标题： 残差连接可以证明缓解图神经网络中的过度平滑问题 显示英文标题

标题： Residual connections provably mitigate oversmoothing in graph neural networks

摘要： 图神经网络（GNNs）在处理和表示跨多个领域的图结构数据方面取得了显著的实证成功。 然而，一个被称为“过度平滑”的重大挑战依然存在，在深度GNN中，顶点特征变得几乎无法区分，严重限制了它们的表达能力和实际应用。 在本工作中，我们通过推导归一化顶点相似性度量的显式收敛速率，分析了带有和不带有残差连接的深度GNN的渐近过度平滑率。 我们的分析框架建立在乘法遍历定理的基础上。 此外，我们证明了添加残差连接可以有效缓解或防止在多个广泛的参数分布家族中出现的过度平滑现象。 理论结果得到了数值实验的强烈支持。 显示英文摘要

摘要： Graph neural networks (GNNs) have achieved remarkable empirical success in processing and representing graph-structured data across various domains. However, a significant challenge known as "oversmoothing" persists, where vertex features become nearly indistinguishable in deep GNNs, severely restricting their expressive power and practical utility. In this work, we analyze the asymptotic oversmoothing rates of deep GNNs with and without residual connections by deriving explicit convergence rates for a normalized vertex similarity measure. Our analytical framework is grounded in the multiplicative ergodic theorem. Furthermore, we demonstrate that adding residual connections effectively mitigates or prevents oversmoothing across several broad families of parameter distributions. The theoretical findings are strongly supported by numerical experiments.