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.Author summary: Animals rely on navigation for a broad repertoire of behaviors, including foraging, returning home, avoiding threats, finding mates, and moving between familiar locations; in turn, to enable efficient navigation, animals need to maintain an internal representation of navigational variables such as heading. Neural head-direction circuits are often modeled as attractor networks, which maintain a stable “bump” of neural activity representing orientation. However, real sensory inputs are noisy, such that animals must estimate how reliable those inputs are to guide their decision-making. We asked how one neural circuit could both maintain a stable head-direction estimate and represent uncertainty. We developed a spiking neural network model that combines attractor dynamics with sampling-based probabilistic inference. In the model, noisy angular-velocity inputs drive samples that are integrated over time into a head-direction estimate that remains constrained to a circular attractor. This means that fluctuations in the activity bump are not simply noise: they reflect uncertainty in the incoming motion signals. The model also explains how visual landmarks can recalibrate the head-direction representation according to cue reliability, and provides experimentally testable predictions regarding structured voltage correlations, multi-timescale interaction patterns, uncertainty-dependent bump movement, and skewed bump-velocity statistics. Our results suggest that combining attractor dynamics with probabilistic sampling allows neural circuits to represent both an estimate and its uncertainty, providing a general computational mechanism that bridges two traditionally separate frameworks for computation in noisy biological systems.