## 5 Experiments
### Model Validation
Enhanced TransD already surpasses TransE, TransH, and TransR at low dimensions (50 and 100) and widens its advantage in medium-to-high dimensions (150-300), achieving MR reductions exceeding one thousand ranks at each dimension. These results indicate that attribute projection enriches local and global semantic features for complex paths and multi-hop inference, while the dual-limit loss effectively constrains distance distributions between positive and negative samples, yielding improved ranking even for long-tail entities. Mean Reciprocal Rank (MRR) also reflects the stability and enhancement brought by our approach; Enhanced TransD's MRR rises from \(\sim\)0.12 to \(\sim\)0.19 as dimensions increase, an improvement of 0.07. In contrast, the original TransD fluctuates from \(\sim\)0.17 to \(\sim\)0.16, showing an early rise followed by a decline. Although TransE, TransH, and TransR exhibit temporary MRR gains at medium dimensions, they fail to sustain growth and decline  
Figure 10: Performance of various translation-based embedding models on the WN18 RR dataset across different embedding dimensions. significantly above 200 dimensions. The continuous upward trend of Enhanced TransD at higher dimensions demonstrates that the dual-limit loss maintains balanced gradient updates across complex relations and multi-hop paths, thereby improving sensitivity to correct head-tail pair ordering. For Hits@k, Enhanced TransD again shows notable gains; Hits@10 increases from ~0.35 to ~0.46 (over 0.10 improvement), while Hits@3 and Hits@1 improve from 0.24 to 0.34 and 0.02\(\rightarrow\)0.039, respectively, underscoring enhanced performance under strict matching criteria. Notably, the most pronounced improvement occurs for Hits@1, which demands precise first-rank retrieval in multi-hop scenarios. By incorporating entity attribute features, the model more effectively distinguishes semantically similar but path-divergent entity pairs, thus achieving superior first-rank accuracy. Finally, classification metrics mirror ranking improvements; accuracy increases from 0.19 to 0.31 and F1 score from 0.16 to 0.28, with gains plateauing beyond 200 dimensions, indicating near-optimal expressive capacity for large-scale entities and complex multi-hop structures. Overall, on the WN18 RR dataset, Enhanced TransD not only significantly surpasses traditional translation-based models but also validates the general effectiveness of attribute projection and dual-limit loss mechanisms across multiple dimensions and metrics, offering a novel paradigm for large-scale knowledge graph embedding and reasoning. In summary, the Enhanced TransD model demonstrates robust and consistent performance gains across two datasets with distinct semantic structures and relational complexities. In retrieval and ranking tasks over entity-relation pairs, its augmented dynamic mapping mechanism and differentiated loss function jointly improve discrimination between positive and negative samples. For classification and hit-rate metrics, the enhanced model significantly outperforms traditional translation-based baselines, with the attribute projection module offering pronounced compensatory benefits in low-dimensional, resource-constrained settings. Moreover, convergence curves on both datasets exhibit greater stability and generalization, indicating that the dual-limit loss not only deepens separation in the embedding space but also mitigates overfitting. To assess the statistical significance of overall differences among paired model results, we conducted a Friedman test. All \(\chi^{2}\) statistics corresponded to \(p<0.05\), thereby rejecting the null hypothesis of \"no difference in model performance\". This confirms that observed variations are not due to random fluctuation and justifies subsequent Nemenyi post-hoc comparisons. We then performed the Nemenyi test to identify pairwise significant differences across evaluation metrics.