Unbiased Approximate Vector-Jacobian Products for Efficient Backpropagation

TL;DR

This paper proposes an unbiased randomized approximation method for vector-Jacobian products in backpropagation, reducing computational costs while maintaining accuracy, validated through theoretical analysis and experiments on various neural network architectures.

Contribution

Introduces a novel unbiased approximation technique for vector-Jacobian products that lowers training costs in deep neural networks with proven optimality properties.

Findings

Theoretical analysis shows a trade-off between epochs and cost reduction.

Unbiased estimates with minimal variance are identified under sparsity.

Experiments confirm the effectiveness of the approach across multiple architectures.

Abstract

In this work we introduce methods to reduce the computational and memory costs of training deep neural networks. Our approach consists in replacing exact vector-jacobian products by randomized, unbiased approximations thereof during backpropagation. We provide a theoretical analysis of the trade-off between the number of epochs needed to achieve a target precision and the cost reduction for each epoch. We then identify specific unbiased estimates of vector-jacobian products for which we establish desirable optimality properties of minimal variance under sparsity constraints. Finally we provide in-depth experiments on multi-layer perceptrons, BagNets and Visual Transfomers architectures. These validate our theoretical results, and confirm the potential of our proposed unbiased randomized backpropagation approach for reducing the cost of deep learning.