## Materials and Methods
### Accuracy Performance Results  
Table 2 summarizes the results obtained by the encoder-decoder networks using CFE configured with both methods, manual and random search, and the alternative state-of-the-art methods, for the three problems of interest.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Hyperparameter** & \multicolumn{2}{c}{**Text Translation**} & \multicolumn{2}{c}{**LaTeX Decompilation**} & \multicolumn{2}{c}{**Audio Transcription**} \\
**Method** & **Manual** & **Random** & **Manual** & **Random** & **Manual** & **Random** \\ \hline Bridge & no & yes & no & yes & no & yes \\ Global attention & general & concat & general & dot & general & dot \\ Position encoding & no & yes & no & no & yes & no \\ RNN layers & 3 & 4 & 2 & 1 & 2 & 1 \\ RNN size & 512 & 238 & 500 & 414 & 500 & 126 \\ CNN kernel width & 5 & 3 & 5 & 11 & 5 & 7 \\ Receptive field & 20 & 13 & 20 & 16 & 20 & 17 \\ Normalization & tokens & sents & sents & sents & sents & tokens \\ Batch size & 64 & 16 & 20 & 12 & 16 & 9 \\ Max grad. norm. & 1 & 14.12 & 20 & 28.68 & 20 & 3.79 \\ Dropout & 0.3 & 0.71 & 0.3 & 0.2 & 0.3 & 0.52 \\ Learning rate decay & 0.5 & 0.654 & 0.5 & 0.576 & 0.5 & 0.465 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hyperparameters of the encoder-decoder networks used in the three problems of interest. Bridge: add a dense layer between encoder and decoder. Global attention: score function used in the attention model. Position encoding: add position information in the encoding. RNN layers: number of layers in the RNN of the decoder. RNN size: number of units in each layer of the RNN. CNN kernel width: size of the convolution filters in CFE. Receptive field: selected receptive field for the CFE. Normalization: method used to normalize the gradients. Batch size: size of the batches used in the training. Max grad. norm.: maximum allowed norm of the gradient. Dropout: dropout rate used. Learning rate decay: value applied to reduce the learning rate.  
\begin{table}
\begin{tabular}{l l c c c} \hline \hline
**Problem** & **Method** & **BLEU/WER \%** & **ACC \%** & **PER** \\ \hline Text translation & CFE Manual & 23.34 & 62.73 & 13.59 \\
75,000 iterations & CFE Random & 27.80 & 63.02 & 13.39 \\  & LSTM & 36.48 & 69.64 & 11.52 \\  & Transformer & 34.95 & 67.78 & 14.30 \\ \hline LaTeX decompilation & CFE Manual & 77.57 & 96.55 & 1.24 \\
25,000 iterations & CFE Random & 75.82 & 96.56 & 1.24 \\  & Im2 Text & 80.46 & 96.78 & 1.13 \\ \hline Audio transcription & CFE Manual & 53.12 & 60.13 & 8.84 \\
60,000 iteration & CFE Random & 55.05 & 59.13 & 22.4 \\  & Lis.-Att.-Spell & 43.14 & 70.98 & 5.37 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental results for the proposed CFE model and other architectures. BLEU/WER: accuracy measures for the test set, bilingual evaluation understudy (text translation and LaTeX decompilation) and word error rate (audio transcription), respectively; ACC and PER: accuracy and perplexity obtained for the validation set, respectively. The total number of iterations applied for each problem in the training process is indicated.  
Figure 3 contains a graphical representation of the training process for these problems, showing the cross entropy of the models throughout the iterations applied.