解决图神经网络过平滑问题，提升异质图分类性能。
Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimization
- 用最优传输与帕累托贝叶斯正则化构建动态层结构
- 线性复杂度训练下实现理论性能边界，9个数据集上超越现有模型
- 提供未见节点的置信区间，适合需要可靠预测的场景
图神经网络在异质图上易出现过平滑，导致节点特征坍缩。尽管层流神经网络部分缓解此问题，但通常依赖静态或高度参数化的层结构，限制泛化与扩展性。现有方法要么预设约束映射，要么引入过多复杂度，且缺乏严格的稳定性保证。本文提出一种新框架SGPC（基于帕累托贝叶斯校准的层图神经网络），融合细胞层消息传递机制，包括基于最优传输的升维、方差减少扩散和帕累托贝叶斯谱正则化，实现鲁棒的半监督节点分类。理论上建立了性能边界，并证明端到端训练可在线性计算复杂度下达到该边界感知目标。在九个同质与异质基准测试中，SGPC优于现有谱方法和层流模型，同时为未见节点提供认证置信区间。代码与证明详见 https://github.com/ChoiYoonHyuk/SGPC。
原文摘要 · Abstract (English)
Over-smoothing in Graph Neural Networks (GNNs) causes collapse in distinct node features, particularly on heterophilic graphs where adjacent nodes often have dissimilar labels. Although sheaf neural networks partially mitigate this problem, they typically rely on static or heavily parameterized sheaf structures that hinder generalization and scalability. Existing sheaf-based models either predefine restriction maps or introduce excessive complexity, yet fail to provide rigorous stability guarantees. In this paper, we introduce a novel scheme called SGPC (Sheaf GNNs with PAC-Bayes Calibration), a unified architecture that combines cellular-sheaf message passing with several mechanisms, including optimal transport-based lifting, variance-reduced diffusion, and PAC-Bayes spectral regularization for robust semi-supervised node classification. We establish performance bounds theoretically and demonstrate that end-to-end training in linear computational complexity can achieve the resulting bound-aware objective. Experiments on nine homophilic and heterophilic benchmarks show that SGPC outperforms state-of-the-art spectral and sheaf-based GNNs while providing certified confidence intervals on unseen nodes. The code and proofs are in https://github.com/ChoiYoonHyuk/SGPC.
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