The geometry of knowledge in the hippocampal-prefrontal system

Decision making is associated with frontal brain circuits ^1–5 and spatial navigation with the hippocampus ^6–8 . In addition, recent work in spatial decision making tasks ^9–11 found single neurons in both areas encoding space conjunctively with other task-relevant variables. However, circuit function is not determined by tuning alone, but also by representational geometry, i.e. the representation of task-relevant variables in neural state space. Here, using Neuropixel ^12,13 recordings in a complex spatial decision making task combined with nonlinear dimensionality reduction ^8,14 , we show an intrinsically low-dimensional neural manifold in medial prefrontal cortex (mPFC) on which key task variables were represented as smooth gradients. This geometry resembled the hippocampal (HPC) map. The mPFC and HPC manifolds from one mouse can predict the behavior across other mice and brain areas. A non-linear representational map between the mPFC and HPC manifolds demonstrates alignment in time. Our work suggests that the representational geometry in HPC and mPFC is distributed and time-aligned using low-dimensional neural codes.