Neural population tuning statistics as priors for multitask generalization

Neural populations exhibit heterogeneous tuning: Neurons differ in their selectivity, gain, and in how their preferred inputs are distributed across stimulus or latent-variable space. While this heterogeneity has been studied extensively in the context of encoding precision, its implications for learning and generalization are less well-understood. Here, we develop a probabilistic theory that links a neural population's tuning statistics to its inductive bias: in large populations, the tuning statistics induce a kernel and, equivalently, a prior of a generative model over functions. This prior in turn predicts the population's ability to generalize across a distribution of related tasks. Our theory determines the population tuning statistics that minimize the generalization error over a distribution of functions. We further present a normative account of tuning adaptation inspired by our probabilistic approach, showing that tuning changes that maximize the marginal likelihood of observed data systematically reduce generalization error relative to non-adapting populations. Applied to the adaptation of hippocampal spatial representations in a reward learning task, we found that our theory could explain the over-representation of rewarding locations through experience in an environment with a localized reward. We further demonstrate how different components of the population's generative model differentially impact the speed and magnitude of tuning adaptation. Overall, our work proposes a novel connection between tuning variability and a population's ability to learn and to generalize across tasks and develops a Bayesian theory of tuning adaptation in neural populations during learning.