Population coding and self-organized ring attractors in recurrent neural networks for continuous variable integration

Representing and integrating continuous variables is a fundamental capability of the brain, often relying on ring attractor circuits that maintain a persistent bump of activity. To investigate how such structures can self-organize, we trained a recurrent neural network (RNN) on a ring-based path integration task using population-coded velocity inputs. The network autonomously developed a modular architecture: one subpopulation formed a stable ring attractor to maintain the integrated position, while a second, distinct subpopulation organized into a dissipative control unit that translates velocity into directional signals. Furthermore, systematic perturbations revealed that the precise topological alignment between these modules is essential for reliable integration. Our findings illustrate how functional specialization and biologically plausible representations can emerge from a general learning objective, offering insights into neural self-organization and providing a framework for designing more interpretable and robust neuromorphic systems for navigation and control.