ADAPTIVE GEOMETRY OF COGNITIVE MAPS GOVERNS BEHAVIOR

Cognitive maps are internal representations of the external world that support flexible behavior and are most often studied in the hippocampal-entorhinal system. While classical views describe cognitive maps as metric representations of physical space, growing evidence shows that representational geometry is shaped by task demands, reflecting factors such as topology and context rather than physical distance alone. Here, we ask what determines the geometry of cognitive maps and whether this geometry causally guides behavior. We trained a memory-augmented neural network with reinforcement learning on goal-memory navigation tasks while systematically varying environmental structure, sensory information, and task requirements. We analyzed internal representations by comparing representational similarity matrices of population activity to heuristic models, complemented by dimensionality reduction and single-unit analyses. In simple open-field navigation, representations exhibited a metric, Euclidean-like geometry consistent with the classical view. As structural constraints increased, representations shifted toward partitioned, relational geometries emphasizing connectivity over physical distance, and in tasks requiring remembered contextual cues, latent states were organized primarily by abstract task context. Crucially, representational geometry causally guided behavior. When environments changed without distinctive cues, the agent navigated according to its learned belief space rather than the external world, generating systematic and interpretable localization errors that parallel distortions observed in hippocampal place-cell activity. Together, these results support a unified view of cognitive maps as adaptive internal belief spaces whose geometry emerges from task demands, guides behavior, and generates testable predictions for both neural representations and behavioral strategies observed in biological systems.