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arXiv · 2002.04026

A Generalized Neural Tangent Kernel Analysis for Two-layer Neural Networks

Zixiang Chen·Yuan Cao·Quanquan Gu·Tong Zhang
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Abstract

A recent breakthrough in deep learning theory shows that the training of over-parameterized deep neural networks can be characterized by a kernel function called \textit{neural tangent kernel} (NTK). However, it is known that this type of results does not perfectly match the practice, as NTK-based analysis requires the network weights to stay very close to their initialization throughout training, and cannot handle regularizers or gradient noises. In this paper, we provide a generalized neural tangent kernel analysis and show that noisy gradient descent with weight decay can still exhibit a "kernel-like" behavior. This implies that the training loss converges linearly up to a certain accuracy. We also establish a novel generalization error bound for two-layer neural networks trained by noisy gradient descent with weight decay.

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Zixiang Chen, Yuan Cao, Quanquan Gu, Tong Zhang. 2020-10-06. A Generalized Neural Tangent Kernel Analysis for Two-layer Neural Networks. https://arxiv.org/abs/2002.04026

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