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\title{DeepSemantics at SemEval-2026 Task 9: Label-Wise Optimization with Adaptive Focal Loss for Polarization Manifestation Identification}

% Author information can be set in various styles:
% For several authors from the same institution:
% \author{Author 1 \and ... \and Author n \\
%         Address line \\ ... \\ Address line}
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\author{
Eliasse Tiao,\quad Josue R. Edou,\quad Mahugnon A. L. Gohouede \\
African Institute for Mathematical Sciences (AIMS), South Africa  \\
\texttt{eliasse@aims.ac.za},\quad \texttt{josue@aims.ac.za} ,\quad \texttt{aimeloick@aims.ac.za} 
}



\begin{document}
\maketitle

\begin{abstract}
In this paper, we present our system for SemEval-2026 Task 9, which focuses on the fine-grained identification of polarization manifestations in multilingual social media content. Our approach combines transformer-based encoders (RoBERTa-base for English and Afro-XLM-R-small for Hausa) within a One-vs-Rest (OvR) framework, complemented by controlled oversampling, Adaptive Focal Loss, and label-wise threshold optimization. To mitigate severe class imbalance and label sparsity, we adopt language-specific optimization strategies supported by pairwise $\chi^2$ independence analysis. Our system achieves macro-F1 scores of 0.464 in English and 0.192 in Hausa on the 
official test sets, ranking 5\textsuperscript{th} in Hausa and 
14\textsuperscript{th} in English on the official leaderboard. Our code is publicly available \footnote{\url{https://github.com/TIAO-Eliasse/DeepSemantics-SemEval}}.
\end{abstract}
\section{Introduction}

Social media messages often reflect strong and opposing attitudes related to social, political, or identity divisions, which contribute to online polarization \citep{conover2011political, garimella2018polarization, barbera2020social, kubin2021three}. Subtask 3 of the POLAR 2026 shared task\citep{naseem-etal-2026-polar}, Manifestation Identification, focuses on classifying messages according to multiple manifestations of polarization, such as Vilification, Dehumanization, Extreme Language, Lack of Empathy,  Invalidation and Stereotype. 

This task is particularly challenging due to severe class imbalance, sparse annotations, and low-resource languages such as Hausa, where training data is limited. Traditional joint multi-label approaches can often underperform in this setting, as rare labels generate sparse gradients that are dominated by frequent manifestations, resulting in poor recall for minority classes.

To address these challenges, we adopt a One-vs-Rest (OvR) strategy that models each manifestation independently. This label-wise formulation is complemented by language-specific optimization: Adaptive Focal Loss for English dynamically reweights gradients to emphasize rare classes, and weighted Binary Cross-Entropy with controlled oversampling for Hausa compensates for extreme imbalance. Thresholds for each label are optimized via stratified $K$-fold validation to improve decision calibration. Transformer encoders (RoBERTa-base for English and Davlan Afro-XLM-R-small for Hausa) provide contextual embeddings that enhance multilingual representation learning.

Experimental comparisons confirm that OvR consistently outperforms joint multi-label models, particularly for rare manifestations where joint modeling often fails. Our system achieves macro-F1 scores of 0.464 in English and 0.192 in Hausa on the official test sets, ranking 5\textsuperscript{th} in Hausa and 14\textsuperscript{th} in English. These results demonstrate robust performance under label sparsity and low-resource conditions, and motivate our label-wise modeling approach, which effectively captures fine-grained polarization manifestations while mitigating gradient interference in highly imbalanced multi-label settings.
\section{Related Work}

Fine-grained polarization analysis extends beyond binary detection by identifying specific manifestations expressed in text. This formulation naturally leads to a multi-label classification setting, where instances may exhibit multiple manifestations simultaneously. Prior work in multi-label learning has shown that joint modeling approaches often struggle under severe class imbalance and sparse label co-occurrence \cite{Tsoumakas2007MultiLabelCA, read2011classifier}.

