## 4 Semi-Supervised Learning Based System
### Main Architecture  
The main ASR architecture used in this work is based on the unsupervised E2E model _wav2 vec2.0_ proposed by Facebook AI [28], which is schematically represented in Figure 1. The _wav2 vec2.0_ model maps speech audio through a multi-layer convolutional feature encoder \(f:\chi\to Z\) to latent speech representations \(z_{1},...z_{T}\), which are fed into a Transformer network \(g:Z\to C\) to output context representations \(c_{1},...c_{T}\). These context representations are then quantized to \(q_{1}...q_{T}\) in order to represent the targets in the self-supervised learning objective [28; 46]. The feature encoder contains seven blocks, and the temporal convolutions in each block include 512 channels with strides \((5,2,2,2,2,2)\) and kernel widths \((10,3,3,3,3,2,2)\). The transformer used had 24 blocks, a model dimension of 1024, an inner dimension of 4096 and a total of 16 attention heads. The model was pretrained by solving a contrastive task over masked feature encoder outputs. Afterwards, it was fine-tuned relative to the aphasia domain by adding a randomly initialized linear projection on top of the context network into C classes representing the vocabulary of the task [47] and optimized by using a Connectionist Temporal Classification (CTC) layer [28; 46; 48].  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**English**} & \multicolumn{2}{c}{**Train**} & \multicolumn{2}{c}{**Validation**} & \multicolumn{2}{c}{**Test**} & \multicolumn{2}{c}{**Total**} \\ \cline{2-9}  & **Speakers** & **Hours** & **Speakers** & **Hours** & **Speakers** & **Hours** & **Speakers** & **Hours** \\ \hline Mild & 105 & 26 & 36 & 9.9 & 48 & 12.8 & 189 & 48.7 \\ \hline Moderate & 79 & 18.7 & 27 & 6.1 & 36 & 8 & 142 & 32.8 \\ \hline Severe & 22 & 3.9 & 8 & 1.3 & 10 & 1.6 & 40 & 6.8 \\ \hline Very severe & 8 & 0.5 & 3 & 0.4 & 4 & 0.7 & 15 & 1.6 \\ \hline
**Total PWA** & 214 & 49.1 & 74 & 17.7 & 98 & 23.1 & 386 & 89.9 \\ \hline Controls & 277 & 51.3 & - & - & - & - & 277 & 51.3 \\ \hline
**Total (PWA + Controls)** & 491 & 100.4 & 74 & 17.7 & 98 & 23.1 & 663 & 141.2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Train, validation and test partitions of the English corpus.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Spanish**} & \multicolumn{2}{c}{**Train**} & \multicolumn{2}{c}{**Validation**} & \multicolumn{2}{c}{**Test**} & \multicolumn{2}{c}{**Total**} \\ \cline{2-9}  & **Speakers** & **Hours** & **Speakers** & **Hours** & **Speakers** & **Hours** & **Speakers** & **Hours** \\ \hline Total PWA & 4 & 0.69 & 4 & 0.23 & 4 & 0.28 & 4 & 1.2 \\ \hline Controls & 415 & 1 & - & - & - & - & 415 & 1 \\ \hline
**Total (PWA + Controls)** & 419 & 1.69 & 4 & 0.23 & 4 & 0.28 & 419 & 2.2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Train, validation and test partitions of the Spanish corpus.  
The pretrained task was based on the _XLSR-53_[46] model, which was originally trained with 56,000 h of nontranscribed speech data in 53 different languages, including English and Spanish. These data were composed of audio from the CommonVoice [43], Babel [49] and Multilingual Librispeech (MLS) [50] datasets. The unsupervised task learns a set of quantized latent speech representations shared across languages that are later combined together on the supervised training to identify the phonemes or characters to decode. The speech audio representations are learned by solving a contrastive task, which requires identifying the true quantized latent speech representation for a masked time step within a set of distractors [28]. This strategy has been shown to be capable of learning non-language-dependent universal quantized representations of speech that can then be combined to train specific phonemes and sounds of each language [46].