We present a new effective and scalable framework for training GNNs in node classification tasks, based on the effective resistance, a powerful tool solidly rooted in graph theory. Our approach progressively refines the GNN weights on an extensive sequence of random spanning trees, suitably transformed into path graphs that retain essential topological and node information of the original graph. The sparse nature of these path graphs substantially lightens the computational burden of GNN training. This not only enhances scalability but also effectively addresses common issues like over-squashing, over-smoothing, and performance deterioration caused by overfitting in small training set regimes. We carry out an extensive experimental investigation on a number of real-world graph benchmarks, where we apply our framework to graph convolutional networks, showing simultaneous improvement of both training speed and test accuracy over a wide pool of representative baselines.

翻译：我们提出了一种新的高效且可扩展的框架，用于节点分类任务中的GNN训练。该框架基于有效电阻这一深植于图论的有力工具。我们的方法通过一系列随机生成树逐步优化GNN权重，将这些生成树适当地转换为路径图，从而保留原始图的关键拓扑与节点信息。这些路径图的稀疏特性大幅减轻了GNN训练的计算负担，不仅增强了可扩展性，还有效解决了常见问题，如过度压缩、过度平滑以及小训练集场景下因过拟合导致的性能退化。我们在多个真实图基准上开展了广泛的实验研究，将所提框架应用于图卷积网络，结果显示其在训练速度和测试准确率上均优于众多代表性基线方法。