Recent studies have shown that novel collective behaviors emerge in complex systems due to higher-order interactions. However, the way in which the structural correlations of these interactions shape such behaviors remains a significant gap in current research. To address this, we use signatures of higher-order behaviors (HOBs) to identify the underlying dynamical rules, or higher-order mechanisms (HOMs). In this work, we compare several HOB measures derived from information theory. Utilizing a simplicial SIS contagion model, we demonstrate that simpler, computationally efficient measures can serve as robust indicators of HOMs. We uncover the novel phenomenon of cross-order induced behaviors, where behavioral signatures emerge at interaction orders where no direct mechanism is present. Crucially, these cross-order HOBs are not simply induced by structural correlations -- such as nestedness and hyperedge overlap -- but they appear in the neighborhood of any HOM. Among the information-theoretic measures we tested, synergy is the most reliable indicator of the true order where the underlying mechanism is at play. These findings offer new insights into the relationship between the network structure and observed dynamics of higher-order systems.

翻译：近期研究表明，复杂系统中因高阶相互作用而涌现出新颖的集体行为。然而，这些相互作用的结构相关性如何塑造此类行为，仍是当前研究中的一个重要空白。为此，我们利用高阶行为特征来识别潜在的动力学规则，即高阶机制。在本工作中，我们比较了若干基于信息论推导的高阶行为度量指标。通过使用单纯SIS传播模型，我们证明了更简单、计算效率更高的度量指标可作为高阶机制的稳健指示器。我们揭示了跨阶诱导行为这一新现象，即行为特征出现在不存在直接机制的相互作用阶数上。关键在于，这些跨阶高阶行为并非仅由结构相关性（如嵌套性与超边重叠）所诱导，而是出现在任何高阶机制的邻近区域。在我们测试的信息论度量指标中，协同性是最能可靠指示潜在机制真实作用阶数的指标。这些发现为理解高阶系统的网络结构与观测动力学之间的关系提供了新的见解。