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cs.LG2024
Linear Independence of Generalized Neurons and Related Functions
Leyang Zhang
The linear independence of neurons plays a significant role in theoretical analysis of neural networks. Specifically, given neurons $H_1, ..., H_n: \bR^N \times \bR^d \to \bR$, we…
cs.LG2024
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…
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…