My name is Binghui Li. I am a fourth-year Ph.D. student in The Center for Machine Learning Research (CMLR), Peking University, where I am extremely fortunate to be advised by Prof. Liwei Wang and Prof. Lei Wu. I am also pleased to have worked closely with Prof. Yuanzhi Li, Prof. Ruoyu Sun, Prof. Jian Li and Prof. Kaifeng Lyu. Before joining CMLR, I received my Bachelor’s degree in Intelligence Science and Technology (Honor Track) from Turing Class, Peking University. My research area is machine learning, with special interests in understanding deep learning and algorithms inspired by theoretical insights.

I currently focus on the theoretical foundations of large language model (LLM) pre-training, particularly scaling laws and optimization dynamics. My recent work explores optimizers [14, 17, 18], learning-rate schedules [10, 15], batch-size schedules [12], and data reuse [11]. In particular, I lead a line of research on functional scaling laws (FSL) [10, 12, 15, 17], developing a framework to characterize learning dynamics and understand how optimization choices shape scaling behavior. Through these efforts, I aim to provide principled guidance for efficient LLM pre-training.

If you are interested, please feel free to contact me (libinghui@pku.edu.cn or WeChat)!

Education

• Ph.D. in Data Science (Computer Science and Technology), Peking University, 2023-2028 (Expected).

• B.S. in Intelligence Science and Technology (Summa Cum Laude), Peking University, 2019-2023.
  Overall GPA: 3.82 / 4.00, Average Score: 90.2 / 100, Rank: 2 / 81

Research Experience

• (Research Intern) ByteDance Seed, Edge Group, 2026.2-now
  Research on scaling laws and optimization dynamics for large language model pre-training.

Publications & Preprints

* indicates equal contribution, † means project lead.

• [18] (Preprint) When and How Does Muon Precondition? The Role of Structured Gradient Noise
  Xiaoran Chen*, Binghui Li* † , Liwei Wang, Pinyan Lu

• [17] (NeurIPS 2026, Spotlight) How Can SignSGD Outperform SGD? A Functional Scaling Law Perspective
  Zilin Wang*, Binghui Li*, Jia-Nan Wang*, Lean Wang*, Jinbo Wang*, Lei Wu

• [16] (Preprint) Negligible in Size, Significant in Effect: On Scale Vectors in Large Language Models
  Mingze Wang, Shuchen Zhu, Yuxin Fang, Binghui Li, Kai Shen, Shu Zhong

• [15] (COLT 2026) Optimal Learning-Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay
  Binghui Li*, Zilin Wang*, Fengling Chen, Shiyang Zhao, Ruiheng Zheng, Lei Wu

• [14] (ICML 2026) Muon in Associative Memory Learning: Training Dynamics and Scaling Laws
  Binghui Li* † , Kaifei Wang*, Han Zhong, Pinyan Lu, Liwei Wang

• [13] (ICLR 2026 Sci4DL Workshop) Scaling-Law Analysis of SignSGD: From Feature-Space Linear Regression to LLM Pre-training
  (α-β order) Binghui Li †, Jianan Wang, Jinbo Wang, Lean Wang, Zilin Wang, Lei Wu

• [12] (ICLR 2026) Fast Catch-Up, Late Switching: Optimal Batch Size Scheduling via Functional Scaling Laws
  Jinbo Wang*, Binghui Li*, Zhanpeng Zhou, Mingze Wang, Yuxuan Sun, Jiaqi Zhang, Xunliang Cai, Lei Wu

• [11] (ICLR 2026) Larger Datasets Can Be Repeated More: A Theoretical Analysis of Multi-Epoch Scaling in Linear Regression
  Tingkai Yan*, Haodong Wen*, Binghui Li*, Kairong Luo, Wenguang Chen, Kaifeng Lyu

• [10] (NeurIPS 2025, Spotlight) Functional Scaling Laws in Kernel Regression: Loss Dynamics and Learning Rate Schedules
  Binghui Li* † , Fengling Chen*, Zixun Huang*, Lean Wang*, Lei Wu

• [9] (Preprint) M2IO-R1: An Efficient RL-Enhanced Reasoning Framework for Multimodal Retrieval Augmented Multimodal Generation
  Zhiyou Xiao*, Qinhan Yu*, Binghui Li* † , Geng Chen, Chong Chen, Wentao Zhang

• [8] (Preprint) New Sphere Packings from the Antipode Construction
  (α-β order) Ruitao Chen, Jiachen Hu, Binghui Li, Liwei Wang, Tianyi Wu

• [7] (ICML 2025) On the Clean Generalization and Robust Overfitting in Adversarial Training from Two Theoretical Views: Representation Complexity and Training Dynamics
  Binghui Li, Yuanzhi Li

• [6] (SIGIR 2025) MRAMG-Bench: A Comprehensive Benchmark for Advancing Multimodal Retrieval-Augmented Multimodal Generation
  Qinhan Yu*, Zhiyou Xiao*, Binghui Li*, Zhengren Wang, Chong Chen, Wentao Zhang

• [5] (ICLR 2025) Feature Averaging: An Implicit Bias of Gradient Descent Leading to Non-Robustness in Neural Networks
  Binghui Li*, Zhixuan Pan*, Kaifeng Lyu, Jian Li

