  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.
