Many node‑classification graph neural networks (GNNs) apply a linear classifier directly to a non‑negative mixture of local messages. An error can stem from either poor mixture weights $w$ or a reachable logit set that is poorly positioned for the classifier. We separate these two causes with an exact‑mass linear program (LP) and introduce two learned post‑hoc repair mechanisms.
Every reweighted prediction can be expressed as an equivalent centered logit translation $t$, yet only translations that belong to the message‑induced displacement set $\mathcal{T}$ are realizable by actual reweighting. Based on this insight we implement (1) an LP‑derived optimal weight re‑allocation, and (2) a learned set‑conditioned translation operating within $\mathcal{T}$.
Across eight datasets, eight GNN backbones, and ten random splits, the frozen models achieve a mean accuracy of 62.6%. Reweighting raises this to 63.8%, and adding set‑conditioned translation further improves it to 65.3%. A parameter‑matched node‑only translator reaches 64.6%, indicating that most of the gain comes from translation while the message set provides a smaller additional benefit.
Although oracle reweighting can correct many errors, label‑free reweighting captures only a tiny fraction of this potential: local evidence is often present but hard to select, and relaxing the evidence constraint (learning in a larger space) proves more effective than learning under a strict constraint.
Review