Deep tensor networks with matrix product operators

TL;DR

This paper introduces deep tensor networks based on tensor network representations of weight matrices, demonstrating their effectiveness in image classification and sequence prediction tasks with significant parameter efficiency.

Contribution

The paper presents a novel deep tensor network architecture that extends tensor network models to exponentially wide neural networks, improving performance and parameter efficiency.

Findings

Achieved 0.49% error on MNIST

Achieved 8.3% error on FashionMNIST

Demonstrated exponential parameter efficiency in sequence prediction

Abstract

We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) and sequence prediction (cellular automata) tasks. In the image classification case, deep tensor networks improve our matrix product state baselines and achieve 0.49% error rate on MNIST and 8.3% error rate on FashionMNIST. In the sequence prediction case, we demonstrate an exponential improvement in the number of parameters compared to the one-layer tensor network methods. In both cases, we discuss the non-uniform and the uniform tensor network models and show that the latter generalizes well to different input sizes.