  Message passing mechanism contributes to the success of GNNs in various
applications, but also brings the oversquashing problem. Recent works combat
oversquashing by improving the graph spectrums with rewiring techniques,
disrupting the structural bias in graphs, and having limited improvement on
oversquashing in terms of oversquashing measure. Motivated by unitary RNN, we
propose Graph Unitary Message Passing (GUMP) to alleviate oversquashing in GNNs
by applying unitary adjacency matrix for message passing. To design GUMP, a
transformation is first proposed to make general graphs have unitary adjacency
matrix and keep its structural bias. Then, unitary adjacency matrix is obtained
with a unitary projection algorithm, which is implemented by utilizing the
intrinsic structure of unitary adjacency matrix and allows GUMP to be
permutation-equivariant. Experimental results show the effectiveness of GUMP in
improving the performance on various graph learning tasks.
