Bayesian inference in ring attractor networks

Abstract

Efficient 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.

Neural Networks for Navigation: From Connections to Computations

“…The problem with rotational velocity cues is that they cannot support an accurate head direction estimate for very long. When rotational velocity cues are integrated over time, the noise or error associated with these inputs accumulates (Cheng et al 2007, Kutschireiter et al 2022). Thus, for example, when we close our eyes, we can briefly maintain our sense of direction by tracking our rotational movements, but we progressively lose our bearings as we move.…”

Representation and computation in working memory

“…While attractor models of WM have typically been designed to maintain only a point estimate of a stimulus, recent work aims to incorporate uncertainty as well, e.g. represented in the amplitude of the population activity (Carroll et al, 2014;Kutschireiter et al, 2022). In future work, neural models of WM could focus on how this richer representation is used in decision-making; trained recurrent networks have already proven useful to yield mechanistic insights in tandem with accounts of behavioural data (Orhan and Ma, 2019).…”