发表机构
Universitat Rovira i Virgili; Luiss University; Central European University; Department ICITA, Università degli Studi “Roma Tre”; “Enrico Fermi” Research Center - CREF（罗维拉-依希尔维尔蒂大学; 卢伊斯大学; 中欧大学; 罗马第三大学ICITA系; 恩里科·费米研究中心-CREF）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文论证高阶相互作用模型中，形式可约性不等于简化，模型选择需基于完整结构-动力学模型的简约性及相对科学问题的充分性，高阶表示在微观信息相关时更直接、可解释且简约。
AI 中文摘要
当前关于高阶相互作用的争论提出了一个基本问题：通过群体相互作用组织的系统何时能被忠实地表示在图论框架内？最近的研究结果表明，图描述能够精确再现高阶动力学或保留选定的宏观可观测量。然而，可约性并不必然意味着简化，因为从相互作用结构中移除的信息可能以有效动力学中的复杂性形式重新出现，而嵌套性、异质性和跨阶相关性等结构特征可能因约化而被掩盖。我们认为，仅凭形式上的可表示性不足以作为模型选择的标准。“更简单”和“等价”都是依赖于所提问题的概念：简约性必须针对完整的结构-动力学模型进行评估，而充分性必须相对于科学问题所需的观测量、尺度和机制来定义。因此，一个约化模型可能完全足以定位相变或识别普适类，但不足以再现微观轨迹、瞬态动力学或结构-功能关系。当群体结构携带相关的微观信息时，高阶表示可能仍然是最直接、可解释且简约的描述，也是理解微观组织如何产生宏观行为与功能的自然框架。
英文摘要
The current debate on higher-order interactions raises a fundamental question: when can systems organized through group interactions be faithfully represented within a graph-based formalism? Recent results show that graph descriptions can reproduce higher-order dynamics exactly or preserve selected macroscopic observables. Yet reducibility does not necessarily imply simplification, as information removed from the interaction structure may reappear as complexity in the effective dynamics, while structural features such as nestedness, heterogeneity, and cross-order correlations may be obscured by the reduction. We argue that formal representability alone is insufficient as a criterion for model choice. Both "simpler" and "equivalent" are question-dependent notions: parsimony must be assessed for the complete structure-dynamics model, and adequacy must be defined relative to the observables, scales, and regimes required by the scientific question. A reduced model may therefore be fully adequate for locating a phase transition or identifying a universality class while being inadequate for reproducing microscopic trajectories, transient dynamics, or structure-function relations. When group structure carries relevant microscopic information, higher-order representations may remain the most direct, interpretable, and parsimonious description, as well as the natural framework for understanding how microscopic organization gives rise to macroscopic behavior and functionality.
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