Interpreting Supervised Pairwise Graph Representations: Local Evidence, Confounding, and Provable Post-hoc Correction

Supervised pairwise graph representations convert pairwise predictive relations into sample-specific graphs, but graph-level accuracy does not by itself show that higher-order topology carries the signal. In a controlled Transformer error-detection task, supervised pairwise graphs outperform attention-as-adjacency (ROC-AUC $0.839$ versus $0.559$; the comparable no-confidence pair is $0.687$ versus $0.559$), but their apparent advantage over model confidence disappears after controlling for sequence length, which is almost perfectly recoverable from the pooled hidden state ($R^2=0.9995$). On published HCP Emotion ensemble graphs, signed node aggregation already acts as an ensemble of supervised pairwise predictions. Edge magnitude alone is near chance; topology-aware augmentations change ROC-AUC by at most $0.004$, with only sign-separated degree showing small positive changes across all tested graph sizes, while a validation-tuned three-layer GCN provides no measurable improvement over the signed node-summary baseline. A Fisher post-hoc corrector satisfies its distribution-agnostic guarantees across the evaluated feature representations and remains stable under reduced labelled budgets; in a near-error-free fMRI calibration regime the bound correctly becomes statistically uninformative. A separate cross-attention analysis identifies a redundant reversal circuit and downstream EOS-timing and copy failures. Higher-order topology should therefore be credited only after local supervised evidence and recoverable nuisance variables have been excluded.