Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, they are unable to capture long-range dependencies between nodes without adding additional layers -- which in turn leads to over-smoothing and increased time and space complexity. Further, the complex dependencies between nodes make mini-batching challenging, limiting their applicability to large graphs. We propose a Scalable Multi-resolution Graph Representation Learning (SMGRL) framework that enables us to learn multi-resolution node embeddings efficiently. Our framework is model-agnostic and can be applied to any existing GCN model. We dramatically reduce training costs by training only on a reduced-dimension coarsening of the original graph, then exploit self-similarity to apply the resulting algorithm at multiple resolutions. The resulting multi-resolution embeddings can be aggregated to yield high-quality node embeddings that capture both long- and short-range dependencies. Our experiments show that this leads to improved classification accuracy, without incurring high computational costs.

翻译：图卷积网络（GCN）使我们能够学习具有拓扑感知能力的节点嵌入，这对分类或链接预测十分有用。然而，若不增加额外层数，GCN无法捕获节点间的长程依赖关系——而增加层数又会导致过平滑问题，并增加时间与空间复杂度。此外，节点间的复杂依赖关系使得小批量训练变得困难，从而限制了GCN在大型图上的应用。我们提出了一种可扩展的多分辨率图表示学习（SMGRL）框架，该框架能够高效地学习多分辨率节点嵌入。该框架具有模型无关性，可应用于任何现有GCN模型。通过仅在原始图的降维粗化版本上进行训练，我们大幅降低了训练成本，并利用自相似性将所得算法推广至多分辨率。由此产生的多分辨率嵌入可通过聚合得到高质量节点嵌入，同时捕获长程与短程依赖关系。实验表明，该方法在不产生高昂计算成本的前提下，提升了分类准确率。