Zhichao Wang

Zhichao Wang (王志超) Ph.D. Student at Department of Mathematics University of California, San Diego Email: zhw036@ucsd.edu [Curriculum Vitae] Google Scholar

About me

I am a PhD student in the Department of Mathematics at UC San Diego. I am very fortunate to be advised by Ioana Dumitriu and Todd Kemp. I interned during Summer 2021 and 2022 with Tony Chiang at Pacific Northwest National Laboratory. Prior to UCSD, I received my M.Sc. degree in Mathematics from Texas A&M University, supervised by Michael Anshelevich, and my B.Sc. degree in Mathematics and Applied Math from Chinese Academy of Sciences Hua Loo-Keng Class at Beihang University.

Research Interests

My current research focuses on theoretically understanding and improving fundamental algorithms in data science, especially in deep learning, using tools from high-dimensional probability.

• Random Matrix Theory and Free Probability Theory

• Deep Learning Theory and Foundations of AI

• High-dimensional Statistics

Publications and Preprints

• Nonlinear spiked covariance matrices and signal propagation in deep neural networks.
  Zhichao Wang, Denny Wu, and Zhou Fan
  Submitted.

• Unlocking Exact Recovery in Semi-Supervised Learning: Analysis of Spectral Method and Graph Convolution Network.
  Haixiao Wang and Zhichao Wang
  Submitted.

• Faithful and Efficient Explanations for Neural Networks via Neural Tangent Kernel Surrogate Models.
  Andrew Engel, Zhichao Wang, Natalie S. Frank, Ioana Dumitriu, Sutanay Choudhury, Anand Sarwate, and Tony Chiang
  ICLR 2024, Spotlight, to appear.

• Learning in the Presence of Low-dimensional Structure: A Spiked Random Matrix Perspective.
  Jimmy Ba, Murat A. Erdogdu, Taiji Suzuki, Zhichao Wang, and Denny Wu
  NeurIPS 2023.

• Spectral evolution and invariance in linear-width neural networks.
  Zhichao Wang, Andrew Engel, Anand Sarwate, Ioana Dumitriu, and Tony Chiang
  NeurIPS 2023.

• Overparameterized random feature regression with nearly orthogonal data.
  Zhichao Wang and Yizhe Zhu
  AISTATS 2023.

• High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation.
  Jimmy Ba, Murat A. Erdogdu, Taiji Suzuki, Zhichao Wang, Denny Wu, and Greg Yang
  NeurIPS 2022.

• Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networks.
  Zhichao Wang and Yizhe Zhu
  Annals of Applied Probability, to appear.

• Tree convolution for probability distributions with unbounded support.
  Ethan Davis, David Jekel, Zhichao Wang
  Latin American Journal of Probability and Mathematics Statistics 18.2 (2021), pp. 1585-1623.

• Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks.
  Zhou Fan and Zhichao Wang
  NeurIPS 2020, Oral Presentation.

• Principal components in linear mixed models with general bulk.
  Zhou Fan, Yi Sun, and Zhichao Wang
  The Annals of Statistics, 49.3 (2021), pp. 1489-1513.

• Higher variations for free Levy processes.
  Michael Anshelevich and Zhichao Wang
  Studia Math. 252 (2020), pp. 49-81.