Geometric Stability of Neural Population Codes: Regional Variation, Behavioral Relevance, and Circuit Dependence

Current models of representational reliability in neural populations focus on temporal stability: whether population centroids are preserved across sessions and days.

This framing leaves a fundamental question unanswered: how reliably does the pairwise distance structure among 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 formalize geometric stability as the Spearman rank correlation between split-half representational dissimilarity matrices (Shesha) and show that it is empirically dissociable from both temporal stability and decoding accuracy.

Across 229 area-session observations spanning 68 brain regions in a visual discrimination task (Steinmetz et al.

2019), geometric stability predicts trial-by-trial neural-behavioral coupling ($\rho = 0.18$, $p = 0.005$) while centroid drift does not ($\rho = 0.002$, $p = 0.976$).

The regional hierarchy, with striatum most stable ($\bar{S} = 0.44$) and hippocampus least ($\bar{S} = 0.19$), runs roughly opposite to the temporal stability hierarchy.

Directionally consistent olfactory data (Bolding \& Franks 2018) motivate an attractor network model in which recurrent excitatory coupling amplifies split-half RDM consistency by completing stimulus patterns from sparse feedforward input ($\rho = +0.64$, $p = 0.010$), providing a circuit-level account of how geometric stability emerges.

These results establish geometric stability as 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 in hippocampal circuits.