# Enhancing Propaganda Detection in Arabic News Context Through Multi-Task Learning
## 3 Methodology
### Mathematical Notations of the Problem  
For a better description of the proposed MTL model for Arabic propaganda detection, the following mathematical notation can be introduced:  
* Let \(\{\,D_{t}\,\}_{t=1}^{T}\) be the data from the task set. Specifically, \[\text{D}_{t} =\{(\text{x}_{1},\text{y}_{1}),(\text{x}_{2},\text{y}_{2}),\ldots,( \text{x}_{n},\text{y}_{n})\}_{i=1}^{N}\] (1) where
* \(D_{t}\) represents the training data for task.
* \(N\) represents the number of examples in \(D_{t}\).
* \(x_{i}\) represents the input text (news text).
* \(y_{i}\) represents the corresponding label of task \(t\). The label for each task is associated with the input \(x_{i}\), where \(y_{i}\) denotes the label for the \(t^{th}\) task. For example, \(y_{1}\) may represent the label for propaganda detection (1--propaganda, 2--nonpropaganda), \(y_{2}\) may represent sentiment analysis labels (1--positive, 2--negative, 3--neutral), and \(y_{3}\) may represent emotion detection labels (1--happiness, 2--sadness, 3--anger, 4--fear, 5--none).
* \(T\) represents the total number of tasks. Each task \(t\) corresponds to a specific task such as propaganda detection, sentiment analysis, or emotion detection.
* Each pair \((x_{i},y_{i})\) is used for training. \[\text{H} =\{\text{h}_{1},\text{h}_{2},\ldots,\text{h}_{M}\}\] (2) where
* \(T\) represents the total number of tasks. Each task \  
* \(H\) represents the set of shared hidden layers across all tasks. These layers are responsible for extracting generalized features from the input text that are relevant to all tasks. \[\left\{Z_{t}\right\}_{t=1}^{T}\] (3) where: \(Z_{t}\) represents the task descriptor, or task-specific dictionary, generated in the shared layers for task t, where \(t\in\left\{1,\,2,\,3,\,\ldots,\,T\right\}\) denotes each task in the MTL framework, as described earlier. Specifically, \(Z_{t}\) is a task-specific feature vector that captures the relevant information for task \(t\) derived from the shared representations learned in the shared layers. This descriptor is then passed to the task-specific layers, where it guides the model's learning process for the corresponding task. \[\mathrm{L}_{t}\left(y_{i}\,^{\wedge},y_{i}\right)\] (4) where \(Z_{t}\) represents the loss function for task \(t\). This loss measures the discrepancy between the predicted label \(y_{i}\,^{\wedge}\) and the true label \(y_{i}\) for task \(t\). \[\theta_{\mathrm{sh}} =\left\{\ \theta_{\mathrm{sh1}},\theta_{\mathrm{sh2}},\ldots, \theta_{\mathrm{shm}}\,\right\}\] (5) where \(\theta_{\mathrm{sh}}\) represents the set of parameters shared across the MTL model during the encoding process. \(\mathrm{n}\) represents the total number of shared parameters in the encoding stage. \[\theta_{t} =\left\{\theta_{t1},\theta_{t2},\ldots,\theta_{\mathrm{tm}}\,\right\}\] (6) where \(\theta_{t}\) represents the task-specific parameters for the output decoder heads corresponding to task t. These parameters are unique to each task and are used to generate final predictions for each task. \(\mathrm{m}\) represents the total number of parameters specific to task t in the output decoder. Table 2 provides summary definitions of the symbols employed throughout the description of the proposed framework.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Explanation** \\ \hline T & Total number of tasks t = (1,..., T) \\ \hline D\({}_{t}\) & Training data for task t \\ \hline N & Number of examples in D\({}_{t}\) \\ \hline \(x_{i}\) & Input text x = (x\({}_{1}\),..., x\({}_{N}\)) \\ \hline \(y_{i}\) & Label set for input text \(x_{i}\) \\ \hline \(Z_{t}\) & Task descriptor generated in the shared layers \\ \hline \(L_{t}\) & Loss function for task \(t\) \\ \hline \(\theta_{\mathrm{sh}}\) & Shared parameters during the encoding stage \\ \hline \(\theta_{t}\) & Task-specific parameters for output decoder heads \\ \hline \hline \end{tabular}
\end{table}
Table 2: Symbols’ definitions in the proposed MTL.