Bayesian inference in ring attractor networks

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 120; no. 9; p. e2210622120
• Main Authors: Kutschireiter, Anna, Basnak, Melanie A., Wilson, Rachel I., Drugowitsch, Jan
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 28.02.2023
• Subjects: Algorithms; Bayes Theorem; Bayesian analysis; Biological Sciences; Biophysics and Computational Biology; Brain - physiology; Head - physiology; Kalman filters; Memory, Short-Term; Models, Neurological; Neural Networks, Computer; Neuroscience; Physical Sciences; Statistical inference; Tracks (paths); Uncertainty; ring attractor networks; Bayesian inference; working memory; Kalman filter; head direction neurons
• ISSN: 0027-8424; 1091-6490; 1091-6490
• DOI: 10.1073/pnas.2210622120

SignificanceData from human subjects as well as animals show 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 working memory. The representation of uncertainty in this model improves the accuracy of its working memory, as compared to conventional models, because it assigns proper weight to new conflicting evidence. Our model provides an interpretation of observed fluctuations in brain activity, and it makes testable predictions. 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 a 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 retuned 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.