Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli which caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. In this paper we present a method for learning to approximate a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of probabilistic population codes to compute Bayes' rule, and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem, and show how the hidden layer of the neural network develops tuning curves which are consistent with findings in experimental neuroscience.