发表机构
École Normale Supérieure, Université PSL; University of Parma（巴黎高等师范学院，巴黎文理研究大学; 帕尔马大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一个可扩展生成框架，通过叠加度量衰减与潜在功能几何，推断加权网络中的隐藏坐标和耦合参数，并在果蝇脑、电网和航空网络中揭示连续的社会-空间拓扑谱。
AI 中文摘要
物理约束和功能需求在现实世界的网络中不断共同演化，然而经验拓扑很少符合纯粹平面网格或无约束关系空间的理想化二分法。在此，我们构建了一个可扩展的生成框架，以解决加权网络中社会-空间推断的逆问题。通过将显式的度量衰减与一个未观测的潜在功能几何结构叠加，我们联合重建隐藏的节点坐标，并推断一个耦合参数 $\lambda \in [0, 1]$，该参数量化了由功能亲和力相对于地理距离衰减所驱动的连接份额。我们的确定性流程将基于物理信息的谱初始化（应用于空间残差）与混合优化（Adam 和 L-BFGS）以及基于经验 Fisher 曲率的轮廓似然置信区间相结合。在多个不同的经验系统中，该框架解析了社会-空间拓扑的连续谱：在果蝇全脑连接组中，无监督推断揭示了从度量感觉外围到无约束联想神经纤维网的架构层级；在欧洲电网中，度量耦合在严重的线路修剪下保持不变，而拓扑重连则引发 $\lambda$ 的爆炸性激增，暴露了具有欺骗性的渗流鲁棒性；在全球航空中，COVID-19 疫情期间的时间追踪捕捉到了向局部度量连接的突然系统性空间化。总之，这些结果确立了我们的框架作为复杂网络系统中结构组织、物理退化和动态弹性的原则性、可扩展的诊断工具。
英文摘要
Complex networks balance metric wiring costs against functional routing demands, rarely conforming to idealized dichotomies of pure planar grids or unconstrained topologies. Yet, existing latent-space models remain computationally bottlenecked by stochastic sampling on small, unweighted graphs. Here, we formulate a scalable generative framework to solve the inverse problem of spatio-functional inference in weighted networks. By coupling explicit metric spaces with an unobserved latent geometry, we jointly reconstruct hidden coordinates and infer a coupling parameter $λ\in [0, 1]$, quantifying the connectivity propensity explained by functional affinity conditioned on metric distance decay. Our deterministic pipeline pairs a physics-informed spectral residual initialization with hybrid first- and quasi-Newton optimization. Across diverse empirical systems, the framework reveals a continuous spatio-functional spectrum. In the Drosophila melanogaster whole-brain connectome, it resolves an architectural progression from metric-constrained sensory circuits to specialized associative and chemo-affinity neuropils. In the continental European power grid, line pruning preserves a strictly metric baseline ($\hatλ \approx 0$), whereas topological rewiring drives a sharp surge in $\hatλ$, demonstrating that macroscopic component connectivity can mask spatial degradation. Finally, tracking global aviation throughout the COVID-19 pandemic captures dynamic regime shifts toward localized metric connectivity, establishing a unified diagnostic to probe structural organization and resilience in spatially embedded networks.
