Enhancing Accuracy in Deep Learning Using Random Matrix Theory

TL;DR

This paper applies random matrix theory to neural network pruning, demonstrating that it reduces parameters without loss of accuracy and can even improve performance, supported by rigorous mathematical proofs.

Contribution

It introduces a novel RMT-based pruning method with theoretical validation, enhancing deep learning model efficiency and accuracy.

Findings

Parameter reduction without accuracy loss

Pruning increases accuracy and reduces variance

Theoretical proof of RMT-based pruning effectiveness

Abstract

We explore the applications of random matrix theory (RMT) in the training of deep neural networks (DNNs), focusing on layer pruning that is reducing the number of DNN parameters (weights). Our numerical results show that this pruning leads to a drastic reduction of parameters while not reducing the accuracy of DNNs and CNNs. Moreover, pruning the fully connected DNNs actually increases the accuracy and decreases the variance for random initializations. Our numerics indicate that this enhancement in accuracy is due to the simplification of the loss landscape. We next provide rigorous mathematical underpinning of these numerical results by proving the RMT-based Pruning Theorem. Our results offer valuable insights into the practical application of RMT for the creation of more efficient and accurate deep-learning models.