Why Neural Networks Work

TL;DR

This paper proposes that the properties and success of fully-connected neural networks can be explained by a simple expand-and-sparsify operation, shedding light on phenomena like the Lottery Ticket Hypothesis and neural network generalization.

Contribution

It introduces a unified explainability framework based on expand-and-sparsify operations that accounts for key neural network behaviors and generalization capabilities.

Findings

Explains the Lottery Ticket Hypothesis through expand-and-sparsify.

Accounts for the effectiveness of Dropout and random initialization.

Provides insights into overparameterized model generalization.

Abstract

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.