Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon

Yu-Xiang Wang (UCSD) · Tongtong Liang (University of California, San Diego) · Dan Qiao (UCSD) · Rahul Parhi (UCSD)
convergence ratescurse of dimensionalityedge-of-stabilityflatnessgeneralization gapimplicit biasloss curvaturemean-squared errorminima stabilityminimax lower boundmultivariate inputsneural shatteringnonparametric function estimationoverparameterized networksupper and lower bounds

We study the implicit bias of flatness / low (loss) curvature and its effects on generalization in two-layer overparameterized ReLU networks with multivariate inputs