# Learning Translation-Based Knowledge Graph Embeddings by \(N\)-Pair Translation Loss
## 5 Experiments
### Experimental Results  
We first examine the effectiveness of negative triples. Thus, the change of performances is investigated according to \(N\), the number of negative triples. The result is shown in Figure 2. Figure 2a,b \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dataset** & **WN18 RR** & **FB15K-237** \\ \hline \# Entities & 93,003 & 14,541 \\ \# Relations & 11 & 237 \\ \hline \# Training Triples & 86,835 & 272,115 \\ \# Validation Triples & 3034 & 17,535 \\ \# Test Triples & 3134 & 20,466 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simple statistics on data sets. are the performances of TransE on WN18 RR and FB15K-237 with a various number of negative triples, while Figure 2c,d show those of TransD. In all figures, the X-axis is the number of epochs, and the Y-axis represents the Hits@10. Here, '1' (expressed as the blue curve) implies that only one negative triple is considered in training the embedding models. Therefore, the embedding model with '1' is equivalent to that trained with the margin-based ranking loss. Similarly, \(N(N>1)\) means \(N\) negative triples are used. Thus, the performances of \(N\) are obtained using the \(N\)-pair translation loss. As these figures show, all non-blue curves are always above the blue curve regardless of epochs. That is, the performances of the \(N\)-pair translation loss are higher than that of the margin-based ranking loss. This proves that considering multiple negative triples in every parameter update leads to significant performance improvement over adopting one negative triple. Another thing to note in Figure 2 is that the Hits@10's of the \(N\)-pair translation loss rise up much faster than that of the margin-based ranking loss (the blue curve). That is, the \(N\)-pair translation loss converges faster than the margin-based ranking loss. In more detail, the margin-based ranking loss does not converge until 1000 epochs in all figures, while the \(N\)-pair translation loss converges to a stable Hits@10 before 400 epochs. This verifies that the \(N\)-pair translation loss is helpful for fast convergence. The convergence speed is an important feature for translation-based knowledge graph embeddings because a number of other knowledge graph embedding models use a translation-based model as its base model. That is, when a new knowledge graph is given, such embedding models require fast vector representation of the knowledge graph as a prerequisite. Therefore, fast convergence of a translation-based knowledge graph embedding by the proposed \(N\)-pair translation loss is worthy. The last observation is that the optimal number of negative triples is not always the largest number. For the WN18 RR data set (Figure 2a,c), the best performance is obtained when 10 negative triples are used. On the other hand, adopting 200 negative triples achieves the best performance for the FB15K-237 data set (Figure 2b,d). This is because negative triples are generated by random  
Figure 2: Hit@10 performances according to various numbers of negative triples. (**a**) WN18 RR—TransE, (**b**) FB15K-237—TransE, (**c**) WN18 RR—TransD, (**d**) FB15K-237—TransD. sampling of entities. All negative triples are not tightly related with the positive triple, and thus some of them behave as noise to learning the embeddings. This result is consistent with the previous study by [PERSON] et al. [37]. Table 2 presents the experimental results on link prediction for all data sets. The proposed translation-based embeddings by the \(N\)-pair translation loss are compared with the state-of-the-art knowledge graph embeddings that use their own negative sampling method. The compared embeddings include KBGAN [15], IGAN [16], and NSCaching [17], and their performances are referred from their reports since we use the same data sets. 'Margin' in this table implies the translation-based embedding with the margin-based ranking loss.