Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach

TL;DR

This paper establishes non-vacuous generalization bounds for large neural networks on ImageNet by linking model compression to generalization, providing the first such guarantees at this scale.

Contribution

It introduces a PAC-Bayesian compression-based generalization bound applicable to realistic architectures on ImageNet, connecting compression limits with overfitting.

Findings

State-of-the-art non-vacuous generalization guarantees for ImageNet models

Overfitting correlates with increased model description length

Compression limits relate to expected generalization error

Abstract

Modern neural networks are highly overparameterized, with capacity to substantially overfit to training data. Nevertheless, these networks often generalize well in practice. It has also been observed that trained networks can often be "compressed" to much smaller representations. The purpose of this paper is to connect these two empirical observations. Our main technical result is a generalization bound for compressed networks based on the compressed size. Combined with off-the-shelf compression algorithms, the bound leads to state of the art generalization guarantees; in particular, we provide the first non-vacuous generalization guarantees for realistic architectures applied to the ImageNet classification problem. As additional evidence connecting compression and generalization, we show that compressibility of models that tend to overfit is limited: We establish an absolute limit on expected compressibility as a function of expected generalization error, where the expectations are over the random choice of training examples. The bounds are complemented by empirical results that show an increase in overfitting implies an increase in the number of bits required to describe a trained network.