Propagate, Then Sharpen: Post-Hoc Refinement of Frozen Node Classifiers

2026-09-28

AI Summary

This study addresses the challenge of optimizing node classification prediction distributions of frozen models using solely graph structure, without access to node features, model parameters, or gradients. To this end, we propose PtS, a post-processing method that decomposes Potts energy into Dirichlet and Gini components and introduces a "propagate-then-sharpen" mechanism. By alternating between anchor-regularized probability propagation and gradient-free mass-conserving sharpening, PtS effectively mitigates deep over-smoothing. Extensive experiments on nine homophilic graph datasets demonstrate that PtS achieves an average accuracy improvement of 1.71% over APPNP, with gains reaching 3.90% under strong noise conditions, significantly alleviating the accuracy degradation associated with deep propagation.

Abstract

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.

Problem

• post-hoc refinement
• frozen node classifiers
• graph neural networks
• node classification

Innovation

• Post-Hoc Refinement
• Potts Energy
• Node Classification
• Graph Neural Networks
• Sharpening