Tackling Graph Oversquashing by Global and Local Non-Dissipativity
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 properties of global and local non-dissipativity, that enable the maintenance of a constant information flow rate. Namely, we present SWAN, a uniquely parameterized model GNN with antisymmetry both in space and weight domains, as a means to obtain non-dissipativity. Our theoretical analysis asserts that by achieving 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.
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Long Range Graph Benchmark (LRGB)
