Why Graph Pretraining Fails to Transfer: Capability Ceiling and Accessibility Deficit

Graph self-supervised learning (SSL) provides the foundation for reusable graph representations. However, cross-domain pretraining often fails to match target-domain SSL performance, leading to incomplete or negative transfer. We decompose this transfer gap into two distinct mechanisms: *capability loss*, where target-task information is not retained, and *finite-supervision accessibility loss*, where retained information is difficult to extract from limited target labels. To unify both mechanisms, we propose the Task–Geometry Profile (TGP), a theoretical framework that models representation-mode strength alongside target-task signal alignment. Our analysis reveals that positive transfer depends not only on how much task-relevant signal is retained, but also on where that signal is organized in representation geometry. Furthermore, we show how graph aggregation architectures distort this profile through distinct inductive biases: GCN's normalized diffusion induces mode-selective spectral attenuation, whereas GIN's unnormalized accumulation causes degree-driven modal reallocation. Across diverse domains, SSL objectives, backbones, and 120 transfer settings, TGP quantities show systematic correspondence with empirical capability and accessibility behavior. Mechanism-guided interventions further reveal that the two components need not improve together: degree-tempered aggregation reduces the trajectory-level transfer deficit by up to 56% on the classical benchmark suite, while large-scale validation shows substantial absolute utility gains.