Representation mitosis in wide neural networks

Deep neural networks (DNNs) defy the classical bias-variance trade-off: adding parameters to a DNN that exactly interpolates its training data will typically improve its generalisation performance. Explaining the mechanism behind the benefit of such over-parameterisation is an outstanding challenge for deep learning theory. Here, we study the last layer representation of various deep architectures such as Wide-ResNets for image classification and find evidence for an underlying mechanism that we call *representation mitosis*: if the last hidden representation is wide enough, its neurons tend to split into groups which carry identical information, and differ from each other only by a statistically independent noise. Like in a mitosis process, the number of such groups, or ``clones'', increases linearly with the width of the layer, but only if the width is above a critical value. We show that a key ingredient to activate mitosis is continuing the training process until the training error is zero. Finally, we show that in one of the learning tasks we considered, a wide model with several automatically developed clones performs significantly better than a deep ensemble based on architectures in which the last layer has the same size as the clones.