Coordinated drift of receptive fields during noisy representation learning

Long-term memories and learned behavior are conventionally associated with stable neuronal representations. However, recent experiments showed that neural population codes in many brain areas continuously change even when animals have fully learned and stably perform their tasks. This representational "drift" naturally leads to questions about its causes, dynamics, and functions. Here, we explore the hypothesis that neural representations optimize a representational objective with a degenerate solution space, and noisy synaptic updates drive the network to explore this (near-)optimal space causing representational drift. We illustrate this idea in simple, biologically plausible Hebbian/anti-Hebbian network models of representation learning, which optimize similarity matching objectives, and, when neural outputs are constrained to be nonnegative, learn localized receptive fields (RFs) that tile the stimulus manifold. We find that the drifting RFs of individual neurons can be characterized by a coordinated random walk, with the effective diffusion constants depending on various parameters such as learning rate, noise amplitude, and input statistics. Despite such drift, the representational similarity of population codes is stable over time. Our model recapitulates recent experimental observations in hippocampus and posterior parietal cortex, and makes testable predictions that can be probed in future experiments.