## 5 Experimental Results
### Ablation Studies  
In this section, we provide some of the aspects of the proposed architectures. **Influence on Training Time:** One of the critical components of any model is the training time. Table 4 shows the comparison between the training time for the baseline network and various RTr models on the Market-1501 dataset. It is evident that the training time increases drastically (from 55 min to 139 min) even employing two transformers in the model. Moreover, the training becomes much slower when the number of transformers increases as the training time is directly proportional to the number of transformers. **Increase in Number of Parameters:** The number of parameters is also increased when transformers are integrated into the baselines, as shown in Table 4 (second row). In this case, the baseline architecture i.e., _ResNet50_ has about 24.94 M parameters compared to 25.34 M parameters with only two transformers i.e., _RTr\({}_{(L_{1}M_{3}h_{4})}\)_. The number of parameters significantly becomes more when the transformers number increases i.e., _RTr\({}_{(L_{4}M_{3}h_{4})}\)_ having 75.11 M parameters due to 12 transformer modules. **Effect on the Computational Cost:** Compared to the base model, the transformer models adversely affect the computational cost in terms of time and number of parameters. Moreover, it should be noted that the parameters due to transformers and computations required for computing the self-attention in multi-head attention also affect the inference time; hence, need more time for re-identification. Overall, the computational cost increases due to the integration of transformers in base models. **Attention Focus in the Images:** In this section, we provide the focus of the transformers against the baselines. Figure 7 provides the focus maps similar to [42; 43] with the corresponding original images. Moreover, for each image, three explanation maps are generated via Grad-CAM++ [44] (1 st row), Score-CAM [45] (2 nd row), and Eigen-CAM [46] (3 rd row). Compared to baseline, our proposed transformer architectures focus on the specific details of the persons; for example, in the second row, the baseline focuses on the whole body while most transformers-based methods focus on the detailed specific body parts. **Number of Attention Heads:** We also investigate the effect of different numbers of self-attention heads employed in transformers. Table 5 shows the results for 1, 2, 4, and 16 headed self-attentions i.e., _h\({}_{1},\) h\({}_{2},\) h\({}_{4}\) and h\({}_{16}\)_ for Market-1501 integrated across three different levels utilizing three transformer modules while keeping all other training factors constant. Most of the best results are achieved for 4-headed attention; hence, we use _h\({}_{4}\)_ in all our experiments. It should also be noted that for _h\({}_{16}\)_, the models failed to converge. \begin{table}
\begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline  & **Baseline** & _RTr\({}_{(L_{1}M_{3}h_{4})}\)_ & _RTr\({}_{(L_{2}M_{3}h_{4})}\)_ & _RTr\({}_{(L_{3}M_{3}h_{4})}\)_ & _RTr\({}_{(L_{2}M_{3}h_{4})}\)_ & _RTr\({}_{(L_{2}M_{3}h_{4})}\)_ & _RTr\({}_{(L_{2}M_{3}h_{4})}\)_ & _RTr\({}_{(L_{2}M_{3}h_{4})}\)_ & _RTr\({}_{(L_{2}M_{3}h_{4})}\)_ \\ \hline Time & 55 min & 139 min & 154 min & 164 min & 178 min & 152 min & 197 min & 212 min & 234 min \\ Parameters & 24.94 M & 25.34 M & 26.91 M & 33.21 M & 58.39 M & 25.34 M & 27.90 M & 37.35 M & 75.11 M \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison on the Market dataset between the Residual Transformers in terms of training time (in minutes) and the number of parameters (in Millions).