Transformer-based models such as BERT and multilingual variants like XLM-R have become the dominant backbone for text classification tasks \cite{devlin2019bert, conneau2020xlmr}. While these models provide strong contextual representations, their effectiveness remains sensitive to imbalance in fine-grained classification scenarios.

To mitigate imbalance, previous studies have explored data-level strategies such as oversampling and text augmentation \cite{wei2019eda, feng2021survey}, as well as loss-level approaches including Focal Loss \cite{Lin2017}. Problem-transformation methods such as One-vs-Rest classifiers have also been shown to improve robustness in highly imbalanced multi-label settings \cite{Tsoumakas2007MultiLabelCA}.

Building on these findings, our approach integrates transformer representations with controlled oversampling, data augmentation, Adaptive Focal Loss, and a One-vs-Rest formulation, explicitly targeting the extreme sparsity and imbalance observed in manifestation identification.

\section{System Overview}
For manifestation identification, the focus shifts to label heterogeneity and rare classes. Traditional monolithic multi-label frameworks, which predict all labels jointly, often underperform on rare labels and fail to capture label-specific decision boundaries \cite{read2011classifier,Tsoumakas2007MultiLabelCA}. 

To address these limitations, we adopt a One-vs-Rest (OvR) strategy, modeling each manifestation independently.

To further address class imbalance, we combine controlled minority oversampling with loss-based reweighting strategies. For English, Adaptive Focal Loss dynamically down-weights easy examples and emphasizes rare manifestations. For Hausa, because of  severe imbalance, we employ cost-sensitive learning via weighted binary cross-entropy combined with controlled oversampling.

\subsection{Controlled Oversampling and Augmentation}
To address the severe class imbalance, we implement a label-wise controlled oversampling strategy within our OvR framework. For each binary classifier, oversampling is triggered only when the imbalance ratio (negative-to-positive) exceeds a threshold of 5:1. 

Specifically, the number of duplications $R$ is dynamically calculated as: 
$R = \lceil (N_{neg} / N_{pos}) / 5 \rceil - 1$, where $N_{neg}$ and $N_{pos}$ are the counts of negative and positive instances for the target label, respectively. Positive instances are then duplicated $R$ times to ensure the final training ratio does not exceed 5:1. 
To prevent the model from overfitting on identical samples, we follow duplication with Easy Data Augmentation (EDA) \cite{wei2019edaeasydataaugmentation}, applying synonym replacement and random insertion to the oversampled set. This approach ensures that sampling is controlled independently for each manifestation, providing the necessary gradient signal for rare labels like lack\_of\_empathy without introducing the noise associated with full class balancing.
\subsection{Dynamic Gradient Optimization via Adaptive Focal Loss}

As introduced in the previous section, data augmentation and controlled oversampling mitigate class imbalance at the data level.
However, these techniques alone are insufficient to address imbalance during optimization, particularly in One-vs-Rest settings where rare polarization labels generate sparse and noisy gradients.
We therefore complement data-level balancing with a loss-level strategy based on Adaptive Focal Loss, which dynamically reweights gradient contributions according to prediction difficulty and class distribution \cite{Lin2017}.

Let $x_i$ denote an input text with binary label $y_i \in \{0,1\}$, and let $\hat{y}_i = \sigma(z_i)$ be the predicted probability.
Unlike standard Binary Cross-Entropy (BCE), which assigns equal importance to all samples, focal loss down-weights well-classified instances and emphasizes hard examples.
The loss for a single instance is defined as:

\begin{equation}
\mathcal{L}_{\mathrm{FL}}(x_i) 
= - \alpha_{y_i} \, (1 - p_i)^{\gamma} \, \log(p_i),
\end{equation}
where
\begin{equation}
p_i = 
\left\{
\begin{array}{lll}
\hat{y}_i & \text{if}&  y_i = 1,\\[1mm]
1 - \hat{y}_i & \text{if}&  y_i = 0.
\end{array}
\right.
\end{equation}


The focusing parameter $\gamma > 0$ controls the degree to which easy examples are down-weighted, thereby preventing dominant negative samples from driving the optimization.
In addition, class-dependent weights $\alpha_{y_i}$ are used to explicitly compensate for label imbalance:


\begin{equation}
\alpha_{y_i} =
\left\{
\begin{array}{ll}
\alpha \cdot w_+ & \text{if } y_i = 1,\\[1mm]
(1 - \alpha) \cdot w_- & \text{if } y_i = 0
\end{array}
\right.
\end{equation}
where $w_+$ and $w_-$ are dynamically computed from inverse class frequencies.

