Geometric Stability of Neural Population Codes: Regional Variation, Behavioral Relevance, and Circuit Dependence
Summary
This paper introduces geometric stability as a measure of how reliably pairwise stimulus distances reproduce across trials, demonstrating its behavioral relevance and circuit dependence across brain regions, with an attractor network model explaining its emergence.
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Paper page - Geometric Stability of Neural Population Codes: Regional Variation, Behavioral Relevance, and Circuit Dependence
Source: https://huggingface.co/papers/2606.29655
Abstract
Geometric stability measures the consistency of pairwise stimulus distances across trials, revealing a distinct aspect of neural representation that differs from temporal stability and decoding accuracy.
Current models ofrepresentational reliabilityin neural populations focus ontemporal stability: whetherpopulation centroidsare preserved across sessions and days. This framing leaves a fundamental question unanswered: how reliably does thepairwise distance structureamong stimuli reproduce across independent observations within a session? We argue that this property,geometric stability, constitutes an independent axis of representational analysis that existing frameworks do not capture. We formalizegeometric stabilityas theSpearman rank correlationbetweensplit-half representational dissimilarity matrices(Shesha) and show that it is empirically dissociable from bothtemporal stabilityand decoding accuracy. Across 229 area-session observations spanning 68 brain regions in a visual discrimination task (Steinmetz et al. 2019),geometric stabilitypredictstrial-by-trial neural-behavioral coupling(ρ= 0.18, p = 0.005) while centroid drift does not (ρ= 0.002, p = 0.976). The regional hierarchy, with striatum most stable (S = 0.44) and hippocampus least (S = 0.19), runs roughly opposite to thetemporal stabilityhierarchy. Directionally consistent olfactory data (Bolding \& Franks 2018) motivate anattractor network modelin whichrecurrent excitatory couplingamplifies split-half RDM consistency by completing stimulus patterns from sparsefeedforward input(ρ= +0.64, p = 0.010), providing a circuit-level account of howgeometric stabilityemerges. These results establishgeometric stabilityas a functionally relevant, circuit-dependent property of neural population codes, orthogonal to temporal drift measures and complementary to recent accounts of how recurrent connectivity balances representational stability with sequential dynamics inhippocampal circuits.
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