Gradients without Backpropagation

TL;DR

The paper introduces the forward gradient, a method to compute unbiased gradient estimates using only forward mode automatic differentiation, eliminating backpropagation and speeding up training.

Contribution

It presents the forward gradient technique, enabling gradient computation solely via directional derivatives, reducing computational costs and simplifying the training process.

Findings

Training speed up to twice as fast in some cases

Substantial savings in computation

Effective in various problem settings

Abstract

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.