## 4 Experiments
### Results  
For evaluation, the captions were generated by random sampling of the latent distribution and their performance was measured. We randomly extracted 100 samples of M-dimension from the standard normal and uniform distributions. Both accuracy and diversity metrics had to be calculated to evaluate the multiple captioning systems. The accuracy, METEOR [20], ROUGE [21], SPICE [22], and CIDEr [23] metrics were measured for the 100 descriptions generated by the models. To improve the reliability of the random extraction evaluation, the sampling and evaluation processes were repeated five times and the mean value is shown in Table 1. Table 2 compares the diversity score of the base model with that of the proposed model. Div-s was measured for \(S_{p}\), which contained all 100 descriptions. In the case of Div-1, other combinations of \(S_{p}\) should be used to match with the scale of the evaluation score [13]. [PERSON] [13] used the GAN network to derive five different descriptions for each image and to evaluate the diversity of these five descriptions. With this method, when the network is trained, five captions are regarded as one set, and the parameters are learned in the direction that increases the variation among the descriptions in the set. However, with the proposed method, only one caption was generated from one sampling in the network, and the performance varied depending on where the latent variable was extracted in the latent space. Therefore, it is difficult to compare this with the results of [13]. The following method was used for numerical comparison. We generated combinations of five different captions out of 100 and they were treated as \(S_{p}\)s. If there were fewer than five different captions, the rest of the captions were filled with the shortest sentence. In Table 2, \(k\) represents the number of images with five or more different captions out of 5000 test sets, and this is represented in the table. The max Div-1 represents \(MEAN_{i}[MAX_{s}(Div-1)]\), where i and s denote the image index and caption combination set index, respectively. The average Div-1 represents \(MEAN_{i}[MEAN_{s}(Div-1)]\). As represented in Table 1, the accuracy of the proposed model and the base one were comparable with N1 sampling. Moreover, the proposed method showed better performance in the diversity evaluation with N1 sampling, as shown in Table 2. Div-s was larger with the proposed model and \(k\) increased greatly from 38 to 133. This means that the model generated more different sentences in 100 samples. Both max Div-1 and average Div-1 values were also larger with the proposed model. U20, U30, and U40 cannot be compared one by one, but the table shows that the larger the sampling \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sampling**} & \multicolumn{4}{c}{**Base Model**} & \multicolumn{4}{c}{**Proposed Model**} \\ \cline{2-9}  & **METEOR** & **ROUGE** & **SPICE** & **CIDEr** & **METEOR** & **ROUGE** & **SPICE** & **CIDEr** \\ \hline N1 & **0.249** & 0.532 & **0.183** & 0.976 & 0.248 & **0.533** & 0.182 & **0.980** \\ U20 & 0.246 & 0.527 & 0.180 & 0.959 & 0.240 & 0.523 & 0.174 & 0.929 \\ U30 & 0.244 & 0.526 & 0.179 & 0.952 & 0.230 & 0.510 & 0.163 & 0.864 \\ U40 & 0.244 & 0.524 & 0.178 & 0.948 & 0.218 & 0.493 & 0.149 & 0.780 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental results of captioning accuracy with the base model and the proposed model. Both evaluation results are comparable with N1 sampling.