A Two-Dimensional Bayesian Continuous Attractor Neural Network for Robust Spatial State Estimation

Continuous Attractor Neural Networks (CANNs) have emerged as prominent bio-inspired models for spatial representation, with recent theoretical advances demonstrating their capacity for optimal Bayesian inference. However, the mathematical equivalence between attractor dynamics and optimal Bayesian inference has been largely confined to 1D circular variables. To bridge this gap, we propose a Bayesian CANN in a 2D Euclidean state space. The network conditions required for optimal inference are analytically derived by matching the network dynamics with the continuous-time Kalman-Bucy filter. Crucially, by introducing an advection-reaction operator splitting method, we resolve a velocity-dependent diffusion artifact, thereby preserving Bayesian consistency without artificially degrading the certainty of the internal representation. The proposed 2D Bayesian CANN achieves estimation accuracy comparable to Kalman and particle-based filters while retaining structural robustness to severe sensory conflict. This robustness arises from the linear superposition of conflicting sensory evidence followed by nonlinear attractor dynamics, which suppress dispersed low-confidence activity and realign the localized representation toward dominant sensory cues. These results bridge theoretical neuroscience and engineering state estimation, suggesting a bio-inspired framework for resilient autonomous navigation in unpredictable environments.