One Coupling, Many Roles: Readout-Dependent Accessibility in GNN Representations

Graph neural network representations with nearly identical supervised linear accessibility can differ sharply in single-prototype recovery, and even a single frozen representation can remain highly linearly accessible while systematically failing single-prototype recovery. On GIN-Cora, we localize this deficit to a single-prototype capacity mismatch within the class-centroid span. This prototype-sensitive failure is accompanied by a recurring degree-conditioned organization on Cora and Amazon-Computers. Training-time manipulation of target-degree message scaling causally shifts the accessibility profile: attenuation in GIN improves prototype accessibility but has different supervised consequences across datasets, whereas amplification in GraphSAGE can induce a large prototype–linear dissociation while largely preserving linear accessibility. These results show that target-degree scaling is a causal lever on representation accessibility, while accessibility itself is readout-dependent rather than a single scalar property of the representation.