  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.
