152 citations · 506 across the 51 of their papers we have counts for
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cs.LG2022
The Mori-Zwanzig formulation of deep learning
Daniele Venturi, Xiantao Li
We develop a new formulation of deep learning based on the Mori-Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duali…
cs.LG2022★ 2 cited
A Local Convergence Theory for the Stochastic Gradient Descent Method in Non-Convex Optimization With Non-isolated Local Minima
Taehee Ko, Xiantao Li
Loss functions with non-isolated minima have emerged in several machine learning problems, creating a gap between theory and practice. In this paper, we formulate a new type of loc…
cs.LG2021★ 2 cited
Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions
He Zhang, John Harlim, Xiantao Li
This paper studies the theoretical underpinnings of machine learning of ergodic Itô diffusions. The objective is to understand the convergence properties of the invariant statistic…