SGD learns over-parameterized networks that provably generalize on linearly separable data

Alon Brutzkus, Amir Globerson, Eran Malach, Shai Shalev-Shwartz

Research output: Contribution to conferencePaperpeer-review

Abstract

Neural networks exhibit good generalization behavior in the over-parameterized regime, where the number of network parameters exceeds the number of observations. Nonetheless, current generalization bounds for neural networks fail to explain this phenomenon. In an attempt to bridge this gap, we study the problem of learning a two-layer over-parameterized neural network, when the data is generated by a linearly separable function. In the case where the network has Leaky ReLU activations and only the first layer is trained, we provide both optimization and generalization guarantees for over-parameterized networks. Specifically, we prove convergence rates of SGD to a global minimum, and provide generalization guarantees for this global minimum that are independent of the network size. Therefore, our result clearly shows that the use of SGD for optimization both finds a global minimum, and avoids overfitting despite the high capacity of the model. This is the first theoretical demonstration that SGD can avoid overfitting, when learning over-specified neural network classifiers.

Original languageEnglish
StatePublished - 2018
Event6th International Conference on Learning Representations, ICLR 2018 - Vancouver, Canada
Duration: 30 Apr 20183 May 2018

Conference

Conference6th International Conference on Learning Representations, ICLR 2018
Country/TerritoryCanada
CityVancouver
Period30/04/183/05/18

Fingerprint

Dive into the research topics of 'SGD learns over-parameterized networks that provably generalize on linearly separable data'. Together they form a unique fingerprint.

Cite this