On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems

A common problem in Message-Passing Neural Networks is oversquashing -- the limited ability to facilitate effective information flow between distant nodes. Oversquashing is attributed to the exponential decay in information transmission as node distances increase. This paper introduces a novel perspective to address oversquashing, leveraging dynamical systems properties of global and local non-dissipativity, that enable the maintenance of a constant information flow rate. We present SWAN, a uniquely parameterized GNN model with antisymmetry both in space and weight domains, as a means to obtain non-dissipativity. Our theoretical analysis asserts that by implementing these properties, SWAN offers an enhanced ability to transmit information over extended distances. Empirical evaluations on synthetic and real-world benchmarks that emphasize long-range interactions validate the theoretical understanding of SWAN, and its ability to mitigate oversquashing.

Authors

• Alessio Gravina University of Pisa
• Moshe Eliasof University of Cambridge
• Claudio Gallicchio University of Pisa
• Davide Bacciu University of Pisa
• Carola-Bibiane Schönlieb Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK

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