While Graph Neural Networks (GNNs) recently became powerful tools in graph learning tasks, considerable efforts have been spent on improving GNNs' structural encoding ability. A particular line of work proposed subgraph GNNs that use subgraph information to improve GNNs' expressivity and achieved great success. However, such effectivity sacrifices the efficiency of GNNs by enumerating all possible subgraphs. In this paper, we analyze the necessity of complete subgraph enumeration and show that a model can achieve a comparable level of expressivity by considering a small subset of the subgraphs. We then formulate the identification of the optimal subset as a combinatorial optimization problem and propose Magnetic Graph Neural Network (MAG-GNN), a reinforcement learning (RL) boosted GNN, to solve the problem. Starting with a candidate subgraph set, MAG-GNN employs an RL agent to iteratively update the subgraphs to locate the most expressive set for prediction. This reduces the exponential complexity of subgraph enumeration to the constant complexity of a subgraph search algorithm while keeping good expressivity. We conduct extensive experiments on many datasets, showing that MAG-GNN achieves competitive performance to state-of-the-art methods and even outperforms many subgraph GNNs. We also demonstrate that MAG-GNN effectively reduces the running time of subgraph GNNs.

翻译：尽管图神经网络（GNN）近期在图学习任务中展现出强大能力，大量研究致力于提升其结构编码能力。其中，利用子图信息增强GNN表达能力的子图GNN方法取得了显著成功。然而，这种有效性是以枚举所有可能子图为代价，牺牲了GNN的计算效率。本文分析了完整子图枚举的必要性，证明模型仅需考虑少量子图即可达到相当的表达能力。我们将最优子集的识别问题形式化为组合优化问题，并提出磁力图神经网络（MAG-GNN）——一种基于强化学习（RL）增强的GNN——来解决该问题。MAG-GNN从候选子图集出发，通过RL代理迭代更新子图以定位最具表达能力的预测子集。该方法将子图枚举的指数复杂度降为子图搜索的常数复杂度，同时保持优良的表达能力。我们在多个数据集上进行了广泛实验，结果表明MAG-GNN在性能上可与现有最优方法媲美，甚至优于多种子图GNN方法。我们还证明MAG-GNN能有效减少子图GNN的运行时间。