Metric space learning in the hippocampus

The hippocampus is the episodic memory and spatial navigation center of the brain. The cognitive map metaphor identifies episodic memory with ``navigation'' through a space of arbitrary learned relationships. However, what structures are admissible as ``cognitive maps'' remains unclear, particularly whether these maps are constrained to obey the same rules as physical space. We hypothesize that the hippocampus learns metric spaces as its cognitive maps. We test this hypothesis by training mice to learn and solve relational queries in a finite metric space which cannot be embedded in 2D Euclidean space, consisting of virtual reality (VR) hallways connected by licking choice ``doors''. By performing two-photon calcium imaging of hippocampal area CA1 during this task, we find behavioral and neural evidence that mice can learn these nonspatial metric spaces. Finally, we construct a modular, ``end-to-end'' model of how the hippocampus (i) segments a stream of high-dimensional, entangled sensory input into discrete concepts via one-shot learning, (ii) learns sequences of these concepts via Hebbian plasticity, and (iii) embeds the structure of the world into the weight matrix of a recurrent network capable of emitting samples (replay) from that structure, which a model-based agent can use to solve reward-seeking tasks. This work experimentally tests a formalization of the widely-used ``cognitive map'' conceptual model decoupled from Euclidean space, with implications for how such maps are used to solve abstract reasoning tasks.