Mining higher-order triadic interactions.

Complex systems often involve higher-order interactions that go beyond pairwise networks. Triadic interactions, where one node regulates the interaction between two others, are a fundamental form of higher-order dynamics found in many biological systems, from neuron-glia communication to gene regulation and ecosystems. However, triadic interactions have so far been mostly neglected. In this article, we propose the Triadic Perceptron Model (TPM) which shows that triadic interactions can modulate the mutual information between the dynamical states of two connected nodes. Leveraging this result, we formulate the Triadic Interaction Mining (TRIM) algorithm to extract triadic interactions from node metadata, and we apply this framework to gene expression data, finding new candidates for triadic interactions relevant for Acute Myeloid Leukemia. Our findings highlight crucial aspects of triadic interactions that are often ignored, offering a framework that can deepen our understanding of complex systems across biology, ecology, and climate science.