Research

My research background is interdisciplinary, rooted in mathematics. My early work (and attempts) spanned spectral geometry, PDEs, microlocal analysis, and probability. In the spring of 2024, I start to study machine learning and AI for science. Noticing that many foundational questions in deep learning remain poorly understood, I transitioned to machine learning theory in the spring of 2025. My current goal is to develop a multi-perspective understanding of deep learning: primarily through the lens of mathematics, particularly approximation theory of neural networks, while also exploring training dynamics and statistic viewpoints.

Notes. * indicates equal contribution. (α-β) indicates alphabetical author order.

Preprints

  1. arXiv
    (α-β) Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain \(L^p\) Ridge Integral Spaces for \(\mathrm{ReLU}^k\) Networks
    Juncai He and Zitong Tian
    Jun 2026
    arXiv
  2. arXiv
    (α-β) Divergence-Free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
    Juncai He, Xinliang Liu, and Zitong Tian
    Mar 2026
    arXiv

Accepted Papers

  1. ICML
    Cross-Chirality Generalization by Axial Vectors for Hetero-Chiral Protein-Peptide Interaction Design
    Ziyi Yang*, Zitong Tian*, Yinjun Jia*, Tianyi Zhang, Jiqing Zheng, Hao Wang, Yubu Su, Juncai He, Lei Liu, and Yanyan Lan
    In Proceedings of the International Conference on Machine Learning (ICML), 2026
    arXiv
  2. NeurIPS
    Manipulating 3D Molecules in a Fixed-Dimensional E(3)-Equivariant Latent Space
    Zitao Chen*, Yinjun Jia*, Zitong Tian*, Wei-Ying Ma, and Yanyan Lan
    In Advances in Neural Information Processing Systems (NeurIPS), 2025
    arXiv

Talks

  1. Jul, 2026. Radon transforms and a new proof of \(L^2\) density correspondence with critical Sobolev space. 2026 Peking University Lectures on Applied Mathematics , Peking University.
  2. Jul, 2026. Sharp Sobolev Sandwich and Approximation for Radon domain \(L^p\) Spaces. International Conference on Scientific Computation and Differential Equations (SciCADE) , University of Edinburgh.