Weight-decay-regularized two-layer ReLU networks need width exponential in the number of samples for a benign loss landscape, and small initialization can still converge to spurious minima.
Du, Wei Hu, Zhiyuan Li, and Ruosong Wang
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Favorability of Loss Landscape with Weight Decay Requires Both Large Overparametrization and Initialization
Weight-decay-regularized two-layer ReLU networks need width exponential in the number of samples for a benign loss landscape, and small initialization can still converge to spurious minima.