## 5 Results  
Having introduced the considered experimental scheme and the different models proposed, we now present and discuss the results obtained. Since the experiments have been performed in a cross-validation scheme, this section provides the average values obtained for each of the cases considered. It must be remarked that the figures reported constitute that of the test data partition for the case in which the validation data achieve their best performances. The results obtained in terms of the Symbol Error Rate (Sym-ER) for the base neural configuration and the three different proposed architectures for each data corpus considered are shown in Figure 5. Note that these recognition models consider the \(\Sigma_{T}\) vocabulary case, i.e., each detected element is represented as the 2-tuple that defines both the shape and pitch of the symbol. An initial remark is that, as it can be appreciated in Figure 5, all proposed architectures improve the results obtained by their respective baselines except for the case of the _PreRNN_ architecture in the _raw_ scenario for the _Capitan_ corpus. By examining this graph, we may also check that the _InterRNN_ model is the one that consistently achieves the best error rates for all scenarios considered, tied only with the _PostRNN_ proposal for the _raw_ case of the _Il Lauro Secco_ set. It must be also noted that, for all cases, the error rates obtained with the _Capitan_ corpus are remarkably higher than the ones obtained with the _II Lauro Secco_ set. This is a rather expected result since the graphical variability inherent to handwritten data compared to the typeset format supposes a drawback to the recognition algorithm. Moreover, the latter corpus depicts a lower vocabulary size, which also simplifies the complexity of the task. Having visually checked the behavior of the different schemes considered, Table 3 numerically reports these Symbol Error Rate (Sym-ER) figures as well as the Sequence Error Rate (Seq-ER) ones for the same scenarios considered for a more detailed analysis. The trends observed in the sequence error rate are consistent with the ones already provided by the symbol error rate metric in Figure 5. In general, for this Seq-ER figure of  
Figure 5: Comparison of the base neural model and the different architectures proposed for the \(\Sigma_{T}\) vocabulary case in terms of the Symbol Error Rate (Sym-ER (%)) and their respective standard deviations. _Pretrained_ and _raw_ denote the cases in which shape and height branches have been trained or not before considering the joint model, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Baseline**} & \multicolumn{2}{c}{**PreRNN**} & \multicolumn{2}{c}{**InterRNN**} & \multicolumn{2}{c}{**PostRNN**} \\ \cline{3-8}  & & **Raw** & **Pretrained** & **Raw** & **Pretrained** & **Raw** & **Pretrained** \\ \hline Sym-ER (\%) & & & & & & & \\ _Capitan_ & 10.32 & 11.12 & 8.62 & 7.68 & 8.18 & 8.30 & 8.39 \\ _Il Lauro Secco_ & 4.87 & 4.54 & 4.70 & 4.35 & 4.17 & 4.36 & 4.42 \\ \hline Seq-ER (\%) & & & & & & & \\ _Capitan_ & 86.53 & 89.37 & 81.39 & 77.15 & 76.41 & 78.21 & 80.70 \\ _Il Lauro Secco_ & 36.16 & 33.40 & 37.47 & 31.26 & 32.75 & 31.45 & 34.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results obtained in terms of the Symbol (Sym-ER) and Sequence (Seq-ER) Error Rates comparing the base neural model with the different architectures proposed for the \(\Sigma_{T}\) vocabulary case. _Pretrained_ and _raw_ denote the cases in which shape and height branches have been trained or not before considering the joint model, respectively. merit, all results improve the base neural configuration considered except for the _PreRNN_ model in two particular situations: when tackling the _Capitan_ set in the _raw_ scenario and for the _Il Lauro Secco_ corpus in the _pretrained_ case.