Foundation models, multi-task learning and in-context learning;
Machine learning for function-valued and measure-valued data;
Approximation theory for deep learning architectures;
Sampling and generative modeling.
Stabilty of Measure-to-Measure Transformers on Sub-Gaussian Data, in collaboration with Nicholas Nelsen and Takashi Furuya. Arxiv.
Universal Approximation of Measure-to-Measure Operators by Pushforwards, in collaboration with Takashi Furuya and Nicholas Nelsen. Arxiv.
A Theory of Diversity for Random Matrices, with Applications to the In-Context Learning of Schrödinger Equations, in collaboration with Yulong Lu and Shaurya Sehgal. Submitted. Arxiv.
In-Context Operator learning on the Space of Probability Measures, in collaboration with Dixi Wang, Yineng Chen, Yulong Lu, and Rongjie Lai. Submitted. Arxiv.
In-Context Learning of Linear Systems: Generalization Theory and Application to Operator Learning, in collaboration with Yulong Lu, Wuzhe Xu, and Tianhao Zhang. To appear in SIAM Journal on Mathematics of Data Science. Arxiv
Flow Matching for Multimodal Distributions, in collaboration with Gaoxiang Luo, Sihang Zang, Yuxiang Wan, Yulong Lu, and Ju Sun. CVPR 2026. Conference proceedings.
In-Context Learning of Linear Dynamical Systems with Transformers: Approximation bounds and Depth-Separation, in collaboration with Yuxuan Zhao, Yulong Lu, and Tianhao Zhang. NeurIPS 2025. Arxiv
Score-Based Generative Models Break the Curse of Dimensionality in Learning a Family of Sub-Gaussian Probability Distributions, in collaboration with Yulong Lu. ICLR 2024 Arxiv, poster
Oden Institute Seminar, The University of Texas Austin, September 2026.
Applied Math Seminar, Montana State University, September 2026.
Mathematics of Machine Learning Seminar, UMASS Amherst, May 2026.
Minisymposium on "In-context learning for PDEs and inverse problems", SIAM UQ 2026, March 2026.
Minisymposium on "Physics-guided and generative AI for scientific computing: theory, algorithms and applications, SIAM NNP Sectional Meeting, November 2025.