Bayesian inference in ring attractor networks

Working memories are thought to be held in attractor networks in the brain. These attractors should keep track of the uncertainty associated with each memory, so as to weigh it properly against conflicting new evidence. However, conventional attractors do not represent uncertainty. Here we show how uncertainty could be incorporated into an attractor, specifically a ring attractor that encodes head direction. First, we introduce the first rigorous normative framework (the circular Kalman filter) for benchmarking the performance of a ring attractor under conditions of uncertainty. Next we show that the recurrent connections within a conventional ring attractor can be re-tuned to match this benchmark. This allows the amplitude of network activity to grow in response to confirmatory evidence, while shrinking in response to poor-quality or strongly conflicting evidence. This “Bayesian ring attractor” performs near-optimal angular path integration and evidence accumulation. Indeed, we show that a Bayesian ring attractor is consistently more accurate than a conventional ring attractor. Moreover, near-optimal performance can be achieved without exact tuning of the network connections. Finally, we use large-scale connectome data to show that the network can achieve near-optimal performance even after we incorporate biological constraints. Our work demonstrates how attractors can implement a dynamic Bayesian inference algorithm in a biologically plausible manner, and it makes testable predictions with direct relevance to the head direction system, as well as any neural system that tracks direction, orientation, or periodic rhythms.Significance StatementData from human subjects as well as animals shows that working memories are associated with a sense of uncertainty. Indeed, a sense of uncertainty is what allows an observer to properly weigh new evidence against their current memory. However, we do not understand how the brain tracks uncertainty. Here we describe a simple and biologically plausible network model that can track the uncertainty associated with a working memory. The representation of uncertainty in this model improves the accuracy of its working memory, as compared to conventional models, because it assigns the proper weight to new conflicting evidence. Our model provides a new interpretation for observed fluctuations in brain activity, and it makes testable new predictions.