From an optimization perspective, this formulation induces a form of dynamic gradient reweighting.
For confidently predicted samples ($p_i \rightarrow 1$), the gradient magnitude decreases proportionally to:
\[
\frac{\partial \mathcal{L}_{\text{FL}}}{\partial z_i}
\propto (1 - p_i)^{\gamma},
\]
which stabilizes training and prevents gradient domination by frequent classes.
Consequently, rare polarization manifestations exert a stronger influence during learning.

Within our One-vs-Rest architecture, Adaptive Focal Loss is applied independently to each binary classifier, enabling label-specific optimization dynamics.
In combination with data augmentation and oversampling, this strategy substantially improves recall for rare labels while maintaining precision on frequent ones.
\subsection{Cost-Sensitive Optimization for Hausa}
Preliminary experiments applying Adaptive Focal Loss to Hausa resulted in 
gradient vanishing and unstable convergence. We attribute this instability 
to the extreme label sparsity of the Hausa dataset ($<1\%$ positive instances 
for several classes) — a regime in which the focal modulation term 
$(1-p_i)^\gamma$ suppresses gradients for the dominant negative class, leaving 
insufficient signal for minority class learning. Weighted BCE, by directly 
scaling the loss via $w_+ = N_{neg}/N_{pos}$, provides more stable gradient 
updates under such extreme imbalance. For an instance $x_i$, the loss is 
defined as:
\begin{equation}
\mathcal{L}_{\mathrm{BCE}}(x_i) = - w_+ y_i \log(\hat{y}_i) - w_- (1-y_i) \log(1-\hat{y}_i)
\end{equation}
where $w_+ = N_{neg}/N_{pos}$ scales the contribution of the minority class 
and $w_- = 1$. This cost-sensitive approach compensates for the imbalance by 
directly inflating the loss of rare manifestations, preventing the model from 
stagnating on the dominant negative class.

\subsection{Threshold Optimization}
Even with data-level balancing and loss reweighting, using a fixed decision threshold (e.g., $0.5$) can be suboptimal, particularly for rare polarization labels. 
To address this, we perform a complementary threshold optimization step at inference time.

Thresholds are selected independently for each One-vs-Rest classifier by maximizing the F1-score on the validation set. 
To improve robustness, the validation data is split into stratified $K=5$folds, thresholds are computed per fold, and the final threshold is obtained by averaging across folds.

It is applied uniformly across English and Hausa classifiers.
\section{Data Exploration}

In this section we begin by analyzing the distributional properties of the datasets , with a particular focus on class imbalance and label
co-occurrence patterns. These aspects are critical, as they directly influence
model design choices and evaluation strategies.

\subsection{Subtask 3: Manifestation Identification}
\subsubsection{Imbalance analysis in dataset}
We analyze the manifestation-level annotations, which further increase
the granularity and sparsity of the task. Figures~\ref{fig:dist3_en}
and~\ref{fig:dist3_hau} show a highly imbalanced label distribution in both
languages.

Most manifestations are extremely rare, reinforcing the need for label-specific
learning strategies.


\subsection{Independence Analysis of Manifestation Identifications}

To examine label interactions, we conduct pairwise $\chi^2$ independence tests on manifestation labels. As shown in Table~\ref{tab:chi2_pvalues_manifestation}, the English dataset exhibits statistically significant dependencies across nearly all label pairs, indicating frequent co-occurrence of manifestations. In contrast, the Hausa dataset shows significant dependencies for only a subset of pairs, while several others display high p-values, suggesting weaker or approximate independence. Overall, the dependency structure is heterogeneous and language-dependent.

