Stack operation of tensor networks

TL;DR

This paper introduces a rigorous mathematical definition for stacking tensor networks, enabling their compression into a single network without altering structure, with applications demonstrated in matrix product states-based machine learning.

Contribution

It provides the first formal definition of tensor network stacking, facilitating efficient compression and manipulation of tensor networks in computational applications.

Findings

The proposed stacking method preserves tensor network structures.

The approach outperforms traditional for loop and coding methods.

Effective on both CPU and GPU implementations.

Abstract

The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network contraction is so far well defined. In this paper, we propose a mathematically rigorous definition for the tensor network stack approach, that compress a large amount of tensor networks into a single one without changing their structures and configurations. We illustrate the main ideas with the matrix product states based machine learning as an example. Our results are compared with the for loop and the efficient coding method on both CPU and GPU.