Learning accurate path integration in a ring attractor model of the head direction system

Ring attractor models for angular path integration have recently received strong experimental support. To function as integrators, head-direction (HD) circuits require precisely tuned connectivity, but it is currently unknown how such tuning could be achieved. Here, we propose a network model in which a local, biologically plausible learning rule adjusts synaptic efficacies during development, guided by supervisory allothetic cues. Applied to the Drosophila HD system, the model learns to path-integrate accurately and develops a connectivity strikingly similar to the one reported in experiments. The mature network is a quasi-continuous attractor and reproduces key experiments in which optogenetic stimulation controls the internal representation of heading, and where the network remaps to integrate with different gains. Our model predicts that path integration requires supervised learning during a developmental phase. The model setting is general and also applies to architectures that lack the physical topography of a ring, like the mammalian HD system.