Understanding deep learning requires rethinking generalization

TL;DR

This paper challenges traditional explanations for why large neural networks generalize well, showing they can fit random data and that expressivity alone accounts for their performance, prompting a rethink of generalization theory.

Contribution

It demonstrates that conventional explanations like regularization are insufficient, and introduces a theoretical perspective on neural network expressivity related to their size and data fitting capabilities.

Findings

Neural networks can perfectly fit random labels regardless of regularization.

Expressivity of neural networks exceeds data points once parameters surpass data size.

Traditional models cannot fully explain neural networks' generalization behavior.

Abstract

Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the model family, or to the regularization techniques used during training. Through extensive systematic experiments, we show how these traditional approaches fail to explain why large neural networks generalize well in practice. Specifically, our experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data. This phenomenon is qualitatively unaffected by explicit regularization, and occurs even if we replace the true images by completely unstructured random noise. We corroborate these experimental findings with a theoretical construction showing that simple depth two neural networks already have perfect finite sample expressivity as soon as the number of parameters exceeds the number of data points as it usually does in practice. We interpret our experimental findings by comparison with traditional models.