An analysis of the emergence of adaptive Bayesian priors from Hebbian learning in a simple attractor network model

Abstract

We have recently shown that the statistical properties of goal directed reaching in human subjects depends on recent experience in a way that is consistent with the presence of adaptive Bayesian priors (Verstynen and Sabes, 2011). We also showed that when Hebbian (associative) learning is added to a simple line-attractor network model, the network provides both a good account of the experimental data and a good approximation to a normative Bayesian estimator. This latter conclusion was based entirely on empirical simulations of the network model. Here we study the effects of Hebbian learning on the line-attractor model using a combination of analytic and computational approaches. Specifically, we find an approximate solution to the network steady-state. We show numerically that the solution approximates Bayesian estimation. We next show that the solution contains two opposing terms: one that depends on the distribution of recent network activity and one that depends on the current network inputs. These results provide additional intuition for why Hebbian learning mimics adaptive Bayesian estimation in this context.