Spectral pruning: Compressing deep neural networks via spectral analysis and its generalization error

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 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.