Why Neural Networks Work
This work addresses the fundamental challenge of understanding why neural networks generalize well, which is crucial for researchers and practitioners in machine learning, though it appears incremental as it builds on existing theoretical frameworks.
The authors tackle the problem of explaining key properties of fully-connected feedforward neural networks, such as generalization in overparameterized models, by proposing that these phenomena arise from a combination of random projection and sparsification operations.
We argue that many properties of fully-connected feedforward neural networks (FCNNs), also called multi-layer perceptrons (MLPs), are explainable from the analysis of a single pair of operations, namely a random projection into a higher-dimensional space than the input, followed by a sparsification operation. For convenience, we call this pair of successive operations expand-and-sparsify following the terminology of Dasgupta. We show how expand-and-sparsify can explain the observed phenomena that have been discussed in the literature, such as the so-called Lottery Ticket Hypothesis, the surprisingly good performance of randomly-initialized untrained neural networks, the efficacy of Dropout in training and most importantly, the mysterious generalization ability of overparameterized models, first highlighted by Zhang et al. and subsequently identified even in non-neural network models by Belkin et al.