Keywords: deep learning theory, adaptive kernel, robust deep learning, neural tangent kernel, adaptive generalization, non-convex optimization
Abstract: While there has been substantial recent work studying generalization of neural networks, the ability of deep nets in automating the process of feature extraction still evades a thorough mathematical understanding. As a step toward this goal, we analyze learning and generalization of a three-layer neural network with ReLU activations in a regime that goes beyond the linear approximation of the network, and is hence not captured by the common Neural Tangent Kernel. We show that despite nonconvexity of the empirical loss, a variant of SGD converges in polynomially many iterations to a good solution that generalizes. In particular, our generalization bounds are adaptive: they automatically optimize over a family of kernels that includes the Neural Tangent Kernel, to provide the tightest bound.
One-sentence Summary: Algorithmically obtaining noise-robust and adaptive generalization bounds for a three layer network model by going beyond the linear approximation of the network
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