Welcome to my personal website! I am currently a senior undergraduate student majoring in computational mathematics at School of Mathematical Sciences, Peking University, fortunately having Prof. Liwei Wang as my research advisor. My research is highly interdisciplinary across statistics, applied probability and operations research. While being trained as a theorist, the ultimate goal of my research is to develop state-of-the-art solutions for important real-world problems. If you share similar interest, feel free to contact me via email or Wechat. In this fall, I am going to join The Institute for Computational and Mathematical Engineering (ICME) at Stanford university as a Ph.D. student.
Download my resumé.
BSc in Computational Mathematics, 2023(expected)
Sept. 2022 Personal website created!
Sept. 2022 Our new paper on minimax optimal kernel operator learning has been posted on ArXiv.
Oct. 2022 Our operator learning paper is accepted by the NeurIPS 2022 AI4Science workshop.
Dec. 2022 I am delighted to receive the 2022 Sensetime Scholarship which is awarded to 30 undergraduate students from Chinese universities in the field of AI.
Jan. 2023 Our operator learning paper is accepted by ICLR 2023 as spotlight presentation.
It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019) – GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.
Oct. 2022 Qin-Jin Scholarship, Peking University.
Oct. 2021 Exceptional award for academic innovation, Peking University.
Jun. 2021 Elite undergraduate training program of Applied Mathematics and Statistics.
May 2021 Bronze Medal, S.T. Yau College Student Mathematics Competition, probability and statistics individual.
Dec. 2020 Qin-Jin Scholarship, Peking University.
Oct. 2020 Yizheng Scholarship, Peking University.
Feb. 2019 Silver Medal, 11th Romania Masters of Mathematics.
Oct. 2018 First Prize (ranked No.6), Chinese Mathematical Olympiad (CMO).
Oct. 2017 First Prize (ranked No.13), Chinese Mathematical Olympiad (CMO).