Place Cells as Proximity-Preserving Embeddings: From Multi-Scale Random Walk to Straight-Forward Path Planning

Abstract

The hippocampus enables spatial navigation through place cell populations forming cognitive maps. We propose proximity-preserving neural embeddings to encode multi-scale random walk transitions, where the inner product h(x, t), h(y, t) = q(y|x, t) represents normalized transition probabilities, with h(x, t) as the embedding at location x and q(y|x, t) as the transition probability at scale t. This scale hierarchy mirrors hippocampal dorsoventral organization. The embeddings h(x, t) reduce pairwise spatial proximity into an environmental map, with Euclidean distances preserving proximity information. We use gradient ascent on q(y|x, t) for straight-forward path planning, employing adaptive scale selection for trap-free, smooth trajectories, equivalent to minimizing embedding space distances. Matrix squaring (P_2t = P_t^2) efficiently builds global transitions from local ones (P_1), enabling preplay-like shortcut prediction. Experiments demonstrate localized place fields, multi-scale tuning, adaptability, and remapping, achieving robust navigation in complex environments. Our biologically plausible framework, extensible to theta-phase precession, unifies spatial and temporal coding for scalable navigation.

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