## 4 Results
### Experimental Setup  
**Datasets**. Open-world KGC tasks are commonly evaluated on Word-Net and Freebase subsets, such as YAGO3 [24] and FB15K-237 [25]. In order to verify the effectiveness of predicate decomposition, we focus on the KG benchmark with many predicates and high difficulty to verify the effectiveness of our method. Therefore, we selected FB15K-237, YAGO3-10, and NELL-995 [26] as the benchmark dataset. * FB15K-237 is a subset of the Freebase knowledge base [10] containing general knowledge facts. * The YAGO3-10 dataset is a subset of YAGO3 that only contains entities with at least 10 relations. In total, YAGO3-10 has 123,182 entities and 37 relations and 1,179,040 triples, and most of the triples describe attributes of persons such as citizenship, gender, and profession. * The NELL-995 dataset is a subset of NELL [27] created from the 995 th iteration of the construction. NELL-995 includes 75,492 entities, 200 relations, and 154,208 triples. To verify the efficacy of this method for knowledge extraction and logical reasoning on large-scale datasets, we also conducted drug rediscovery experiments on the open-source biochemical knowledge graph RTX-KG2c [28]. RTX-KG2c integrates data from 70 public knowledge sources into a comprehensive graph where all biological entities (e.g., \"ibuprofen\") are represented as nodes and all concept-predicate-concept relationships (e.g., \"ibuprofen increases activity of GP1 BA gene\") are encoded as edges. This dataset comprises approximately 6.4 M entities across 56 distinct categories, with 39.3 M relationship edges described by 77 distinct relations. The objective of this experiment is to employ the KGC model to learn the interactions between diseases and drugs from RTX-KG2c, aiming to predict potential therapeutic relationships between drugs and diseases. **Baselines**. In order to test the effectiveness and universality of PDEC, we have extensively selected some mature KG inference models. We use the KG inference model running on the original dataset as the baseline. For each baseline, we use them in conjunction with PDEC to conduct performance testing and record their performance improvement. The baseline model we have chosen includes TransE, TransH [29], TransR [30], TransD [31], ComplEX [32], DistMult [2], TuckER [13], RotatE, CompGCN [33], RelEns-DSC [16], etc. **Experiment setting details**. We implement the baseline model and its corresponding PDEC framework based on the OPENKE project [34]. We set the entity and relation embedding size to 200 for experiments. We use Adam optimization [35] and search the learning rate (0.001-0.005) and minibatch size (64-256). We apply dropout to the entity and relation embeddings and all feed-forward layers, and search the dropout rates within 0.6. In line with the common practices described in [5,7], we compute standard evaluation metrics for the KGC reasoning task, \(Hit@k\), which counts the number of correctly predictedhead terms among the top \(k\) predictions, and the mean reciprocal rank (MRR), calculated as the mean of the reciprocal rank of the correct answer in the list of predictions. These ranking-based metrics are defined as follows:  
\[MPR=\frac{1}{R}\sum\limits_{r\in R}r^{-1}\quad Hit@k=\frac{1}{R}\sum\limits_{r \in R}|r\leq k| \tag{13}\]  
where \(R\) is a list of ranks of all true-positive triples in the test dataset. For drug rediscovery experiments, we excluded all existing edges connecting potential drug nodes (nodes labeled \"Drug\" or \"SmallMolecule\") with potential disease nodes (nodes labeled \"Disease\", \"PhenotypicFeature\", \"BehavioralFeature\", or \"DiseaseOrPhenotypicFeature\") in RTX-KG2c to prevent information leakage during training. We then added drug-disease pairs that were confirmed true positives (pairs with the relation \"indication\" from MyChem datasets [36] or the predicate \"treats\" from SemMedDB datasets [37]). A new predicate treat was introduced to represent this therapeutic relationship in the experimental KG.