A Bayesian perspective on the ring attractor for heading-direction tracking in the Drosophila central complex

Abstract

SummaryEfficient navigation requires animals to track their position, velocity and heading direction (HD). Bayesian inference provides a principled framework for estimating these quantities from unreliable sensory observations, yet little is known about how and where Bayesian algorithms could be implemented in the brain’s neural networks. Here, we propose a class of recurrent neural networks that track both a dynamic HD estimate and its associated uncertainty. They do so according to a circular Kalman filter, a statistically optimal algorithm for circular estimation. Our network generalizes standard ring attractor models by encoding uncertainty in the amplitude of a bump of neural activity. More generally, we show that near-Bayesian integration is inherent in ring attractor networks, as long as their connectivity strength allows them to sufficiently deviate from the attractor state. Furthermore, we identified the basic network motifs that are required to implement Bayesian inference, and show that these motifs are present in the Drosophila HD system connectome. Overall, our work demonstrates that the Drosophila HD system can in principle implement a dynamic Bayesian inference algorithm in a biologically plausible manner, consistent with recent findings that suggest ring-attractor dynamics underlie the Drosophila HD system.