发现图神经网络性能提升主要来自训练动态，而非图结构重连。
Bilevel Graph Structure Learning, Revisited: Inner-Channel Origins of the Reported Gain
- 通过冻结图结构但保留内层训练过程，分离出训练动态的影响。
- 在时空流量预测任务中，训练动态贡献了78%~101%的性能提升。
- 提出标准诊断方法 frozen-ϕ，适用于所有图结构学习场景。
双层图结构学习普遍被认为通过联合优化模型参数与学习到的图结构来提升图神经网络性能，现有研究将增益归因于图邻接矩阵的重连。我们发现这一归因可能被夸大：内层训练动力学的影响，而非图重连本身，占据了显著部分。为此，我们引入 frozen-ϕ 控制实验，冻结图结构但保留内层训练流程，从而将双层增益分解为两个通道：包含 T 步训练动态与隐式梯度正则化的内层通道，以及图结构重连本身的图通道。在时空流量预测任务中，内层通道表现达到或超过完整双层管道，贡献了78%~101%的性能增益；在节点分类任务中（采用伯努利边级参数化），内层通道贡献37%~44%。我们还验证了经典谱诊断指标与任务性能增益之间可解耦。本文提出 frozen-ϕ 作为双层图结构学习的标准诊断工具，并以图蒸馏作为方法无关的补充。此外，三前提框架可预测六个基准上的双层增益符号。
原文摘要 · Abstract (English)
Bilevel graph structure learning is widely understood to improve graph neural networks by jointly optimizing model parameters and a learned graph structure, with the resulting performance gain attributed to the rewired adjacency. We find that this attribution may be overstated: training-dynamics effects in the inner loop, rather than the rewiring itself, capture a substantial share of the gain. To establish this, we introduce frozen-$ϕ$, a control that freezes the graph while retaining the inner-loop training schedule. This decomposes the bilevel gain into an inner channel of $T$-step training dynamics with implicit gradient regularization and a graph channel of the graph rewiring itself. On spatio-temporal flow forecasting the inner channel matches or exceeds the full bilevel pipeline, accounting for 78-101% of the gain; on node classification it accounts for 37-44% under a Bernoulli edge-level parameterization. We also verify that classical spectral diagnostics can dissociate from task gain. We propose frozen-$ϕ$ as a standardized diagnostic for bilevel graph structure learning, with graph distillation as a method-agnostic complement. A three-precondition framework further predicts the sign of the bilevel gain on all six benchmarks.
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