We establish a geometric framework for zero-shot transfer learning across graphs of varying topology, node count, and signal semantics. The central question we are trying to address is: when can a predictor trained on one graph family deploy on entirely unseen topologies without retraining? We show that transfer is reliable when graph-specific semantic signals embed into a common latent space on which a size-adaptive decoder can realize the task across topologies.

 

We implement this idea through an asymmetric dual-path architecture: a semantic teacher encoder uses dense graph signals to shape the latent space during training, while a structure-aware encoder using sparse observations and graph positional descriptors is used at deployment. A shared adaptive decoder reconstructs node- or graph-level outputs on graphs of arbitrary size. We first interpret the theory through the lenses of Bayesian theory. Then suggest diagnostics for transfer compatibility based on reconstruction fidelity, latent distribution proximity, cross-modal alignment, and latent-space connectedness and provide numerical examples to demonstrate the efficacy of the proposed framework.