Graph Neural Networks (GNNs) have been shown to achieve competitive results to tackle graph-related tasks, such as node and graph classification, link prediction and node and graph clustering in a variety of domains. Most GNNs use a message passing framework and hence are called MPNNs. Despite their promising results, MPNNs have been reported to suffer from over-smoothing, over-squashing and under-reaching. Graph rewiring and graph pooling have been proposed in the literature as solutions to address these limitations. However, most state-of-the-art graph rewiring methods fail to preserve the global topology of the graph, are neither differentiable nor inductive, and require the tuning of hyper-parameters. In this paper, we propose DiffWire, a novel framework for graph rewiring in MPNNs that is principled, fully differentiable and parameter-free by leveraging the Lov\'asz bound. The proposed approach provides a unified theory for graph rewiring by proposing two new, complementary layers in MPNNs: CT-Layer, a layer that learns the commute times and uses them as a relevance function for edge re-weighting; and GAP-Layer, a layer to optimize the spectral gap, depending on the nature of the network and the task at hand. We empirically validate the value of each of these layers separately with benchmark datasets for graph classification. We also perform preliminary studies on the use of CT-Layer for homophilic and heterophilic node classification tasks. DiffWire brings together the learnability of commute times to related definitions of curvature, opening the door to creating more expressive MPNNs.

翻译：显示神经网图( GNNs) 是为了实现具有竞争力的结果, 以解决与图表有关的任务, 如节点和图表分类、 链接预测、 节点和图表组合等。 大多数 GNNs 使用信息传递框架, 因而被称为 MPNNs 。 尽管其结果令人乐观, MPNes 却被报告为过度移动、 过度抖动和影响不足。 文献中提出了图表重新连线和图集作为解决这些限制的解决方案。 然而, 大多数最先进的图形重新连线方法未能保存图表的全球表层, 既不不同, 也不感性, 需要调整超分数参数框架 。 在本文中, 我们提议Differal Wirre, 通过利用Lov\' as block 来重新连结图解。 拟议的方法为图表重新连线提供了一种统一理论, 在 MPNS 中提出两个新的、 互补的层次: CT 明示- Layeral- deal, 也要求调整超文本 定义, 学习 GServilal- brealalalal 任务, ladeal- 和 liver ladeal- real- ladeal- ladeal ladeal- lex legal- legal- legal- labal- legal- legal- lection 和 legal- legal- legal- legal- legal- legal- legal) 。