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math.DS2023
Gradient Flow in Morse and Analytic Settings
Leyang Zhang
This report is actually the in-class project of MATH489 FA2022, Dynamics and Differential Equations in University of Illinois Urbana-Champaign. The report is mainly about gradient…
cs.LG2023
Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization
Leyang Zhang, Yaoyu Zhang, Tao Luo
Under mild assumptions, we investigate the geometry of the loss landscape for two-layer neural networks in the vicinity of global minima. Utilizing novel techniques, we demonstrate…
cs.LG2023
Optimistic Estimate Uncovers the Potential of Nonlinear Models
Yaoyu Zhang, Zhongwang Zhang, Leyang Zhang +3
We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models. It yields an optimistic sample size that quantifies the smallest possible s…