Relational Alignment Profiles: The Geometry of Graph-Learning Problems

Graph learning is usually architecture-first: for a new attributed graph, the appropriate computational bias (local smoothing, multihop propagation, heterophily-aware filtering, role-based reasoning, or global attention) is typically discovered only after training several competing models. We ask whether the graph-learning problem itself can be diagnosed first, so that the needed computation can be inferred before model search. We introduce the Relational Alignment Profile (RAP), which characterizes how structural, feature, and task geometries align, conflict, and vary across relational scale. RAP provides a compact coordinate for architecture selection and dictionary-free curves that reveal whether relational organization is local, delayed, oppositional, feature-explained, or role-driven. We train RAP-based selectors only on controlled synthetic problems and evaluate them under generator shift and frozen synthetic-to-real transfer. Across 22 real node-classification benchmarks, the label-free native coordinate $\alpha$ is the strongest zero-shot selector among the tested representations, achieving only $2.22$ percentage points of regret and outperforming conventional graph statistics. At matched dimension, $\alpha$ also outperforms PCA/NMF compressions of the same native alignment fields. These results support a problem-first view of graph learning: diagnose relational organization before deciding what computation an unseen problem requires.