Distributive Pre-Training of Generative Modeling Using Matrix-Product States

TL;DR

This paper introduces a novel pre-training method for generative models using tensor network operations, offering an efficient alternative to gradient descent, with promising results on image generation and classification tasks.

Contribution

It proposes a tensor network-based pre-training algorithm that compresses training data into a superposition state, enabling parallelizable and single-pass training.

Findings

Reasonable image generation results on MNIST

Effective classification performance

Interpretation as quantum kernel density estimation

Abstract

Tensor networks have recently found applications in machine learning for both supervised learning and unsupervised learning. The most common approaches for training these models are gradient descent methods. In this work, we consider an alternative training scheme utilizing basic tensor network operations, e.g., summation and compression. The training algorithm is based on compressing the superposition state constructed from all the training data in product state representation. The algorithm could be parallelized easily and only iterates through the dataset once. Hence, it serves as a pre-training algorithm. We benchmark the algorithm on the MNIST dataset and show reasonable results for generating new images and classification tasks. Furthermore, we provide an interpretation of the algorithm as a compressed quantum kernel density estimation for the probability amplitude of input data.