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arXiv · 2506.04943

The Hippocampal Place Field Gradient: An Eigenmode Theory Linking Grid Cell Projections to Multiscale Learning

Shujun Zhou·Guozhang Chen
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Abstract

The hippocampus encodes space through a striking gradient of place field sizes along its dorsal-ventral axis, yet the principles generating this continuous gradient from discrete grid cell inputs remain debated. We propose a unified theoretical framework establishing that hippocampal place fields arise naturally as linear projections of grid cell population activity, interpretable as eigenmodes. Critically, we demonstrate that a frequency-dependent decay of these grid-to-place connection weights naturally transforms inputs from discrete grid modules into a continuous spectrum of place field sizes. This multiscale organization is functionally significant: we reveal it shapes the inductive bias of the population code, balancing a fundamental trade-off between precision and generalization. Mathematical analysis and simulations demonstrate an optimal place field size for few-shot learning, which scales with environment structure. Our results offer a principled explanation for the place field gradient and generate testable predictions, bridging anatomical connectivity with adaptive learning in both biological and artificial intelligence.

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Shujun Zhou, Guozhang Chen. 2025-06-05. The Hippocampal Place Field Gradient: An Eigenmode Theory Linking Grid Cell Projections to Multiscale Learning. https://arxiv.org/abs/2506.04943

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