Credit Assignment via Neural Manifold Noise Correlation

Credit assignment, the process of determining how changes in individual neurons and synapses influence a network’s output, is central to learning in brains and machines. Noise correlation-based methods, which estimate gradients by correlating perturbations of activity with changes in output, provide 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.

When an AI system or brain makes an error, it must figure out which internal components should change to do better next time. Backpropagation solves this problem in artificial neural networks, but it is not considered a fully plausible model of how the brain learns. A more biologically plausible approach is to use small random changes or noise in neural activity to estimate which changes would improve performance. A major obstacle is that random changes in all possible directions become inefficient in large networks. We investigate a different strategy inspired by the fact that brain activity is highly structured: neurons tend to vary together along a relatively small number of patterns. We show that the signals needed for learning are also concentrated along these patterns. Based on this, we introduce a learning algorithm called neural manifold noise correlation, which restricts random perturbations to this low-dimensional activity structure. This method improves the efficiency of perturbation-based learning and leads to more brain-like neural activity patterns. Overall, this work suggests a possible link between structured neural variability in the brain and the ability of biological circuits to learn from experience.