# Automatic Translation between Mixtec to Spanish Languages Using Neural Networks
## 4 Methodology
### Phase 2: Developing and Applying the Corpus Processing Module
The distribution was as follows: 70% (3197 pairs) were allocated for training, 15% (685 pairs) for validation, and the remaining 15% (685 pairs) for testing. The focus was specifically on educational texts, which included materials such as the Mexican national anthem, everyday dialogues, descriptions of objects, and sentences in the past tense. Table 12 shows the outcomes of the automatic evaluation, employing both the BLEU and TER metrics, for translations from Spanish to Mixtec. The highest scores obtained in the experiments are highlighted in bold. Table 13 shows the results of the automatic evaluation with the Mixtec-Spanish BLEU and TER metrics. Table 14 provides example predictions from Mixtec to Spanish. Each sentence from the first column represents the input to the model to predict the output shown in the second column. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Approaches** & **BLEU \(\times\) 100** & **TER** \\ \hline RNN + Dropout 0.0 + 1 Layer + Batch Size 16 & 5.08 & 84.21 \\ RNN + Dropout 0.1 + 3 Layer + Batch Size 16 & 0.50 & 90.44 \\ BRNN + Dropout 0.0 + 1 Layer + Batch size 16 & 0.73 & 90.32 \\ BRNN + Dropout 0.1 + 3 Layer + Batch size 16 & 1.46 & 95.31 \\ Transformer + Dropout 0.1 + 6 Layer + Batch size 4096 & **95.66** & **16.5** \\ Transformer + Dropout 0.2 + 6 Layer + Batch size 4096 & 95.59 & 16.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Mixtec-to-Spanish evaluation using BLEU and TER metrics. The table compares different model architectures—such as RNN, BRNN with Dropout, and Transformer with Dropout—across varying layers. The highest-scoring results are highlighted in bold for easy identification. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Approaches** & **BLEU \(\times\) 100** & **TER** \\ \hline RNN + Dropout 0.0 + 1 Layer + Batch Size 16 & 0 & 100 \\ RNN + Dropout 0.1 + 3 Layer + Batch Size 16 & 1.44 & 98.86 \\ BRNN + Dropout 0.0 + 1 Layer + Batch Size 16 & 0.2 & 99.35 \\ BRNN + Dropout 0.1 + 3 Layer + Batch Size 16 & 0 & 100 \\ Transformer + Dropout 0.1 + 6 Layer + Batch size 4096 & **99.87** & 0.5 \\ Transformer + Dropout 0.2 + 6 Layer + Batch size 4096 & 99.80 & **0.10** \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Spanish-to-Mixtec evaluation using BLEU and TER metrics. The table compares different model architectures—such as RNN, BRNN with Dropout, and Transformer with Dropout—across varying layers. The highest-scoring results are highlighted in bold for easy identification. The best Spanish-to-Mixtec translation model was the Transformer with six layers and Dropout of 0.1, achieving a BLEU score of 99.87 and a TER of 0.5. For the Mixtec-to-Spanish translation, the best model was the same Transformer architecture with six layers and a Dropout of 0.1, achieving a BLEU score of 95.66 and TER of 16.5. In terms of training durations, the RNN and BRNN models completed their training in an average of 30 min, whereas the training time for the Transformer models extended to four hours. Table 15 offers a comparative analysis between our translation approach for Mixtec-Spanish and related low-resource language work highlighted in the literature review. These results demonstrate a significant improvement, showing a 28% increase in BLEU score with respect to scores obtained in related studies. ## 6 Discussion

Our review of the state of the art in machine translation revealed several challenges in translating low-resource languages, including the absence of natural language processing tools, limited text availability, and the complexity of tonal variations. The following points detail these challenges:

* Lack of Natural Language Processing Tools: Resources such as grammatical taggers, normalizers, and automatic tokenizers, crucial for processing these languages, are often unavailable. * Restricted Corpus Size: Corpora in low-resource languages are typically small, leading to a lack of sufficient texts for experimentation and validation in translation processes.