• [4] (ICLR 2025) Adversarial Training Can Provably Improve Robustness: Theoretical Analysis of Feature Learning Process Under Structured Data
  Binghui Li, Yuanzhi Li

• [3] (NeurIPS 2022) Why Robust Generalization in Deep Learning is Difficult: Perspective of Expressive Power
  Binghui Li*, Jikai Jin*, Han Zhong, John E. Hopcroft, Liwei Wang

• [2] (Preprint) Reconstruction Task Finds Universal Winning Tickets
  Ruichen Li, Binghui Li, Qi Qian, Liwei Wang

• [1] (Preprint) Boosting Certified ℓ_∞ Robustness with EMA Method and Ensemble Model
  Binghui Li*, Shiji Xin*, Qizhe Zhang*

Invited Talks

• 2025.11, At the Eleventh Beijing Computational Mathematics Postgraduate Forum, Peking University, Functional Scaling Laws in Kernel Regression: Loss Dynamics and Learning Rate Schedules [Slides]

• 2025.11, At the Yao Class Seminar, Tsinghua University, Functional Scaling Laws in Kernel Regression: Loss Dynamics and Learning Rate Schedules [Slides]

• 2025.04, At the Applied Mathematics Youth Seminar, Peking University, Theoretical Understanding of Adversarial Examples: Expressive Power and Training Dynamics [Slides]

• 2024.11, At the Turing Student CS Frontier Tutorial, Peking University, Theoretical Understanding of Adversarial Examples: Expressive Power and Training Dynamics [Slides]

• 2024.11, At the Tenth Beijing Computational Mathematics Postgraduate Forum, Peking University, Theoretical Understanding of Adversarial Examples: Expressive Power and Training Dynamics [Slides]

• 2024.05, At the Turing Student Research Forum, Peking University, Understanding Adversarial Examples and Adversarial Training in Deep Learning: A Feature Learning View [Slides]

• 2023.08, At International Joint Conference on Theoretical Computer Science – Frontier of Algorithmic Wisdom (IJTCS-FAW 2023), Robust Generalization Requires Exponentially Large Models [Slides]

• 2023.05, At the Turing Student Research Forum, Peking University, Robust Generalization Requires Exponentially Large Models [Video]

• 2022.05, At the Fourth BAAI Conference, Robust Generalization Requires Exponentially Large Models [Slides] [Video]

Selected Awards

• The CAST Youth Science and Technology Talent Cultivation Program for Doctoral Students, 2025
• National Scholarship, 2025, 2026 (top 1% in the nation)
• Peking University Elite Student Program for Applied Mathematics, 2024-2028 (Expected)
• President Scholarship of PKU, 2023
• Weiming Scholar of PKU, 2023 (top 1%, the highest honor for undergraduates in Peking University)
• Top 10 Bachelor Thesis of School of EECS, PKU, 2023
• Third Class Scholarship of PKU, 2022
• John Hopcroft Scholarship, 2021
• Peking University Collegiate Programming Contest, Third Prize, 2021
• Third Class Scholarship of PKU, 2020
• Chinese Mathematical Olympiad, Bronze Medal, 2018
• Chinese Southeast Mathematical Olympiad, Gold Medal, 2017
• Physics Olympiad of Shaanxi, Third Prize, 2017

Teaching

• 2025 Fall: CS 34100 Mathematical Foundations for the Information Age, PKU (TA, with Prof. Yuqing Kong)

• 2025 Fall: CS 33400 Discrete Mathematics and Structures, PKU (TA, with Prof. Tianren Liu)

• 2025 Spring: CS 34010 Randomness and Computation, PKU (TA, with Prof. Yuqing Kong)

• 2024 Fall: CS 33400 Discrete Mathematics and Structures, PKU (TA, with Prof. Tianren Liu)

• 2023 Fall: CS 33400 Discrete Mathematics and Structures, PKU (TA, with Prof. Tianren Liu)

• 2022 Fall: CS 33400 Discrete Mathematics and Structures, PKU (TA, with Prof. Xiaotie Deng)

• 2021 Fall: CS 33400 Discrete Mathematics and Structures, PKU (TA, with Prof. Xiaotie Deng)

Professional Service

• Conference reviewer of ICLR 2023/ NeurIPS 2024/ ICLR 2025/ AISTATS 2025/ ICML 2025/ NeurIPS 2025/ AAAI 2026/ AISTATS 2026/ ICLR 2026/ CVPR 2026/ ICML 2026/ ECCV 2026/ NeurIPS 2026/ AAAI 2027/ ICLR 2027/ AISTATS 2027
• Committee member of Turing Class Research Committee since 2020

Selected Courses

• Machine Learning: 93/100
• Numerical Methods (B): 95/100
• High-Dimensional Probability: 90/100
• Study and Practice on Topics of Frontier Computing (II): 96/100
• Introduction to the Theory of Computation: 92/100
• Mathematical Analysis (I): 97.5/100
• Discrete Mathematics and Structures (I): 97/100
• Probability Theory and Statistics (A): 96/100
• Python Programming and Application: 96/100
• Advanced Algebra (II): 99/100
• Practice of Programming in C&C++: 93/100
• Algorithm Design and Analysis (Honor Track): 91.5/100
• Information Theory: 90/100
• Mathematical Foundations for the Information Age: 92/100
• The Brain and Cognitive Science: 91/100