Some neurons have stimulus responses that are stable over days, whereas other neurons have highly plastic stimulus responses. Using a recurrent network model, we explore whether this could be due to an underlying diversity in their synaptic plasticity. We find that, in a network with diverse learning rates, neurons with fast rates are more coupled to population activity than neurons with slow rates. This plasticity-coupling link predicts that neurons with high population coupling exhibit more long-term stimulus response variability than neurons with low population coupling. We substantiate this prediction using recordings from the Allen Brain Observatory, finding that a neuron’s population coupling is correlated with the plasticity of its orientation preference. Simulations of a simple perceptual learning task suggest a particular functional architecture: a stable ‘backbone’ of stimulus representation formed by neurons with low population coupling, on top of which lies a flexible substrate of neurons with high population coupling.