Combining sampling and attractor dynamics in spiking models of head direction systems

Neural populations can maintain stable representations of navigation-related variables while integrating uncertain sensory signals. Experimental evidence showed that the precision of head-direction (HD) representations in flies and mice depends on the reliability of sensory cues, highlighting the influence of input uncertainty in attractor-based neural circuits. How do neural dynamics maintain stability while computing under uncertainty? Here, we propose a spiking neural network that unifies two principles - stability through attraction and uncertainty through fluctuation - and reinterpret the HD circuit as an uncertainty-aware integrator rather than a deterministic compass. Specifically, the network uses sampling-based probabilistic inference, where a neural population represents input uncertainty by rapidly fluctuating among likely hypotheses about the world while preserving a stable representation of head direction along an attractor manifold. This formulation suggests why a classical HD "bump" becomes less precise, namely due to rapid fluctuations, reflecting the uncertainty in angular velocity inputs. Our implementation yields experimentally testable predictions: correlated subthreshold voltage fluctuations, multi-timescale nonlinear interaction patterns, and characteristic statistics of bump movement. By combining probabilistic inference with attractor dynamics within one single circuit, our framework suggests how neural populations across species can represent an estimate and its uncertainty through fluctuations while maintaining stability, which could be a general principle for uncertainty-aware computation in noisy biological systems.