Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz

TL;DR

This paper introduces a tensorization method for neural networks using the Multi-scale Entanglement Renormalization Ansatz (MERA), achieving significant parameter reduction while maintaining high accuracy on image classification tasks.

Contribution

It proposes replacing fully connected layers with MERA tensor networks, offering a more efficient compression method than tensor trains for neural networks.

Findings

MERA-based layers have 14,000 times fewer parameters.

Achieves less than 1% accuracy loss compared to fully connected layers.

Outperforms tensor train factorization in compression efficiency.

Abstract

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for the fully connected layers in a convolutional neural network and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA layers with 14000 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers, scaling like O(N).