Seminar on Graphs are maximally expressive for higher-order interactions скачать в хорошем качестве

Seminar on Graphs are maximally expressive for higher-order interactions

Abstract: In this talk, I discuss a recent work [1] where we demonstrate that graph-based models are fully capable of representing higher-order (multibody) interactions, challenging the common claim that only hypergraphs can capture such dependencies. We emphasize that graphs are not limited to pairwise interactions and that hypergraphs are actually special, more constrained cases of general graph-based representations. We show that phenomena often attributed uniquely to hypergraphs, such as abrupt transitions, can also be reproduced with standard graph models, often even locally tree-like ones. Overall, we suggest that the perceived need for hypergraphs stems from misconceptions about the expressive power of graph-based models and advocate for a clearer distinction between multivariate interactions, parametrized by graphs, and the functions that define them. [1] https://arxiv.org/abs/2602.16937