Why do larger models generalize better? A theoretical perspective via the XOR problem

Alon Brutzkus, Amir Globerson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Empirical evidence suggests that neural networks with ReLU activations generalize better with over-parameterization. However, there is currently no theoretical analysis that explains this observation. In this work, we provide theoretical and empirical evidence that, in certain cases, overparame-terized convolutional networks generalize better than small networks because of an interplay between weight clustering and feature exploration at initialization. We demonstrate this theoretically for a 3-layer convolutional neural network with max-pooling, in a novel setting which extends the XOR problem. We show that this interplay implies that with overparameterization, gradient descent converges to global minima with better generalization performance compared to global minima of small networks. Empirically, we demonstrate these phenomena for a 3-layer convolutional neural network in the MNIST task.

Original languageEnglish
Title of host publication36th International Conference on Machine Learning, ICML 2019
PublisherInternational Machine Learning Society (IMLS)
Pages1310-1318
Number of pages9
ISBN (Electronic)9781510886988
StatePublished - 2019
Event36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States
Duration: 9 Jun 201915 Jun 2019

Publication series

Name36th International Conference on Machine Learning, ICML 2019
Volume2019-June

Conference

Conference36th International Conference on Machine Learning, ICML 2019
Country/TerritoryUnited States
CityLong Beach
Period9/06/1915/06/19

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