Redundant representations help generalization in wide neural networks
This addresses the challenge of explaining why overfitting can improve generalization in deep networks, which is an incremental insight into neural network behavior.
The study investigated the mechanism behind benign overfitting in deep neural networks by analyzing last hidden layer representations, finding that neurons split into redundant groups with independent noise when the layer is wide enough and training error is zero.
Deep neural networks (DNNs) defy the classical bias-variance trade-off: adding parameters to a DNN that interpolates its training data will typically improve its generalization performance. Explaining the mechanism behind this ``benign overfitting'' in deep networks remains an outstanding challenge. Here, we study the last hidden layer representations of various state-of-the-art convolutional neural networks and find that if the last hidden representation is wide enough, its neurons tend to split into groups that carry identical information, and differ from each other only by statistically independent noise. The number of such groups increases linearly with the width of the layer, but only if the width is above a critical value. We show that redundant neurons appear only when the training process reaches interpolation and the training error is zero.