GNN在不同图尺度下表现不连续，新方法让模型跨尺度保持一致
Graph Neural Networks Are Not Continuous Across Graph Resolutions
- 发现标准GNN在图尺度变化时输出差异大，源于信息传播机制缺陷
- 提出改进架构，使模型在不同分辨率图上输出稳定一致
- 适合需要多尺度图分析的场景，如生物网络、复杂系统建模
我们证明，与学界普遍认知相反，图神经网络（GNN）在所有自然图收敛模式下并不连续。因此，即使图结构非常相似，GNN也可能生成显著不同的潜在表示；尤其当同一对象以不同分辨率表示时，其嵌入向量差异巨大。我们追溯此不连续性根源，发现来自常用信息传播机制的结构性障碍。基于这一洞察，我们推导出对标准GNN架构的合理修正，使模型具备跨尺度连续性。该改进支持不同分辨率的可靠融合与泛化。我们在广泛的数值实验中系统验证了理论结果。
原文摘要 · Abstract (English)
We show that contrary to conventional wisdom in the community, graph neural networks (GNNs) are not continuous with respect to all natural modes of graph convergence. As a result, GNNs may generate substantially different latent representations for graphs that are very similar. In particular they assign vastly different latent embeddings to graphs that represent the same underlying object at different resolution scales. We trace this failure of continuity back to a structural obstruction arising from commonly used information-propagation schemes. Building on this insight we then derive a principled modification to standard GNN architectures which equips models with continuity across scales. The proposed modification enables consistent integration of distinct resolutions and reliable generalization between them. We systematically validate our theoretical findings in a wide range of numerical experiments.
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