4 papers
Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting
Leyang Zhang, Yaoyu Zhang, Tao Luo
This paper investigates the sample dependence of critical points for neural networks. We introduce a sample-independent critical lifting operator that associates a parameter of one…
Local Linear Recovery Guarantee of Deep Neural Networks at Overparameterization
Yaoyu Zhang, Leyang Zhang, Zhongwang Zhang +1
Determining whether deep neural network (DNN) models can reliably recover target functions at overparameterization is a critical yet complex issue in the theory of deep learning. T…
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…
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…