Graph Neural Networks (GNNs) have succeeded in various computer science applications, yet deep GNNs underperform their shallow counterparts despite deep learning's success in other domains. Over-smoothing and over-squashing are key challenges when stacking graph convolutional layers, hindering deep representation learning and information propagation from distant nodes. Our work reveals that over-smoothing and over-squashing are intrinsically related to the spectral gap of the graph Laplacian, resulting in an inevitable trade-off between these two issues, as they cannot be alleviated simultaneously. To achieve a suitable compromise, we propose adding and removing edges as a viable approach. We introduce the Stochastic Jost and Liu Curvature Rewiring (SJLR) algorithm, which is computationally efficient and preserves fundamental properties compared to previous curvature-based methods. Unlike existing approaches, SJLR performs edge addition and removal during GNN training while maintaining the graph unchanged during testing. Comprehensive comparisons demonstrate SJLR's competitive performance in addressing over-smoothing and over-squashing.

翻译：图神经网络（GNN）在计算机科学领域已取得广泛应用，但深度GNN的性能却不及浅层模型——尽管深度学习在其他领域表现优异。堆叠图卷积层时，过平滑与过挤压是阻碍深层表示学习及远距离节点信息传播的核心挑战。本研究表明，过平滑与过挤压本质上与图拉普拉斯算子的谱隙相关，导致这两种问题存在不可避免的权衡，无法同时缓解。为达成适当折中，我们提出增删边作为一种可行方案。我们引入随机Jost与Liu曲率重连（SJLR）算法，该算法计算高效，且相较于现有基于曲率的方法保留了基本性质。与现有方法不同，SJLR在GNN训练过程中执行边的增删操作，而在测试阶段保持图结构不变。综合对比表明，SJLR在解决过平滑与过挤压方面具有竞争力。