08 February 2023
Graphs are an extremely powerful tool to represent systems of relations and interactions and are extensively employed in many domains. For example, they can model social networks, molecular structures, protein-protein interaction networks, recommender systems, and traffic networks. For that reason, representation learning for graphs has become one of the most prominent fields in machine learning. The primary challenge in this field is how we capture and encode structural information in the learning model.
Common methods used in representation learning for graphs usually employ Deep Graph Networks (DGNs). They currently dominate the research landscape of learning from graphs, due to their efficiency and ability to implement an adaptive message-passing scheme between the nodes. However, DGNs are typically limited in their ability to propagate and preserve long-term dependencies between nodes, i.e., they suffer from the over-squashing phenomena. This reduces their effectiveness, since predictive problems may require capturing interactions at different, and possibly large, radii in order to be effectively solved.
In this work, EMERGE partners from the University of Pisa present the Anti-Symmetric Deep Graph Network (A-DGN), a framework for effective long-term propagation of information in DGN architectures designed through the lens of ordinary differential equations (ODEs). Leveraging the connections between ODEs and deep neural architectures, they provide theoretical conditions for realizing a stable and non-dissipative ODE system on graphs using anti-symmetric weight matrices.
The authors empirically validate the proposed approach on several graph benchmarks, showing that A-DGN yields improved performance and enables to learn effectively even when dozens of layers are used.
Read the paper: https://doi.org/10.48550/arXiv.2210.09789
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