Velocity Integration in a Multilayer Neural Field Model of Spatial Working Memory

We analyze a multilayer neural field model of spatial working memory, focusing on the impact of interlaminar connectivity, spatial heterogeneity, and velocity inputs. Models of spatial working memory typically employ networks that generate persistent activity via a combination of local excitation and lateral inhibition. Our model comprises a multilayer set of equations that describes connectivity between neurons in the same and different layers using an integral term. The kernel of this integral term then captures the impact of different interlaminar connection strengths, spatial heterogeneity, and velocity input. We begin our analysis by focusing on how interlaminar connectivity shapes the form and stability of (persistent) bump attractor solutions to the model. Subsequently, we derive a low-dimensional approximation that describes how spatial heterogeneity, velocity input, and noise combine to determine the position of bump solutions. The main impact of spatial heterogeneity is to break the translation symmetry of the network, so bumps prefer to reside at one of a finite number of local attractors in the domain. With the reduced model in hand, we can then approximate the dynamics of the bump position using a continuous time Markov chain model that describes bump motion between local attractors. While heterogeneity reduces the effective diffusion of the bumps, it also disrupts the processing of velocity inputs by slowing the velocity-induced propagation of bumps. However, we demonstrate that noise can play a constructive role by promoting bump motion transitions, restoring a mean bump velocity that is close to the input velocity.