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

TL;DR

This paper presents a theoretical framework explaining how hippocampal place fields form a gradient from grid cell inputs, linking neural projections to multiscale spatial learning and providing insights into biological and artificial intelligence systems.

Contribution

It introduces a novel eigenmode-based model showing how grid-to-place projections create a continuous spectrum of place field sizes through frequency-dependent decay, explaining the hippocampal gradient.

Findings

Place fields arise as eigenmodes of grid cell activity.

A frequency-dependent decay transforms discrete grid modules into a continuous size spectrum.

Optimal place field size enhances few-shot learning, scaling with environment complexity.

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.