Semi-tensor Product-based TensorDecomposition for Neural Network Compression

TL;DR

This paper introduces semi-tensor product-based tensor decompositions to improve neural network compression, achieving higher compression ratios with minimal accuracy loss compared to traditional methods.

Contribution

It generalizes classical tensor decompositions using semi-tensor products, enabling more flexible and compact neural network compression techniques.

Findings

Semi-tensor tensor decompositions outperform traditional methods in compression ratio.

Higher compression factors achieved with similar accuracy.

Reduced training times for compressed models.

Abstract

The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper, the semi-tensor product is used to generalize classical matrix product-based mode product to semi-tensor mode product. As it permits the connection of two factors with different dimensionality, more flexible and compact tensor decompositions can be obtained with smaller sizes of factors. Tucker decomposition, Tensor Train (TT) and Tensor Ring (TR) are common decomposition for low rank compression of deep neural networks. The semi-tensor product is applied to these tensor decompositions to obtained their generalized versions, i.e., semi-tensor Tucker decomposition (STTu), semi-tensor train(STT) and semi-tensor ring (STR). Experimental results show the STTu, STT and STR achieve higher compression factors than the conventional tensor decompositions with the same accuracy but less training times in ResNet and WideResNetcompression. With 2% accuracy degradation, the TT-RN (rank = 14) and the TR-WRN (rank = 16) only obtain 3 times and99t times compression factors while the STT-RN (rank = 14) and the STR-WRN (rank = 16) achieve 9 times and 179 times compression factors, respectively.