On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems
This addresses a key bottleneck in GNNs for tasks requiring long-range dependencies, offering a novel solution with theoretical and empirical validation.
The paper tackles the problem of oversquashing in Graph Neural Networks, where information flow between distant nodes decays exponentially, by introducing SWAN, a model with antisymmetry properties that maintains constant information flow, resulting in improved performance on benchmarks emphasizing long-range interactions.
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.