Abstract

One of the most fundamental concepts in theoretical neuroscience is that of an attractor neural network, in which recurrent synaptic connectivity constrains the joint activity of neurons into a highly restricted repertoire of population activity patterns. In continuous attractor networks, these activity patterns span a continuous, low-dimensional manifold. Neural networks with such dynamics are thought to enable storage, in short-term memory, of low-dimensional continuous variables such as an angle or position.  I will survey several recent works that are concerned with the consequences of noise in such neural networks. In one work, we examined how neural noise affects the dynamics of the oculomotor integrator, a memory network in the brainstem which is responsible for maintenance of a steady eye position between saccades. We showed that noise is expected to drive random diffusion in the state of the network. Consequently, we propose that this is the underlying mechanism behind fixational drift, a form of small eye motion that occurs during fixation. I will also discuss works concerned with memory networks that track an animal's position in space: grid cells in the entorhinal cortex, and place cells in area CA3 of the hippocampus. It is thought that the synaptic connectivity between CA3 place cells supports multiple attractors, each mapped to a different environment. Naively, the embedding of multiple attractors is expected to introduce frozen noise that disrupts the continuity of each attractor. We recently showed that small corrections to the synaptic connectivity can restore the existence of nearly continuous attractor manifolds.