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.

翻译：消息传递机制促成了图神经网络（GNN）在各种应用中的成功，但也带来了过度压缩问题。近期研究通过重连技术改进图谱以对抗过度压缩，破坏了图中的结构偏差，且在过度压缩度量上对过度压缩问题的改进有限。受酉循环神经网络（Unitary RNN）启发，我们提出图统一消息传递（GUMP），通过应用酉邻接矩阵进行消息传递来缓解GNN中的过度压缩问题。为设计GUMP，首先提出一种变换使一般图具有酉邻接矩阵并保持其结构偏差，随后通过利用酉邻接矩阵的内在结构并保证GUMP具有置换等变性的酉投影算法获得酉邻接矩阵。实验结果表明，GUMP在提升多种图学习任务性能方面具有有效性。