AI 中文总结
该研究揭示稀疏兴奋-抑制阈值重置网络中，带符号突触核的分量弱收敛无法确定快速突触极限，因微观到达顺序差异会引发宏观发放计数差，且该差异可在特定图结构与延迟下持续存在。
AI 中文摘要
带符号突触核的分量弱收敛本身并不能确定稀疏阈值重置网络的快速突触极限。在具有钳制不应性和平滑正延迟核的因果事件协议中，我们构造了两类网络，其兴奋和抑制测度弱收敛到δ₀，而它们的微观到达顺序相反。当x+a-b<θ≤x+a时，目标在兴奋优先的网络中发放，而在抑制优先的网络中不发放。严格余量在目标状态、聚合兴奋/抑制脉冲质量及有界漂移的扰动下保持该响应。该宏观效应在适度稀疏的Dale兼容随机块图（q_N→∞且q_N/N→0）上持续存在，两类网络共享图结构和初始数据。沿每个确定性联合尺度ε_N↓0，它们的平均发放计数相差1/2+o_{L^1}(1)。有界度构造及后续探测表明，该差异是宏观的且可在重置过程中持续。具有有限类的固定正延迟核存在稳定 regime。在 grazing 前，类型混合的稀疏网络收敛到延迟类平均场系统。当λ_N→∞且λ_N/N→0时，有向Erdős–Rényi图给出界O_P(λ_N^{-1/2}+∥π_N−π∥₁)，这将固定延迟的稳定平均与奇异崩溃区分开；在后一情形中，分量弱收敛丢弃了阈值重置响应所需的带符号到达顺序信息。
英文摘要
Componentwise weak convergence of signed synaptic kernels does not, by itself, determine the fast-synapse limit of a sparse threshold-reset network. Within a causal event protocol with clamped refractoriness and smooth positive-delay kernels, we construct two families whose excitatory and inhibitory measures converge weakly to $δ_0$ while their microscopic arrival orders are reversed. A target fires in the excitatory-first family and not in the inhibitory-first family precisely when $x+a-b<θ\le x+a$. Strict margins preserve this response under perturbations of the target state, aggregate E/I pulse masses, and bounded drift. The macroscopic effect persists on a moderately sparse Dale-compatible random block graph with $q_N\to\infty$ and $q_N/N\to0$. The two systems share their graph and initial data. Along every deterministic joint scale $\varepsilon_N\downarrow0$, their population-averaged firing counts differ by $1/2+o_{L^1}(1)$. A bounded-degree construction and a later probe show that the discrepancy is macroscopic and can persist through reset. Fixed positive-delay kernels with finitely many classes admit a stable regime. Before grazing, typewise-mixing sparse networks converge to a delayed class mean-field system. Directed Erdos-Renyi graphs yield the bound $O_P(λ_N^{-1/2}+\|π_N-π\|_1)$ when $λ_N\to\infty$ and $λ_N/N\to0$. This separates stable averaging at a fixed delay from singular collapse. In the latter, componentwise weak convergence discards signed arrival-order information needed by the threshold-reset response.
Comments17 pages, 2 figures
