Oscillatory neurocomputing with ring attractors: a network architecture for mapping locations in space onto patterns of neural synchrony

Abstract

Theories of neural coding seek to explain how states of the world are mapped onto states of the brain. Here, we compare how an animal's location in space can be encoded by two different kinds of brain states: population vectors stored by patterns of neural firing rates, versus synchronization vectors stored by patterns of synchrony among neural oscillators. It has previously been shown that a population code stored by spatially tuned ‘grid cells’ can exhibit desirable properties such as high storage capacity and strong fault tolerance; here it is shown that similar properties are attainable with a synchronization code stored by rhythmically bursting ‘theta cells’ that lack spatial tuning. Simulations of a ring attractor network composed from theta cells suggest how a synchronization code might be implemented using fewer neurons and synapses than a population code with similar storage capacity. It is conjectured that reciprocal connections between grid and theta cells might control phase noise to correct two kinds of errors that can arise in the code: path integration and teleportation errors. Based upon these analyses, it is proposed that a primary function of spatially tuned neurons might be to couple the phases of neural oscillators in a manner that allows them to encode spatial locations as patterns of neural synchrony.

Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex

“…The phase of other interneurons would be updated consistently so that at a turning location, the stellate activity could transition to interacting with an interneuron with the correct connectivity and phase to allow movement in the opposite direction. Thus, the update of position owing to rebound spiking needs to interact with phase reset of cells responding to other directions, consistent with previous oscillatory interference models [5] and ring attractor models [6,28,61]. In figure 4, a single interneuron received output from a full stellate cell population (e.g.…”

Space in the brain: how the hippocampal formation supports spatial cognition

“…In general, the view that spatial translation might be encoded using the theta oscillation remains influential and controversial. In this special issue, several authors explore this possibility [36,41,42], whereas others take issue with it [43]. Jacobs in this issue [44] considers the possibility that there is a navigation-related oscillation in humans which is homologous to rodent theta, but which occurs at a lower frequency [45,46].…”

“…Several explore how their characteristic firing patterns might be derived and maintained, including that in different environments [41,43,97,99]. What is the function of grid cells?…”

“…Indeed, Blair et al [41] put forward one such model in which populations of interconnected theta cells form ring attractors within which the phases of theta bursts are modulated by the velocity of movement. The joint activity of these cells constitutes a synchrony code for location and, when they converge on a grid cell, both spatial periodicity and temporal properties are captured.…”

Spatial Theta Cells in Competitive Burst Synchronization Networks: Reference Frames from Phase Codes

“…The Mehta mechanism can yield highly correlated rate and phase, 388 which raised the question whether temporal codes carry information distinct from firing rate. In 389 place-field phase precession, there is evidence that phase and rate distinctly encode distance 390 and speed (Huxter et al, 2003), which inspired the oscillatory interference theory whereby path synchrony into the firing-rate representations of grid and place cells (Blair et al, 2008(Blair et al, , 2014.…”