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.
Penalising the biases in norm regularisation enforces sparsity https://papers.neurips.cc/paper_files/paper/2023/hash/b444ad72520a5f5c467343be88e352ed-Abstract-Conference.html
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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.