Group-invariant tensor train networks for supervised learning

TL;DR

This paper introduces a fast algorithm for constructing group-invariant tensor train networks, enhancing supervised learning by incorporating invariance properties, demonstrated on protein binding classification with competitive accuracy.

Contribution

A novel, efficient method for creating group-invariant tensors and integrating them into tensor train networks for supervised learning tasks.

Findings

Algorithm is up to several orders of magnitude faster than previous methods.

Group-invariant tensor train networks achieve accuracy comparable to deep learning.

Effective incorporation of problem-specific invariances improves model performance.

Abstract

Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that are invariant under the action of normal matrix representations of an arbitrary discrete group. This method can be up to several orders of magnitude faster than previous approaches. The group-invariant tensors are then combined into a group-invariant tensor train network, which can be used as a supervised machine learning model. We applied this model to a protein binding classification problem, taking into account problem-specific invariances, and obtained prediction accuracy in line with state-of-the-art deep learning approaches.