Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network

TL;DR

This paper introduces a novel stable low-rank tensor decomposition method for compressing convolutional neural networks, effectively reducing overparameterization and computational costs while maintaining high accuracy.

Contribution

It is the first to address degeneracy issues in tensor decomposition of convolutional kernels, providing a stabilization technique for better neural network compression.

Findings

Significantly reduces accuracy loss in CNN compression.

Ensures numerical stability in tensor approximation.

Maintains high performance across popular architectures.

Abstract

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the Canonical Polyadic tensor Decomposition is one of the most suited models. However, fitting the convolutional tensors by numerical optimization algorithms often encounters diverging components, i.e., extremely large rank-one tensors but canceling each other. Such degeneracy often causes the non-interpretable result and numerical instability for the neural network fine-tuning. This paper is the first study on degeneracy in the tensor decomposition of convolutional kernels. We present a novel method, which can stabilize the low-rank approximation of convolutional kernels and ensure efficient compression while preserving the high-quality performance of the neural networks. We evaluate our approach on popular CNN architectures for image classification and show that our method results in much lower accuracy degradation and provides consistent performance.