Contrastive Hebbian Learning with Random Feedback Weights

TL;DR

This paper introduces a novel variant of contrastive Hebbian learning that replaces symmetric feedback weights with random matrices, enhancing biological plausibility and demonstrating effective learning in various tasks.

Contribution

It proposes random contrastive Hebbian learning, removing the need for weight symmetry and analyzing the effects of random feedback matrices on learning performance.

Findings

Successfully solved Boolean logic, classification, and autoencoding tasks.

Random feedback matrices influence learning dynamics and effectiveness.

Pseudospectra analysis reveals how randomness impacts convergence.

Abstract

Neural networks are commonly trained to make predictions through learning algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by gradient backpropagation, is based on Hebb's rule and the contrastive divergence algorithm. It operates in two phases, the forward (or free) phase, where the data are fed to the network, and a backward (or clamped) phase, where the target signals are clamped to the output layer of the network and the feedback signals are transformed through the transpose synaptic weight matrices. This implies symmetries at the synaptic level, for which there is no evidence in the brain. In this work, we propose a new variant of the algorithm, called random contrastive Hebbian learning, which does not rely on any synaptic weights symmetries. Instead, it uses random matrices to transform the feedback signals during the clamped phase, and the neural dynamics are described by first order non-linear differential equations. The algorithm is experimentally verified by solving a Boolean logic task, classification tasks (handwritten digits and letters), and an autoencoding task. This article also shows how the parameters affect learning, especially the random matrices. We use the pseudospectra analysis to investigate further how random matrices impact the learning process. Finally, we discuss the biological plausibility of the proposed algorithm, and how it can give rise to better computational models for learning.