Geometry of Critical Sets and Existence of Saddle Branches for Two-layer Neural Networks
L Zhang, Y Zhang, T Luo - arXiv preprint arXiv:2405.17501, 2024 - arxiv.org
This paper presents a comprehensive analysis of critical point sets in two-layer neural
networks. To study such complex entities, we introduce the critical embedding operator and …
networks. To study such complex entities, we introduce the critical embedding operator and …
Connectivity Shapes Implicit Regularization in Matrix Factorization Models for Matrix Completion
Matrix factorization models have been extensively studied as a valuable test-bed for
understanding the implicit biases of overparameterized models. Although both low nuclear …
understanding the implicit biases of overparameterized models. Although both low nuclear …
Local Linear Recovery Guarantee of Deep Neural Networks at Overparameterization
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 …
functions at overparameterization is a critical yet complex issue in the theory of deep …
Disentangle Sample Size and Initialization Effect on Perfect Generalization for Single-Neuron Target
Overparameterized models like deep neural networks have the intriguing ability to recover
target functions with fewer sampled data points than parameters (see arXiv: 2307.08921). To …
target functions with fewer sampled data points than parameters (see arXiv: 2307.08921). To …