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