揭示GNN在图半监督学习中的性能边界，解析标签比例与图结构的影响。
Semi-Supervised Learning on Graphs using Graph Neural Networks
- 构建聚合-读出模型，统一多种消息传递架构
- 给出非渐近风险界，量化标签比例与图依赖对性能的影响
- 理论可指导GNN应用，适合研究者与工程落地参考
图神经网络（GNN）在半监督节点回归任务中表现优异，但其成功的原因与适用条件尚缺乏严格理论支持。为此，本文研究一种包含多种常见消息传递架构的聚合-读出模型：先在图上传播节点特征，再通过非线性函数映射为输出。针对采用线性图卷积和深层ReLU读出的最小二乘估计，我们推导出一个精确的非渐近风险上界，明确分离了近似误差、随机误差与优化误差。该界揭示了性能随标记节点比例及图诱导相关性的变化规律。进一步地，对图平滑后接平滑非线性读出的情形，给出了逼近保证，当全监督时恢复经典非参数收敛率，并刻画了标签稀缺时的表现。数值实验验证了理论分析，为理解GNN的性能与局限提供了系统框架。
原文摘要 · Abstract (English)
Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses several common message passing architectures: node features are first propagated over the graph then mapped to responses via a nonlinear function. For least-squares estimation over GNNs with linear graph convolutions and a deep ReLU readout, we prove a sharp non-asymptotic risk bound that separates approximation, stochastic, and optimization errors. The bound makes explicit how performance scales with the fraction of labeled nodes and graph-induced dependence. Approximation guarantees are further derived for graph-smoothing followed by smooth nonlinear readouts, yielding convergence rates that recover classical nonparametric behavior under full supervision while characterizing performance when labels are scarce. Numerical experiments validate our theory, providing a systematic framework for understanding GNN performance and limitations.
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