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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 2: Focus Session: Machine Learning for Complex Socio-economic Systems

SOE 2.7: Talk

Monday, March 18, 2024, 11:30–11:45, MA 001

How much do nodes in socioeconomic networks rely on their neighborhood? — •Nimrah Mustafa and Rebekka Burkholz — Stuhlsatzenhaus 5, 66123 Saarbrücken, Germany.

A fundamental question in complex network science is to which degree a node's state is determined by network effects, as interactions with network neighbors may change the node's state. To model the associated process that evolves on the network, Graph Attention Networks (GATs) provide a flexible approach to learning heterogeneous dependencies from data. In practice, however, we find that GATs are limited in their ability to represent such processes due to constrained trainability and failure to recognize the relevance of the neighborhood for a node's state in a task-adaptive manner. We identify the root cause for these phenomena by deriving a conservation law that follows from Noether's theorem. Based on this law, we show how constraints on parameter norms that lead to conditions unfavorable for learning can be mitigated by an initialization scheme and architectural variation of GAT that instead facilitate better trainability. This, in turn, enables us to leverage GATs to identify the degree to which nodes in socioeconomic networks rely on their neighborhood. From a technical perspective, this also allows us to model long-range dependencies and more complex, nonlinear interactions between nodes via deeper GATs.

Keywords: complex networks; Graph Attention Networks; Noether's theorem; trainability; initialization