## 4 Experiments and Numerical Results
### Parameter Evaluation  
We hypothesized that the quantity of multi-hop neighbor information may have an impact on relation instantiation. Figure 8 illustrates the impact of the number of one-hop neighbors (left figure) and the number of multi-hop neighbors (right figure) on model performance. For the one-hop neighbors, the number of neighbors significantly influences the model's performance, and the optimal number varies across different datasets. The FB15K237 and CoDEx-M datasets exhibit optimal performance with 40 one-hop neighbors, while the WN18 RR and CoDEx-L datasets perform best with 30 and 20 one-hop neighbors, respectively. The experimental results across the four datasets indicate that the increase in the number of one-hop neighbors correlates positively with the model's performance, particularly when the number of neighbors is small. However, beyond a certain performance threshold, the additional increase in one-hop neighbors no longer contributes significantly to the model's performance. For the multi-hop neighbors, we conducted further experiments with varying multi-hop neighbor settings, as listed in Table 6. For the multi-hop neighbors, their influence on the model's performance was not substantial. This is attributed to the fact that the embeddings of multi-hop neighbors are indirectly utilized in the instantiation for relation modules through an average pooling operation, which is not directly employed in constructing the features of the target entity. In terms of specific datasets, FB15K237 and CoDEx-L achieved their best performance in Setting-2, whereas WN18 RR and CoDEx-M attained their optimal performance in Setting-3. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**FB15K-237**} & \multicolumn{4}{c}{**WN18 RR**} \\ \hline
**Model** & **MRR** & **H@1** & **H@3** & **H@10** & **MRR** & **H@1** & **H@3** & **H@10** \\ \hline DisMult [27] & 0.241 & 0.155 & 0.263 & 0.419 & 0.430 & 0.390 & 0.440 & 0.490 \\ RotatE [20] & 0.338 & 0.241 & 0.375 & **0.533** & 0.476 & 0.428 & 0.492 & 0.571 \\ QuatE [23] & 0.311 & 0.221 & 0.342 & 0.495 & 0.481 & 0.436 & 0.500 & 0.564 \\ MuRP [33] & 0.335 & 0.243 & 0.367 & 0.518 & 0.481 & 0.440 & 0.495 & 0.566 \\ MuRE [33] & 0.336 & 0.245 & 0.370 & 0.521 & 0.475 & 0.436 & 0.487 & 0.554 \\ ConvVE [36] & 0.325 & 0.237 & 0.356 & 0.501 & 0.430 & 0.400 & 0.440 & 0.520 \\ HypER [37] & 0.341 & 0.252 & 0.376 & 0.520 & 0.465 & 0.436 & 0.477 & 0.522 \\ MTL-KGC [21] & 0.267 & 0.172 & 0.298 & 0.458 & 0.331 & 0.203 & 0.383 & 0.597 \\ StAR [41] & 0.296 & 0.205 & 0.322 & 0.482 & 0.401 & 0.243 & 0.491 & 0.709 \\ KGLM [44] & 0.289 & 0.200 & 0.314 & 0.468 & 0.467 & 0.330 & **0.538** & **0.741** \\ \hline RiQ-KGC (ours) & **0.346** & **0.257** & **0.378** & 0.524 & **0.496** & **0.457** & 0.509 & 0.572 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of model results on FB15K-237 and WN18 RR datasets, where the bold font represents the optimal result and the underlined font represents the sub-optimal result. The results of these baselines are taken from their original article. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**FB15K-237**} & \multicolumn{4}{c}{**WN18 RR**} \\ \hline
**Model** & **MRR** & **H@1** & **H@3** & **H@10** & **MRR** & **H@1** & **H@3** & **H@10** \\ \hline TransE [19] & 0.303 & 0.223 & 0.336 & 0.454 & 0.187 & 0.116 & 0.218 & 0.317 \\ RESCAL [29] & 0.317 & 0.244 & 0.347 & 0.456 & 0.304 & 0.242 & 0.331 & 0.419 \\ ComplEx [28] & 0.337 & **0.262** & **0.370** & 0.476 & 0.294 & 0.237 & 0.318 & 0.400 \\ ConvVE [36] & 0.318 & 0.239 & 0.355 & 0.464 & 0.303 & 0.240 & 0.330 & 0.420 \\ TuckER [45] & 0.328 & 0.259 & 0.360 & 0.458 & 0.309 & **0.244** & 0.339 & 0.430 \\ \hline RiQ-KGC (ours) & **0.339** & **0.262** & 0.368 & **0.484** & **0.313** & 0.242 & **0.340** & **0.448** \\ \hline \hline \end{tabular}
\end{table}