传播，然后锐化：冻结节点分类器的后置精炼

中文摘要 AI 辅助

我们研究冻结节点分类器的后置精炼问题：给定图$G$和冻结模型预测的类别分布$Q$，在不访问节点特征、模型参数或梯度的前提下，能否提高准确率？APPNP通过向初始预测重启的传播logits来回答这一问题，最小化锚定Dirichlet能量。相反，我们考虑Potts能量，并将其分解为Dirichlet项（惩罚相邻节点间的不一致）和Gini项（惩罚每个节点内部的不确定性）。这一分解催生了“传播，然后锐化”（PtS）方法，该方法在类别概率传播和逐节点、保持质量的锐化之间交替进行，仅需一个额外的超参数，该超参数使用带标签的验证节点进行选择。在九个同质图上，以冻结的MLP骨干网络为基础，PtS在干净输入上的平均测试准确率比独立调优的APPNP提高了$1.71$个百分点，在严重高斯特征损坏下提高了$3.90$个百分点。与APPNP相比，PtS的优势在冻结的GCN和GraphSAGE骨干网络下变小，但仍然为正。锐化还消除了深度传播的大部分准确率损失：在干净输入且无重启的情况下，PtS在$2$到$100$次传播步骤之间准确率下降$2.2$个百分点，而APPNP下降$33.8$个百分点。

英文摘要

We study post-hoc refinement of frozen node classifiers: given only the graph $G$ and class distributions $Q$ predicted by a frozen model, can we improve accuracy without access to node features, model parameters, or gradients? APPNP answers this by propagating logits with a restart towards the initial predictions, minimizing the anchored Dirichlet energy. Instead, we consider the Potts energy, and decompose it into a Dirichlet term, which penalizes disagreement between neighbouring nodes, and a Gini term, which penalizes indecision within each node. This decomposition motivates Propagate, Then Sharpen (PtS), which alternates between propagation of class probabilities and node-wise, mass-preserving sharpening, with only one additional hyperparameter selected using labelled validation nodes. Across nine homophilic graphs, with a frozen MLP backbone, PtS improves mean test accuracy over independently tuned APPNP by $1.71$ percentage points on clean inputs and $3.90$ under severe Gaussian feature corruption. Gains over APPNP become smaller, but remain positive with frozen GCN and GraphSAGE backbones. Sharpening also removes most of the accuracy loss of deep propagation: on clean inputs without restart, accuracy falls by $2.2$ points between $2$ and $100$ propagation steps under PtS, compared with $33.8$ for APPNP.

发表机构

• University of Bergen（卑尔根大学）
• Norwegian Research Centre (NORCE)（挪威研究中心（NORCE））

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