Hidden symmetries in network connectivity support ring attractor dynamics in the fly's neural compass

Theoretical models can explain how network structure shapes neural computation, but they typically assume idealized connectivity that is inconsistent with the heterogeneous wiring of biological circuits. We address this issue in the Drosophila head-direction system, a recurrent network with ring-attractor dynamics that enable angular velocity integration. The networks symmetric wiring motifs are reminiscent of classical models, but with additional heterogeneity that should, in principle, destabilize attractor dynamics. Inspired by novel architectures discovered through machine-learning-based optimization, we develop an algorithm that transforms attractor models with symmetric connectivity into functionally equivalent models with heterogeneous connectivity. By replacing each unit with multiple clones that preserve its output, the algorithm embeds hidden symmetries in heterogeneous connectivity, maintaining ring-attractor dynamics and accurate integration. Analysis of multiple fly connectomes provides evidence for duplicated units whose connectivity reflects hidden symmetries, consistent with our theory. Our framework helps reconcile idealized models of neural computation with heterogeneous biological circuits.