Importantly, statistical dependence between labels does not necessarily imply that joint multi-label modeling is optimal. Prior work in multi-label learning highlights that explicitly modeling label correlations is not universally beneficial and may depend on data characteristics \cite{Tsoumakas2007MultiLabelCA}. Under severe class imbalance, joint optimization can amplify gradient dominance of frequent labels, potentially limiting the learning of rare manifestations.

Given the imbalance-sensitive nature of the POLAR task and the uneven dependency patterns observed across languages, we adopt a One-vs-Rest formulation. This approach enables label-specific optimization, stabilizes training for minority classes, and remains robust to varying levels of inter-label dependence.




\section{Experimental Setup}

For Subtask 3 (manifestation identification), we split the initial training data into training and validation sets using a Multilabel Stratified Shuffle Split (80/20), preserving the distribution of all polarization labels. The validation set was used for model selection, hyperparameter tuning, and threshold optimization.

Hyperparameters such as learning rate, batch size, number of epochs, and loss-specific parameters were tuned on the validation set. Thresholds for each One-vs-Rest classifier were optimized per label via grid search over [0.01, 0.99] using stratified $K$-fold splits, with final thresholds averaged across folds to improve robustness.

To address class imbalance, different strategies were adopted for each language. For English, Adaptive Focal Loss dynamically reweighted gradients to improve recall for rare manifestations while preserving precision. For Hausa, cost-sensitive learning with weighted BCE combined with controlled oversampling (triggered when imbalance ratio exceeded 5:1) was applied.

RoBERTa-base \cite{DBLP:journals/corr/abs-1907-11692} (English) and Afro-XLM-R-small (Hausa) \cite{alabi-etal-2022-adapting} encoders were fine-tuned for Subtask 3.

\section{Results}

\subsection{Validation results and model selection}

We first compare the One-vs-Rest (OvR) and Multi-label (ML) approaches on the English validation set. 
As shown in Table~\ref{tab:merged_val_results}, OvR consistently outperforms the joint Multi-label formulation across most manifestations.

In particular, substantial gains are observed for Extreme Language (+0.27), Invalidation (+0.24), and Lack of Empathy (+0.36). 
The latter is especially notable, as the Multi-label model completely fails to detect this rare class (F1 = 0.00), while OvR achieves 0.36. 

Overall, OvR reaches a macro-F1 of 0.50, compared to 0.33 for the Multi-label approach. 
This 17-point improvement confirms that independent label modeling is better suited to the sparse and weakly co-occurring manifestation structure of the dataset.

These findings support our hypothesis that joint modeling struggles under extreme label imbalance and limited co-occurrence patterns, as minority-class gradients become dominated by frequent manifestations.

For Hausa, only the OvR framework was adopted based on the strong validation results obtained in English. 
Using Davlan Afro-XLM-R-small, the model achieves a macro-F1 of 0.20 on the validation set (Table~\ref{tab:merged_val_results}). 
Performance varies considerably across labels. 
Extreme Language (0.375) and Dehumanization (0.364) show relatively stronger detection capability, whereas Lack of Empathy (0.057) and Invalidation (0.00) remain highly challenging.



