About

Research profile

I am a quantitative researcher at Engineers Gate. I have a Statistics PhD from the University of Wisconsin-Madison, advised by Nicolás García Trillos. My thesis was about theoretical foundations and machine learning applications of graph Laplacians. I received my master's degree in Statistics from the University of Wisconsin-Madison in 2020 and my master's degree in Mathematics from the University of Wisconsin-Madison in 2025. I obtained my bachelor's degree in Mathematics from Zhejiang University in 2019, supervised by Professor Zhiyi Tan.

In my academic pursuits, I am interested in exploring topology and geometric perspectives to gain a deeper understanding of complex problems. This interest further motivates my study of algorithms and their concrete mathematical formulations. Additionally, I am passionate about designing fast and interpretable algorithms for statistical problems. My academic background is a diverse blend of mathematics, statistics, and computer science.

Working papers

  1. N. García Trillos*, B. Hosseini*, C. Li*. “Operator Learning on Grassmannian Manifold: from Distribution to Eigenfunction.” In preparation.

Preprints

  1. C. Li, N. García Trillos, H. Li, L. Suchan. “Central limit theorems for the eigenvalues of graph Laplacians on data clouds.” 2025.
  2. N. García Trillos*, C. Li*, R. Venkatraman*. “Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds.” 2025.
  3. C. Li, J. Cisewski-Kehe. “A divide-and-conquer approach to persistent homology.” 2024.

Publications

  1. C. Li*, A. M. Neuman*. “Consistency of augmentation graph and network approximability in contrastive learning.” Accepted by Journal of Machine Learning Research (JMLR), 2026.
  2. C. Li, R. Sonthalia, N. García Trillos. “Spectral neural networks: approximation theory and optimization landscape.” Journal of Machine Learning, ISSN 2790-2048(e), 2790-203X(p), 2025.
  3. N. García Trillos*, P. He*, C. Li*. “Large sample spectral analysis of graph-based multimanifold clustering.” Journal of Machine Learning Research (JMLR), 24(143):1–71, 2023.
  4. J. Diakonikolas*, C. Li*, S. Padmanabhan*, C. Song*. “A Fast Scale-Invariant Algorithm for Non-negative Least Squares with Non-negative Data.” Neural Information Processing Systems (NeurIPS), 35:6264–6277, 2022.
  5. J. Zhao, C. Li, F. Sala, K. Rohe. “Quantifying Structure in CLIP Embeddings: A Statistical Framework for Concept Interpretation.” Transactions on Machine Learning Research, 2026.

Workshops

  1. C. Li, R. Sonthalia, N. García Trillos. “The optimization landscape of Spectral neural network.” ICML 2024 Workshop: High-dimensional Learning Dynamics.
  2. A. M. Neuman, C. Li. “Consistency of augmentation graph and network approximability in contrastive learning.” 15th International Conference on Sampling Theory and Applications, 2025.

Teaching

  • Spring 2024 [TA]: STAT 301 Introduction to Statistical Methods

  • Fall 2023 [TA]: STAT 609 Mathematical Statistics I

  • Spring 2023 [TA]: STAT 324 Introductory Applied Statistics for Engineers

  • Fall 2022 [TA]: STAT 371 Introductory Applied Statistics for the Life Sciences

  • Fall 2020 [TA]: STAT 301 Introduction to Statistical Methods

  • Spring 2020 [Grader]: MATH 629 Introduction to Measure and Integration

Talks

  • AMS sectional meeting: Geometric variational problems and applications, Saint Louis, Oct. 2025

  • Institute for Foundation of Data Science seminar, University of Wisconsin-Madison, Apr. 2025

  • Institute for Foundation of Data Science seminar, University of Wisconsin-Madison, Nov. 2024

  • Poster at DeepMath 2024, Philadelphia, Nov. 2024

  • Poster presentation and online talk at NeurIPS 2023, New Orleans, Dec. 2023

  • Institute for Foundation of Data Science seminar, University of Wisconsin-Madison, Nov. 2023

  • Graph-based Techniques in Machine Learning minisymposium, Michigan State University, Oct. 2023

  • Geometry and topology seminar at Max Planck Institute for Mathematics, Leipzig, Germany, June 2023

  • SIAM Conference on geometric and topological techniques in machine learning minisymposium, Utah State University, Apr. 2023

  • Poster presentation and online talk at NeurIPS 2022, New Orleans, Sep. 2022

  • Fall Workshop on Computational Geometry, Oct. 2021

  • Second Graduate Student Conference: Geometry and Topology Meet Data Analysis and Machine Learning, July 2021

Service