Precise Spatial Memory in Local Random Networks

Abstract: Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of the most well-known modeling frameworks for persistent activity, have been able to model crucial aspects of such spatial memory. These models tend to require highly structured or regular synaptic architectures. In contrast, we elaborate a geometrically-embedded model with a local but otherwise random connectivity profile which, combined with a global regulation of the mean firing rate, produces localized, finely spaced discrete attractors that effectively span a 2D manifold. We demonstrate how the set of attracting states can reliably encode a representation of the spatial locations at which the system receives external input, thereby accomplishing spatial memory via attractor dynamics without synaptic fine-tuning or regular structure. We measure the network's storage capacity and find that the statistics of retrievable positions are also equivalent to a full tiling of the plane, something hitherto achievable only with (approximately) translationally invariant synapses, and which may be of interest in modeling such biological phenomena as visuospatial working memory in two dimensions.