Spectral Pruning: Compressing Deep Neural Networks via Spectral Analysis and its Generalization Error

TL;DR

This paper introduces spectral pruning, a theoretically grounded method for compressing deep neural networks by analyzing their spectral properties, which improves efficiency and provides insights into generalization error.

Contribution

It develops a new theoretical framework for model compression based on spectral analysis and proposes a novel spectral pruning method with proven generalization bounds.

Findings

Spectral pruning effectively compresses neural networks.

The method's compression ability is linked to the eigenvalue distribution.

Experimental results demonstrate the superiority of spectral pruning.

Abstract

Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for analyzing the generalization error of deep learning, known as the compression-based error bound. However, there is still huge gap between a practically effective compression method and its rigorous background of statistical learning theory. To resolve this issue, we develop a new theoretical framework for model compression and propose a new pruning method called {\it spectral pruning} based on this framework. We define the ``degrees of freedom'' to quantify the intrinsic dimensionality of a model by using the eigenvalue distribution of the covariance matrix across the internal nodes and show that the compression ability is essentially controlled by this quantity. Moreover, we present a sharp generalization error bound of the compressed model and characterize the bias--variance tradeoff induced by the compression procedure. We apply our method to several datasets to justify our theoretical analyses and show the superiority of the the proposed method.