Continuous representations in small, discrete circuits
Many animals rely on persistent internal representations of continuous angular variables for working memory, motor control, and navigation. Theories have proposed that such representations are maintained by a class of recurrently connected networks called ring attractor networks. These networks rely on large numbers of neurons to maintain continuous and stable representations and to accurately integrate incoming signals. The head direction system of the fruit fly, however, seems to achieve these properties with a remarkably small network. These findings challenge our understanding of ring attractors and their putative implementation in neural circuits. In this talk, I will show analytically how small networks can overcome the constraints of their size to generate a ring attractor and are hence capable of stably maintaining an internal representation of a continuous, periodic variable. Further, I will show how ring attractors emerge in small threshold linear networks through the coordination of a discrete set of line attractors. More broadly, this work informs our understanding of the functional capabilities of small, discrete systems. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-02-04. Recording duration: 00:44:59.
Population dynamics of the thalamic head direction system during drift and reorientation
The head direction (HD) system is classically modeled as a ring attractor network which ensures a stable representation of the animal’s head direction. This unidimensional description popularized the view of the HD system as the brain’s internal compass. However, unlike a globally consistent magnetic compass, the orientation of the HD system is dynamic, depends on local cues and exhibits remapping across familiar environments5. Such a system requires mechanisms to remember and align to familiar landmarks, which may not be well described within the classic 1-dimensional framework. To search for these mechanisms, we performed large population recordings of mouse thalamic HD cells using calcium imaging, during controlled manipulations of a visual landmark in a familiar environment. First, we find that realignment of the system was associated with a continuous rotation of the HD network representation. The speed and angular distance of this rotation was predicted by a 2nd dimension to the ring attractor which we refer to as network gain, i.e. the instantaneous population firing rate. Moreover, the 360-degree azimuthal profile of network gain, during darkness, maintained a ‘memory trace’ of a previously displayed visual landmark. In a 2nd experiment, brief presentations of a rotated landmark revealed an attraction of the network back to its initial orientation, suggesting a time-dependent mechanism underlying the formation of these network gain memory traces. Finally, in a 3rd experiment, continuous rotation of a visual landmark induced a similar rotation of the HD representation which persisted following removal of the landmark, demonstrating that HD network orientation is subject to experience-dependent recalibration. Together, these results provide new mechanistic insights into how the neural compass flexibly adapts to environmental cues to maintain a reliable representation of the head direction.