A generalized neural tangent kernel analysis for two-layer neural networks

A recent breakthrough in deep learning theory shows that the training of overparameterized deep neural networks can be characterized by a kernel function called 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.