Understanding Deep Learning (Still) Requires Rethinking Generalization

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. For centuries, scientists, policy makers, actuaries, and salesmen alike have exploited the empirical fact that unknown outcomes, be they future or unobserved, often trace regularities found in past observations. We call this idea generalization: finding rules consistent with available data that apply to instances we have yet to encounter. Supervised machine learning builds on statistical tradition in how it formalizes the idea of generalization. We assume observations come from a fixed data generating process, such as samples drawn from a fixed distribution. In a first optimization step, called training, we fit a model to a set of data.