Low-Variance Forward Gradients using Direct Feedback Alignment and Momentum

Supervised learning in Deep Neural Networks (DNNs) is commonly performed using the error Backpropagation (BP) algorithm. The sequential propagation of errors and the transport of weights during the backward pass limits its efficiency and scalability. Therefore, there is growing interest in finding local alternatives to BP. Recently, methods based on Forward-Mode Automatic Differentiation have been proposed, such as the Forward Gradient algorithm and its variants. However, Forward Gradients suffer from high variance in large DNNs, which affects convergence. In this paper, we address the large variance of Forward Gradients and propose the Forward Direct Feedback Alignment (FDFA) algorithm that combines Activity-Perturbed Forward Gradients with Direct Feedback Alignment and momentum to compute low-variance gradient estimates in DNNs. Our results provides both theoretical proof and empirical evidence that our proposed method achieves lower variance compared to previous Forward Gradient techniques. By reducing the variance of gradient estimates, our approach enables faster convergence and better performance when compared to other local alternatives to backpropagation.