## 3 KGs Learning
### TransE-Based Approaches  
**TransE**[79] learns embeddings for triples (h, r, t) by representing entities (h, t) and relations (r) as low-dimensional vectors that ideally satisfy using a margin-based ranking loss that pulls real triples closer while pushing negative (corrupted) triples apart. Its simplicity, rapid training on large datasets, and scalability have made it a popular foundational method.  
\[\text{h}+\text{r}\approx\text{t} \tag{1}\]  
However, a single-vector operation often struggles to capture complex relational patterns. In particular, one-to-many or many-to-one relationships pose a significant challenge. For example, by constructing a KG from patent and technical report data, basic embeddings are obtained with TransE and then enhanced by training additional diffusion and absorption vectors to predict \"how ideas flow between technological domains\" in Technological Knowledge Flow models [80]. To further improve accuracy, the Multi-Filter Soft Shrinkage technique combines convolutional layers with TransE embeddings as initialization, suppressing noise while modeling higher-order interactions [81].  
Because TransE embeddings can degrade on sparse or incomplete graphs, iterative rule-guided reasoning methods employing reinforcement learning (RL) have been proposed to dynamically supplement \"missing paths\" and update embeddings [82]. The SSKGE framework integrates structural reinforcement and semantic guidance to reduce the training time and improve link prediction performance [83]. HolmE extends TransE by capturing compositional patterns in Riemannian space, providing a generalized embedding framework that encompasses models like TransE and RotatE [84].  
Another extension employs TransE as the embedding backbone with a two-level RL mechanism for multi-hop reasoning. In this hierarchical RL approach, a high-level agent decides which relation to explore while a low-level agent selects the appropriate node for that relation, effectively compressing the action space and updating the model end-to-end [85]. To handle continuously emerging entities and relations, embedding generators are trained to create vectors dynamically from side information (e.g., text or attributes), preserving the overall vector space structure for real-time or online KG completion [86].  
Finally, for temporal knowledge graphs (TKGs), techniques such as the Temporal-Structural Adaptation Network (TSA-Net) incorporate specialized embedding modules or recurrent mechanisms to capture complex temporal dependencies among temporal, relational, and entity representations [87].  
Collectively, these studies demonstrate that while TransE [79] provides a simple and scalable foundation for knowledge graph embedding, its inherent limitations--such as difficulty in capturing complex relational patterns and sensitivity to data sparsity--have spurred various enhancements. For example, hierarchical and convolutional extensions [80,81] improve the modeling of knowledge flow and noise suppression, whereas iterative rule-guided reasoning frameworks using reinforcement learning [82,85] effectively supplement the missing paths in sparse graphs. Additionally, approaches for open-world and temporal graph completion [86,87] have been developed to dynamically adapt to emerging entities and time-dependent data.