DRGFM: Dynamic Riemannian Graph Foundation Models via Learnable Curvature Spectrum

Graph foundation models (GFMs) require structural knowledge that transfers across domains and remains useful as tasks evolve. Yet implicit structural encodings make it difficult to specify what should transfer and what should be preserved. Curvature and spectral analysis offer complementary descriptions of local geometry and multi-scale propagation, but predefined geometric operators cannot themselves adapt to learning objectives across domains. We propose DRGFM, a Dynamic Riemannian Graph Foundation Model that models structural knowledge through a learnable curvature spectrum. A learned curvature-weighted Laplacian provides graph-dependent spectral coordinates and filters, coupling mixed-curvature representations with spectral attention to accommodate geometric heterogeneity. This formulation further supports structural knowledge evolution: during continual learning, importance-weighted regularization constrains spectral-coordinate drift on bounded anchor subgraphs in frozen reference bases, while the current curvature estimator and backbone remain adaptable. A conditional local analysis relates this displacement to historical-loss drift. Experiments on few-shot classification, zero-shot link prediction, and temporal continual learning evaluate transfer and retention, while matched ablations support the contribution of learnable curvature beyond a fixed prior. Together, these results support a unified approach to learning transferable structural representations and preserving them during subsequent adaptation.