Compositional generalization is a critical ability in learning and decision-making. We focus on the setting of reinforcement learning in object-oriented environments to study compositional generalization in world modeling. We (1) formalize the compositional generalization problem with an algebraic approach and (2) study how a world model can achieve that. We introduce a conceptual environment, Object Library, and two instances, and deploy a principled pipeline to measure the generalization ability. Motivated by the formulation, we analyze several methods with exact or no compositional generalization ability using our framework, and design a differentiable approach, Homomorphic Object-oriented World Model (HOWM), that achieves soft but more efficient compositional generalization.

Background:Polycystic ovary syndrome (PCOS) is the most common endocrine and metabolic disease in women of childbearing age worldwide. Traditional Chinese Medicine (TCM) effectively alleviates the clinical symptoms of PCOS. Methods: Relevant literature on TCM for treating PCOS was collected from the China National Knowledge Infrastructure (CNKI), and data mining tools identified the core drug group. The TCMSP database retrieved the active ingredients and targets of the core drug group and through screening data from GeneCard, OMIM, PharmGkb, DrugBank, and Uniprot disease databases to obtain common targets for drugs and diseases. The Cytoscape software constructed the “ingredients-targets” network. Meanwhile, the protein interaction database (STRING) constructed the potential target protein interaction network. The CytoNCA plug-in of Cytoscape screened the core targets. GO functional, and KEGG enrichment analyses of intersection targets were performed using the R statistical software. The molecular docking technology verified the relationship between the core ingredients and targets. Results: A total of 175 prescriptions were extracted from the CNKI literature, including 212 Chinese medicinals. Angelica sinensis, Cuscuta chinensis, and Rehmannia root were selected as the core drug group. Preliminary screening obtained 13 active ingredients and 446 potential targets. The mechanism of action is related to the 175 significantly enriched pathways, including lipid and atherosclerosis, fluid shear stress and atherosclerosis, AGE-RAGE signaling pathway in diabetic complications, MAPK, TNF, and PI3K-Akt signaling pathways. The absolute value of binding energies of quercetin, kaempferol, and isorhamnetin with NCOA2, PGR, and PTGS2 were over 5.0 Kcal / mol, indicating good docking results. Conclusions: The main active ingredients, action targets, and related pathways for treating PCOS using Angelica sinensis, Cuscuta chinensis, and Rehmannia root is discussed. The study confirmed the effects of Angelica sinensis, Cuscuta chinensis, and Rehmannia root for treating PCOS, providing a reference for clinical practice.