Graph Transfer Learning via Shared Latent Geometry: Theory and Applications

• URL: http://arxiv.org/abs/2606.00716v1
• Date: Sat, 30 May 2026 13:00:13 GMT
• Title: Graph Transfer Learning via Shared Latent Geometry: Theory and Applications
• Abstract summary: Inference and control in engineered physical systems pay a heavy physics cost at deployment.<n>We propose an asymmetric two-pathway architecture that resolves both issues.<n>A teacher encoder consumes privileged dense states from a high-fidelity simulator and represents the system through operator-polynomial features stable under spectral perturbation.<n>A student encoder learns the same latent geometry from sparse field data and operator descriptors.
• Score: 12.735610064958712
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Inference and control in engineered physical systems pay a heavy physics cost at deployment: state estimators, inverse-problem solvers, model-predictive controllers, schedulers, and observers are often not closed-form and must re-solve a numerical optimization per instance, with the operator re-supplied each time. Physics-informed learning moves this cost to training, but uses a single encoder pathway whose latent geometry de-learns under fine-tuning and admits no quantitative transfer guarantee. We propose an asymmetric two-pathway architecture that resolves both issues. A teacher encoder consumes privileged dense states from a high-fidelity simulator and represents the system through operator-polynomial features stable under spectral perturbation; a student encoder learns the same latent geometry from sparse field data and operator descriptors. At deployment the teacher is discarded, and the frozen student runs in a single forward pass with a transfer certificate. The design connects to privileged-information learning, knowledge distillation, and cross-modal distillation, but targets cross-instance transfer rather than fixed-instance prediction: topology and operator may change, while the latent task does not. We establish sufficient and near-necessary transfer conditions via Wasserstein proximity between latent laws, yielding a zero-shot error bound, and develop a finite-sample certification protocol with active expansion when coverage is incomplete. The framework applies wherever a system admits an operator with reportable spectrum. On power-system estimation, it achieves zero-shot transfer to 100 unseen topologies, a 95% certificate pass rate, accuracy competitive with topology-aware Newton--Raphson, and sub-millisecond inference. These results suggest asymmetric pathways plus operator-anchored latent geometry provide a foundation for certified zero-shot inference and control.

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