Markovian Semantic Transport for Heterogeneous Graph Learning

Heterogeneous graphs contain multiple node and relation types, and predictive information often depends on long-range semantic dependencies formed by se- quences of different relations. Existing heterogeneous GNNs typically capture such structure through predefined meta-paths or by repeatedly stacking local message-passing and attention layers, which increases computational cost, can amplify hub-dominated propagation, and makes deep models susceptible to over- smoothing. We propose MC-HGNN, a Markovian semantic transport frame- work that interprets relation-aware graph attention as conditional typed transi- tions and couples them through learned node-dependent relation selection. A hub-aware correction limits excessive transport toward highly influential nodes, while relation-dependent continuation allows different semantic channels to learn different propagation ranges. The resulting all-hop transport implicitly aggregates variable-length heterogeneous paths without explicit meta-path enumeration and decouples transport depth from neural-network depth. Theoretically, we establish adaptive meta-path composition, exponentially convergent finite transport approx- imation, distance-decaying robustness to localized perturbations, and quantitative resistance to over-smoothing. Experiments on seven heterogeneous graph bench- marks show that MC-HGNN consistently improves predictive performance while maintaining favorable memory and computational efficiency.