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Counterfactual explanations of Graph Neural Networks (GNNs) offer a powerful way to understand data that can naturally be represented by a graph structure. Furthermore, in many domains, it is highly desirable to derive data-driven global explanations or rules that can better explain the high-level properties of the models and data in question. However, evaluating global counterfactual explanations is hard in real-world datasets due to a lack of human-annotated ground truth, which limits their use in areas like molecular sciences. Additionally, the increasing scale of these datasets provides a challenge for random search-based methods. In this paper, we develop a novel global explanation model RLHEX for molecular property prediction. It aligns the counterfactual explanations with humandefined principles, making the explanations more interpretable and easy for experts to evaluate. RLHEX includes a VAE-based graph generator to generate global explanations and an adapter to adjust the latent representation space to human-defined principles. Optimized by Proximal Policy Optimization (PPO), the global explanations produced by RLHEX cover 4.12% more input graphs and reduce the distance between the counterfactual explanation set and the input set by 0.47% on average across three molecular datasets. RLHEX provides a flexible framework to incorporate different human-designed principles into the counterfactual explanation generation process, aligning these explanations with domain expertise. The code and data are released at https://github.com/dqwang122/RLHEX. 

This paper describes how two-dimensional plasmonic nanoparticle latticescovered with microscale arrays of dielectric patches can show superlattice surface latticeresonances (SLRs). These optical resonances originate from multiscale diffractive coupling thatcan be controlled by the periodicity and size of the patterned dielectrics. The features in theoptical dispersion diagram are similar to those of index-matched microscale arrays of metalnanoparticle lattices, having the same lateral dimensions as the dielectric patches. With anincrease in nanoparticle size, superlattice SLRs can also support quadrupole excitations withdistinct dispersion diagrams. The tunable optical band structure enabled by patterned dielectricson plasmonic nanoparticle arrays offers prospects for enhanced nonlinear optics, nanoscalelasing, and engineered parity-time symmetries.