神經群體編碼的幾何穩定性：區域變異、行為相關性與電路依賴性

摘要

當前神經群體表徵可靠性的模型聚焦於時間穩定性：即群體質心在不同場次與天數之間是否得以保存。此一架構遺留了一個根本問題未解：同一場次內獨立觀測之間，刺激的成對距離結構重現的可靠性如何？我們主張，此一屬性——幾何穩定性——構成表徵分析中的獨立軸向，而現有框架未能捕捉。我們將幾何穩定性形式化為分裂半樣本表徵差異矩陣（Shesha）之間的斯皮爾曼等級相關，並顯示其在經驗上可與時間穩定性及解碼正確率分離。在視覺辨識任務（Steinmetz et al. 2019）中，涵蓋229個區域-場次觀察、跨越68個腦區，幾何穩定性可預測逐試次的神經-行為耦合（ρ = 0.18, p = 0.005），而質心漂移則無此預測力（ρ = 0.002, p = 0.976）。區域階層中，紋狀體最穩定（S = 0.44），海馬體最不穩定（S = 0.19），其排序大致與時間穩定性的階層相反。來自嗅覺資料（Bolding & Franks 2018）的方向一致結果，啟發了一個吸引子網路模型，其中迴旋興奮性耦合透過從稀疏前饋輸入中完成刺激模式，增強了分裂半樣本RDM的一致性（ρ = +0.64, p = 0.010），從而提供了幾何穩定性如何產生的電路層級解釋。這些結果確立了幾何穩定性為神經群體編碼中一種具功能相關性、依賴電路特性的屬性，與時間漂移測量正交，並補充了近期關於迴旋連結如何在海馬電路中平衡表徵穩定性與序列動態的論述。

English

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 (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 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 (ρ= +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.