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

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