Speeding-Up Back-Propagation in DNN: Approximate Outer Product with Memory

TL;DR

This paper introduces Mem-AOP-GD, an approximation method for back-propagation in DNN training that reduces computation by selectively using outer products and maintaining memory of omitted terms, improving efficiency and accuracy.

Contribution

The paper proposes Mem-AOP-GD, a novel algorithm that approximates backpropagation using subset outer products with memory correction, enhancing training speed and accuracy.

Findings

Significant reduction in computational complexity.

Improved training accuracy with approximation.

Effective outer product selection policies.

Abstract

In this paper, an algorithm for approximate evaluation of back-propagation in DNN training is considered, which we term Approximate Outer Product Gradient Descent with Memory (Mem-AOP-GD). The Mem-AOP-GD algorithm implements an approximation of the stochastic gradient descent by considering only a subset of the outer products involved in the matrix multiplications that encompass backpropagation. In order to correct for the inherent bias in this approximation, the algorithm retains in memory an accumulation of the outer products that are not used in the approximation. We investigate the performance of the proposed algorithm in terms of DNN training loss under two design parameters: (i) the number of outer products used for the approximation, and (ii) the policy used to select such outer products. We experimentally show that significant improvements in computational complexity as well as accuracy can indeed be obtained through Mem-AOPGD.