Gradient Estimation for Attractor Networks

It has been hypothesized that neural network models with cyclic connectivity may be more powerful than their feed-forward counterparts. This thesis investigates this hypothesis in several ways. We study the gradient estimation and optimization procedures for several variants of these networks. We show how the convergence of the gradient estimation procedures are related to the properties of the networks. Then we consider how to tune the relative rates of gradient estimation and parameter adaptation to ensure successful optimization in these models. We also derive new gradient estimators for stochastic models. First, we port the forward sensitivity analysis method to the stochastic setting. Secondly, we show how to apply measure valued differentiation in order to calculate derivatives of long-term costs in general models on a discrete state space. Throughout, we emphasize how the proper geometric framework can simplify and generalize the analysis of these problems