复杂网络的通用容量边界
A General Capacity Frontier of Complex Networks
浏览论文内容
中文总结 AI 辅助
本研究提出结构容量理论，证明复杂网络存在通用容量边界，该边界可从网络结构向量学习并约束不同领域的动力学过程峰值，且具有跨域泛化性和稳定性。
中文摘要 AI 辅助
从细胞到城市，从生态系统到经济体系，复杂网络展现出定义其经验极限的峰值强度。传统上，估算这些极限需要特定领域的知识。我们证明，广泛的复杂网络共享一个约束这些最大值的容量边界。我们通过提出网络基底结构化系统的结构容量理论来形式化这一规律。这些系统将固定的网络基底与可观测的动力学过程耦合。该边界从网络基底的向量表示中学习，并由动力学过程的向量表示以对数加性方式调制。在一个领域集合上训练的边界能够可靠地约束完全不同领域的经验最大值，而无需观察其峰值强度或模拟其动力学。独立的学习范式收敛于一致的上界。边界性能在扰动下保持稳定，但在故意伪造下退化，且在消融下无性能提升。这些发现支持容量边界作为一种可泛化的约束，描述了网络结构如何跨看似无关的系统约束动力学过程。
英文摘要
From cells to cities, ecosystems to economies, complex networks exhibit peak intensities that define their empirical limit. Estimating these limits traditionally requires domain-specific knowledge. We demonstrate that a wide range of complex networks share a capacity frontier that constrains these maxima. We formalize this regularity by proposing Structural Capacity Theory for Network Substrate Structured Systems. These systems couple a fixed network substrate with an observable dynamical process. The frontier is learned from a vector representation of the network substrate and modulated log-additively by a vector representation of the dynamical process. Frontiers trained on one set of domains reliably bound empirical maxima of entirely different ones without observing their peak intensities or simulating their dynamics. Independent learning paradigms converge on consistent upper bounds. Frontier performance is stable under perturbation, yet degrades under deliberate falsification, with no performance gain under ablation. These findings support the capacity frontier as a generalizable constraint that describes how network structure bounds dynamical processes across otherwise unrelated systems.
发表机构
- Cornell University（康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。
