Understanding deep learning (still) requires rethinking generalization

2021/02/22 by Chiyuan Zhang, Samy Bengio, Moritz Hardt +2 · 137 citations
Computer Science · #Domain Adaptation and Few-Shot Learning #Gaussian Processes and Bayesian Inference #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.1145/3446776

openalex publication_date 2021/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small gap 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. We supplement this republication with a new section at the end summarizing recent progresses in the field since the original version of this paper.

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