My research interests are approximation and generalization theory via transformer neural networks, graph-based learning and clustering, manifold learning, data-driven metrics for high-dimensional unsupervised learning, mathematics of data science and their intersections. Below are the topics I have been worked on previously and currently.
Approximation for high dimensional functions via Kolmogorov superposition theorem
Nonparametric regression on manifolds via transformer neural networks
In-context learning via transformer neural networks
Compressed sensing and its application to signal recovery and image reconstruction
Graph-based learning and clustering
Graph Ricci curvature and its applications to data science
Physics informed neural networks for solving Poisson-Boltzmann equation
Low rank matrix cross approximationÂ
Out-of-distribution detection