Bayesian inference in ring attractor networks

Anna Kutschireite, Melanie A. Basnak, Rachel I. Wilson, Jan Drugowitsch

Abstract:

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.