Hyperbolic Neural Population Geometry Benefits Computation

2026-06-08

AI Summary

This study investigates the origins of hyperbolic geometric structure in hippocampal neural population activity and its implications for downstream computation. By constructing a tuning curve model that induces hyperbolic geometry and integrating modern Hopfield networks with minimum mean squared error estimation, the work provides the first theoretical account of the neural mechanisms underlying this geometric organization. Building on this insight, the authors propose a novel associative memory model defined in hyperbolic space, which substantially enhances both memory capacity and the precision of spatial information decoding. These findings offer theoretical support for the hypothesis that animals exploit an intrinsic hyperbolic cognitive map to encode spatial representations.

Abstract

Neural population geometry shapes downstream computation. Recent empirical findings in neurobiology suggest that a hyperbolic structure underlies population activity in the hippocampus. Here we provide a theoretical framework for this phenomenon. First, we propose a plausible construction of hippocampal tuning curves that statistically induces hyperbolic geometry. Next, we establish a connection between neural decoding and associative memory by demonstrating that the Modern Hopfield Network update rule computes the minimum mean-squared-error (MMSE) estimator. Finally, we introduce a novel associative memory model defined in hyperbolic space that yields significantly larger capacity than leading models. Our results suggest that animals encode spatial information as a latent hyperbolic cognitive map, improving both memory capacity and decoding accuracy.

Problem

• hyperbolic geometry
• neural population
• hippocampus
• associative memory
• cognitive map

Innovation

• hyperbolic geometry
• neural population coding
• associative memory
• Modern Hopfield Network
• cognitive map