Nash-Guided Compatible Optimal Transport for Multimodal Knowledge Graph Fusion

Multimodal Knowledge Graphs (MMKGs) integrate heterogeneous modalities to enhance knowledge representation. Yet, a fundamental challenge lies in multimodal representation fusion, where modality inputs often contain substantial target-irrelevant semantics (i.e., low-target relevance), and different modalities contribute unevenly during fusion (i.e., modality imbalance). Existing approaches typically align all modality representations indiscriminately and rely on pre-defined fusion strategies, making them sensitive to noisy or dominant modalities. To address these limitations, this paper proposes a Nash-guided Compatible Optimal Transport algorithm (NaCOT), which formulates multimodal fusion as an Optimal Transport (OT) problem. Specifically, NaCOT first constructs cascaded representation candidates and then employs sliced Wasserstein distance (SWD)-based selection to identify compatible source-target scales for OT alignment. Importantly, NaCOT introduces a Nash bargaining-based fusion mechanism that refines transport plans under fusion and OT constraints, jointly mitigating low-target relevance and modality imbalance. Experiments on four MMKG benchmarks show that NaCOT achieves state-of-the-art performance, with average relative improvements of 24.68% in MRR and 23.51% in Hit@1 over the strongest baselines.