Graph neural networks (GNNs) have shown state-of-the-art performances in various applications. However, GNNs often struggle to capture long-range dependencies in graphs due to oversmoothing. In this paper, we generalize the concept of oversmoothing from undirected to directed graphs. To this aim, we extend the notion of Dirichlet energy by considering a directed symmetrically normalized Laplacian. As vanilla graph convolutional networks are prone to oversmooth, we adopt a neural graph ODE framework. Specifically, we propose fractional graph Laplacian neural ODEs, which describe non-local dynamics. We prove that our approach allows propagating information between distant nodes while maintaining a low probability of long-distance jumps. Moreover, we show that our method is more flexible with respect to the convergence of the graph's Dirichlet energy, thereby mitigating oversmoothing. We conduct extensive experiments on synthetic and real-world graphs, both directed and undirected, demonstrating our method's versatility across diverse graph homophily levels. Our code is available at https://github.com/RPaolino/fLode .

该文研究了图神经网络中过度平滑问题，并针对无向图将其概念推广至有向图，通过引入指向对称规范化拉普拉斯算子并提出分数图拉普拉斯神经ODE框架，实现了在节点间传播信息的同时缓解了过度平滑问题，证明了该方法的有效性并在合成和真实世界的有向无向图上进行了广泛实验。

一种用分数图拉普拉斯算子解决过度平滑问题的方法