While our method is primarily designed for synthesis evaluation, it holds potential for broader applications involving permutation-invariant data, such as graph-based or set-based data. This includes fields like protein structures, molecular graphs, and network embeddings. The potential applications is broad for our pipeline of complementing data-driven machine learning with expert augmentation. For instance, expert knowledge in fields like finance-such as credit scoring, loan approval models, and risk management-or healthcare, particularly in medical diagnosis and image analysis, could enhance both outcomes and safety.