Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach
This addresses the theoretical understanding of generalization in deep learning for researchers, offering a novel approach but is incremental in linking existing compression methods to generalization bounds.
The paper tackles the problem of explaining why overparameterized neural networks generalize well by connecting generalization to compressibility, providing the first non-vacuous generalization bounds for ImageNet-scale models using PAC-Bayesian compression, with state-of-the-art guarantees.
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.