Can Forward Gradient Match Backpropagation?

TL;DR

This paper explores the use of biased directional guesses from local auxiliary networks to improve forward gradient methods for neural network training, aiming to match backpropagation performance.

Contribution

It introduces a method to bias gradient guesses using local feedback, enhancing forward gradient accuracy and effectiveness in neural network training.

Findings

Biased gradient guesses from local networks significantly outperform random guesses.

Using local loss feedback improves forward gradient estimates.

The approach enhances training efficiency without backpropagation.

Abstract

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.