Noisy SGD in the mean-field regime forces wide multivariate ReLU networks to an effective width of at most 2P-1, yielding a continuous piecewise-affine predictor whose hyperplanes are non-redundant with respect to the training data.
Testing sets for properness of polynomial mappings , Ty =
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Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse
Noisy SGD in the mean-field regime forces wide multivariate ReLU networks to an effective width of at most 2P-1, yielding a continuous piecewise-affine predictor whose hyperplanes are non-redundant with respect to the training data.