phenomenon; see Table 2)

  • Alignment property of SGD noise & flat minima selection (NeurIPS 2022)

  • Stable and flat minima provably generalize well (ICML 2023)

  • Enhancing implicit regularization for generalization & convergence (NeurIPS 2024)

• Approximation theory of machine learning.
  

  • A priori population-risk estimates for two-layer networks (CMS 2019)

  • Barron space and flow-induced function spaces (Constructive Approximation 2021)

  • Inductive biases in deep convolutional networks (NeurIPS 2023)

  • Sobolev-norm convergence of kernel ridge regression (arXiv 2024)

  • Duality framework for random features and two-layer networks (AoS 2025)

Recent News

• 2026-02: Constant-depth network with smooth activations released on arXiv.

  • Establishes that smooth activations (e.g., GELU, SiLU) enable smoothness adaptivity in constant-depth neural networks, achieving optimal approximation and statistical rates.

• 2026-02: Optimal learning-rate schedules under FSL released on arXiv.

  • proves that the optimal learning-rate schedule follows a warmup–stable–decay (WSD) structure.

• 2026-02: Fast catch-up, late switching accepted to ICLR 2026.

  • reveals a fast catch-up effect in batch-size scheduling, which holds across linear regression and LLM pre-training.

• 2025-09: Functional Scaling Laws accepted to NeurIPS 2025 (Spotlight).

  • introduces the FSL framework, characterizing the entire loss trajectory rather than only the final-step scaling behavior, from linear regression to LLM pre-training.