The sum of tensor networks

TL;DR

This paper introduces a rigorous framework for summing tensor networks to enhance feature fusion, demonstrating improved classification performance on related image groups compared to standard machine learning methods.

Contribution

It proposes a novel tensor network summation framework that leverages their structure for better feature fusion and classification.

Findings

Outperforms standard machine learning algorithms in image classification

Enables feature combination for multiple tensors with isomorphic topologies

Provides a structured approach to tensor network summation

Abstract

Tensor networks (TNs) have been gaining interest as multiway data analysis tools owing to their ability to tackle the curse of dimensionality and to represent tensors as smaller-scale interconnections of their intrinsic features. However, despite the obvious advantages, the current treatment of TNs as stand-alone entities does not take full benefit of their underlying structure and the associated feature localization. To this end, embarking upon the analogy with a feature fusion, we propose a rigorous framework for the combination of TNs, focusing on their summation as the natural way for their combination. This allows for feature combination for any number of tensors, as long as their TN representation topologies are isomorphic. The benefits of the proposed framework are demonstrated on the classification of several groups of partially related images, where it outperforms standard machine learning algorithms.