Tensor network compressibility of convolutional models

TL;DR

This paper investigates why tensorization-based compression of CNNs often preserves accuracy, revealing that internal correlation structures can be truncated with minimal impact, enabling effective model compression and re-training.

Contribution

It demonstrates that CNN kernels can be truncated along multiple cuts with little accuracy loss, highlighting the intrinsic correlation compression in CNNs and informing better tensorization strategies.

Findings

Kernel truncation often preserves classification accuracy

Deep layer kernels are more amenable to truncation

Re-training can recover accuracy after aggressive truncation

Abstract

Convolutional neural networks (CNNs) are one of the most widely used neural network architectures, showcasing state-of-the-art performance in computer vision tasks. Although larger CNNs generally exhibit higher accuracy, their size can be effectively reduced by ``tensorization'' while maintaining accuracy, namely, replacing the convolution kernels with compact decompositions such as Tucker, Canonical Polyadic decompositions, or quantum-inspired decompositions such as matrix product states, and directly training the factors in the decompositions to bias the learning towards low-rank decompositions. But why doesn't tensorization seem to impact the accuracy adversely? We explore this by assessing how \textit{truncating} the convolution kernels of \textit{dense} (untensorized) CNNs impact their accuracy. Specifically, we truncated the kernels of (i) a vanilla four-layer CNN and (ii) ResNet-50 pre-trained for image classification on CIFAR-10 and CIFAR-100 datasets. We found that kernels (especially those inside deeper layers) could often be truncated along several cuts resulting in significant loss in kernel norm but not in classification accuracy. This suggests that such ``correlation compression'' (underlying tensorization) is an intrinsic feature of how information is encoded in dense CNNs. We also found that aggressively truncated models could often recover the pre-truncation accuracy after only a few epochs of re-training, suggesting that compressing the internal correlations of convolution layers does not often transport the model to a worse minimum. Our results can be applied to tensorize and compress CNN models more effectively.