UniCO: Fostering Cross-Domain and Cross-Modal Generalization for Graph Foundation Models via Unified Covariance Operators

Input feature heterogeneity across domains severely impairs the transferability of graph foundation models. Although natural language instructions provide task priors, existing cross-domain heterogeneous graph models are restricted to the graph-only modality, while current graph-text models suffer from either topological distortion induced by graph serialization or rigid dependency on domain-specific alignment. To this end, we propose UniCO, a cross-domain graph-text framework based on unified covariance operators. UniCO conceptualizes text instructions as "text graphs", thereby casting the dual cross-domain and cross-modal challenge into a singular heterogeneous graph generalization problem. Building upon this, we construct unified multi-order covariance operators for fine-grained cross-modal interactions, and design an asymmetric mask to preserve instruction temporal order while isolating the graph from instruction noise. Theoretically, we prove that these operators exhibit joint distributional and expectation invariance under input feature basis transformations, and reconcile "macroscopic modal decoupling" with "microscopic graph-text interactions" in expectation, eliminating dependence on domain-specific feature spaces and laying a theoretical foundation for cross-domain transfer. Experiments on multiple molecular graph and text-attributed graph benchmarks demonstrate that UniCO achieves superior zero-shot cross-domain generalization and efficient few-shot fine-tuning performance.