让图神经网络学会识别结构模式，提升模型表达能力
Invariant-Based Weight Sharing for Message Passing
- 权重按图不变量索引，实现结构等价子图的共享
- 在合成与真实数据上均优于标准MPNN，超越1-WL测试表达力
- 适合需要结构敏感建模的图学习任务，如子图计数
消息传递神经网络（MPNNs）是学习图结构数据表示的强大框架，但其权重仅作用于特征，难以捕捉结构模式。本文提出一种基于图不变量的新型权重共享机制，显式引入图结构固有信息。权重直接由用户选择的图不变量（即节点置换下保持不变的函数）索引，实现对结构等价子图的系统性复用。我们构建了ShareGNN，将其嵌入简单编码器-解码器架构中，形成具备可学习邻接关系和类Transformer连接方式的MPNN。实验表明，其表达能力至少等同于所选不变量的判别力，可明确控制模型复杂度。在合成数据、真实世界数据及子图计数任务上的结果一致优于标准MPNN，表达力竞争性超越1-WL测试，并支持大规模数据集扩展。
原文摘要 · Abstract (English)
Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a novel structure-aware weight sharing principle that explicitly incorporates information inherent to the graph structure. Weights are indexed directly by user-chosen graph invariants, i.e., functions preserved under node permutations, enabling systematic reuse across structurally equivalent subgraphs. We present ShareGNNs, which instantiate this principle within a simple encoder-decoder architecture, resulting in an MPNN with learnable adjacency and transformer-like connectivity. We show that their expressivity is at least as strong as the discriminative power of the chosen invariants, providing explicit control over the model complexity. Experiments on synthetic and real-world data, as well as subgraph counting tasks, demonstrate consistent improvements over standard MPNNs, competitive expressivity beyond the 1-WL test, and scalability to large datasets.
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