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cs.LG2025
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…
cs.LG2025
Embedding principle of homogeneous neural network for classification problem
Jiahan Zhang, Yaoyu Zhang, Tao Luo
In this paper, we study the Karush-Kuhn-Tucker (KKT) points of the associated maximum-margin problem in homogeneous neural networks, including fully-connected and convolutional neu…
cs.LG2024
Geometry of Critical Sets and Existence of Saddle Branches for Two-layer Neural Networks
Leyang Zhang, Yaoyu Zhang, Tao Luo
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 c…