Credit Assignment via Neural Manifold Noise Correlation

TL;DR

This paper introduces neural manifold noise correlation (NMNC), a biologically plausible method for credit assignment that improves learning efficiency by restricting perturbations to neural manifolds, aligning with neurobiological observations.

Contribution

The paper proposes NMNC, a novel credit assignment method that uses manifold-restricted perturbations, enhancing scalability and biological plausibility in neural networks.

Findings

NMNC outperforms vanilla noise correlation in image classification tasks.

Neural activity in trained networks aligns with the neural manifold.

Manifold dimensionality scales slowly with network size.

Abstract

Credit assignment--how changes in individual neurons and synapses affect a network's output--is central to learning in brains and machines. Noise correlation, which estimates gradients by correlating perturbations of activity with changes in output, provides a biologically plausible solution to credit assignment but scales poorly as accurately estimating the Jacobian requires that the number of perturbations scale with network size. Moreover, isotropic noise conflicts with neurobiological observations that neural activity lies on a low-dimensional manifold. To address these drawbacks, we propose neural manifold noise correlation (NMNC), which performs credit assignment using perturbations restricted to the neural manifold. We show theoretically and empirically that the Jacobian row space aligns with the neural manifold in trained networks, and that manifold dimensionality scales slowly with network size. NMNC substantially improves performance and sample efficiency over vanilla noise correlation in convolutional networks trained on CIFAR-10, ImageNet-scale models, and recurrent networks. NMNC also yields representations more similar to the primate visual system than vanilla noise correlation. These findings offer a mechanistic hypothesis for how biological circuits could support credit assignment, and suggest that biologically inspired constraints may enable, rather than limit, effective learning at scale.