Deep Graph Networks (DGNs) currently dominate the research landscape of learning from graphs, due to their efficiency and ability to implement an adaptive message-passing scheme between the nodes. However, DGNs are typically limited in their ability to propagate and preserve long-term dependencies between nodes, i.e., they suffer from the over-squashing phenomena. This reduces their effectiveness, since predictive problems may require to capture interactions at different, and possibly large, radii in order to be effectively solved. In this work, we present Anti-Symmetric Deep Graph Networks (A-DGNs), a framework for stable and non-dissipative DGN design, conceived through the lens of ordinary differential equations. We give theoretical proof that our method is stable and non-dissipative, leading to two key results: long-range information between nodes is preserved, and no gradient vanishing or explosion occurs in training. We empirically validate the proposed approach on several graph benchmarks, showing that A-DGN yields to improved performance and enables to learn effectively even when dozens of layers are used.

翻译：深度图网络（DGNs）凭借其高效性以及在节点间实现自适应消息传递机制的能力，当前主导了图学习的研究格局。然而，DGNs在传播和保持节点间长程依赖关系方面通常存在局限性，即它们会遭受过压缩（over-squashing）现象的影响。这降低了其有效性，因为预测问题可能需要捕获不同半径（可能较大）范围内的相互作用才能得到有效解决。本文提出了反称深度图网络（Anti-Symmetric Deep Graph Networks, A-DGNs），这是一种基于常微分方程视角设计的稳定且非耗散的DGN框架。我们从理论上证明了该方法的稳定性和非耗散性，从而得出两个关键结果：节点间的长程信息得以保持，且在训练过程中不会出现梯度消失或爆炸。我们在多个图基准数据集上对方法进行了实证验证，结果表明A-DGN能提升性能，即使在数十层网络的情况下也能有效学习。