3 papers
cs.LG2026
Mathematical Foundations of Deep Learning
Xiaojing Ye
This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the appro…
math.OC2026
Maximum Principle of Optimal Probability Density Control
Nathan Gaby, Xiaojing Ye
We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In part…
math.NA2025
A parameterized Wasserstein Hamiltonian flow approach for solving the Schrödinger equation
Hao Wu, Shu Liu, Xiaojing Ye +1
In this paper, we propose a new method to compute the solution of time-dependent Schrödinger equation (TDSE). Using push-forward maps and Wasserstein Hamiltonian flow, we reformul…