Soft Specialization via Mixture-of-Experts Enables Accurate Prediction of Superconducting Tc from Crystal Structures

Abstract Predicting superconducting critical temperature (T$_c$) from crystal structure is challenging due to diverse material families with distinct physical mechanisms and structural complexities like site-occupation disorder. We introduce Superconductor Mixture of Experts (SuMoE), a Mixture-of-Experts (MoE) architecture using multiple Graph Neural Network experts with learned routing, achieving MAE of 0.671 logK on the SuperCon3D dataset, significantly outperforming both a state-of-the-art single generalist Graph Neural Network (0.709 logK) and isolated family-specific specialists (0.683 logK). While traditional intuition suggests models should specialize in rigid material families, our analysis reveals a more sophisticated regime of soft specialization. We find that experts specialize in underlying physical mechanisms rather than arbitrary labels, for instance, a single expert dominates predictions for both Cuprates and Heavy Fermion systems, effectively capturing the physics of strongly correlated electrons across chemically distinct families. Crucially, the model couples this specialized knowledge with a diffuse routing mechanism that synthesizes insights from multiple experts, ensuring robustness through redundancy. Our work demonstrates that for complex structure-property relationships, the most effective paradigm is not specialization but integrative prediction, where the model learns to synthesize complementary insights to form a single, robust prediction.