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Under mild assumptions, we investigate the structure of loss landscape oftwo-layer neural networks near global minima, determine the set of parameterswhich give perfect generalization, and fully characterize the gradient flowsaround it. With novel techniques, our work uncovers some simple aspects of thecomplicated loss landscape and reveals how model, target function, samples andinitialization affect the training dynamics differently. Based on theseresults, we also explain why (overparametrized) neural networks couldgeneralize well.

Structure and Gradient Dynamics Near Global Minima of Two-layer Neural Networks