Translating Subgraphs to Nodes Makes Simple GNNs Strong and Efficient for Subgraph Representation Learning

TL;DR

This paper tackles the challenge of subgraph representation learning on large graphs, where traditional methods incur high memory and computation costs. It introduces Subgraph-To-Node (S2N) translation, which compresses a set of subgraphs into a coarse graph whose nodes represent subgraphs and whose edges encode inter-subgraph relations, enabling simple GNNs to operate efficiently. To address data scarcity, it further proposes Coarsened S2N (CoS2N), which uses graph coarsening to create virtual subgraphs that bridge distant parts of the global graph, improving representation quality. Theoretical analyses show substantial reductions in computational complexity and an approximation bound relating S2N to subgraph representations, while extensive experiments on eight datasets demonstrate dramatic throughput gains (up to $183$--$711\times$) with competitive or improved accuracy and reduced memory usage. Overall, S2N/CoS2N offer a scalable, effective framework for subgraph representation learning that leverages simple GNNs and graph-coarsening ideas to handle large-scale graphs and data-scarce regimes.

Abstract

Subgraph representation learning has emerged as an important problem, but it is by default approached with specialized graph neural networks on a large global graph. These models demand extensive memory and computational resources but challenge modeling hierarchical structures of subgraphs. In this paper, we propose Subgraph-To-Node (S2N) translation, a novel formulation for learning representations of subgraphs. Specifically, given a set of subgraphs in the global graph, we construct a new graph by coarsely transforming subgraphs into nodes. Demonstrating both theoretical and empirical evidence, S2N not only significantly reduces memory and computational costs compared to state-of-the-art models but also outperforms them by capturing both local and global structures of the subgraph. By leveraging graph coarsening methods, our method outperforms baselines even in a data-scarce setting with insufficient subgraphs. Our experiments on eight benchmarks demonstrate that fined-tuned models with S2N translation can process 183 -- 711 times more subgraph samples than state-of-the-art models at a better or similar performance level.

Figures (6)

• Figure 1: Overview of the Subgraph-To-Node (S2N) translation and models for translated graphs.
• Figure 2: Overview of Coarsened Subgraph-To-Node (CoS2N) Translation with virtual subgraphs generated by graph coarsening.
• Figure 3: Efficiency of S2N models and baselines on real-world datasets. The ratio of the best S2N model and the state-of-the-art model for each metric is notated in the figure (dashed lines).
• Figure 4: Performance and efficiency on PPI-BP of S2N, CoS2N, connected, and separated forms by the number of training samples in a data-scarce setting.
• Figure 5: Performance and efficiency on EM-User of S2N, CoS2N, connected, and separated forms by the number of training samples in a data-scarce setting.

Theorems & Definitions (14)

• Proposition 4.1
• Proposition 4.2
• Proposition 4.3
• Proposition 4.1: Proposition \ref{['proposition:time_complexity']}
• proof
• Proposition 4.2: Proposition \ref{['proposition:edge_cm']}
• proof
• Lemma 4.3
• proof
• Proposition 4.4: Proposition \ref{['proposition:single_gcn_approx']}