\begin{table}[t]
\centering
\small % Slightly larger than footnotesize for readability, change to \footnotesize if desperate
\begin{tabular}{lccc}
\toprule
& \multicolumn{2}{c}{\textbf{English}} & \textbf{Hausa} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-4}
\textbf{Label} & \textbf{OvR} & \textbf{Multi-label} & \textbf{OvR} \\
\midrule
Stereotype        & 0.560 & 0.420 & 0.286 \\
Vilification      & 0.590 & 0.580 & 0.111 \\
Dehumanization    & 0.430 & 0.380 & 0.364 \\
Extreme Language  & 0.570 & 0.300 & 0.375 \\
Lack of Empathy   & 0.360 & 0.000 & 0.057 \\
Invalidation      & 0.530 & 0.290 & 0.000 \\
\midrule
\textbf{Macro-F1} & \textbf{0.500} & 0.330 & \textbf{0.200} \\
\bottomrule
\end{tabular}
\caption{Validation set F1-scores for Subtask 3. The One-vs-Rest (OvR) approach consistently outperforms the joint Multi-label baseline across both languages.}
\label{tab:merged_val_results}
\end{table}



\subsection{Test Results}

Based on validation performance, the OvR approach was selected for official submission in both languages. 
Table~\ref{tab:subtask3_test_compact} reports the test results.

In English, the system achieves a macro-F1 of 0.464. Strongest performance is observed for Vilification (0.625) and Extreme Language (0.564), while Dehumanization (0.378) and Lack of Empathy (0.356) remain comparatively difficult.

For Hausa, the macro-F1 reaches 0.192. Although lower than English, the model achieves non-trivial detection across most manifestations, though performance remains limited throughout, with Stereotype (0.297) and Dehumanization (0.252) showing relatively stable performance.

\begin{table}[t]
\centering
\footnotesize
\resizebox{\columnwidth}{!}{
\begin{tabular}{lcc}
\toprule
{Label} & {English F1} & {Hausa F1} \\
\midrule
Stereotype        & 0.420 & 0.297 \\
Vilification      & 0.625 & 0.165 \\
Dehumanization    & 0.378 & 0.252 \\
Extreme Language  & 0.564 & 0.185 \\
Lack of Empathy   & 0.356 & 0.102 \\
Invalidation      & 0.442 & 0.154 \\
\midrule
Macro-F1          & 0.464 & 0.192 \\
\bottomrule
\end{tabular}
}
\caption{F1-scores for Subtask 3 (Manifestation Identification) on the test set: English vs Hausa (One-vs-Rest).}
\label{tab:subtask3_test_compact}
\end{table}

\section{Error Analysis}
Analysis of model predictions reveals distinct structural challenges across both languages.

\paragraph{English System} 
As shown in Figure \ref{fig:confusion_english}, closely related categories such as dehumanization and stereotype are frequently absorbed into the broader vilification class. Furthermore, invalidation and lack\_of\_empathy act as attractor classes, being consistently over-predicted. Error rate analysis (see Fig \ref{fig:error_labelcomplexity_english} in Appendix) indicates that performance degradation is triggered by the mere presence of polarization (error rates $>92\%$) rather than multi-label complexity. Sensitivity to contextual length is also high, with error rates increasing by +1.18\% per additional word(Figure \ref{fig:error_rate_vs_text_length_english}).

\paragraph{Hausa System} 
The Hausa system exhibits a prediction collapse into a limited subset of classes. Figure \ref{fig:confusion_hausa} shows that stereotype and dehumanization are frequently misclassified as invalidation. Unlike the English case, the primary bottleneck in Hausa is positive-class sparsity rather than semantic boundary modeling; 92.5\% of polarized texts contain only a single label (Figure \ref{fig:error_labelcomplexity_Hausa}). Contextual length plays a secondary role (+0.45\% error increase per word, Figure \ref{fig:error_rate_vs_text_length_Haussa}) compared to the extreme data imbalance documented in Section 4. To address potential concerns regarding the highly optimized thresholds (0.990) for certain Hausa labels like Vilification and Extreme Language, our error analysis confirms the model does not degenerate into a trivial majority-class (all-negative) classifier. As shown in the FP Co-confusion matrix (Figure \ref{fig:confusion_hausa}), the model actively triggers positive predictions that cross this strict threshold. For instance, it generates at least 45 positive predictions for Vilification and 7 for Extreme Language just among its inter-class confusions alone. This confirms that the threshold effectively isolates the strongest signals in a severely imbalanced setting (e.g., 1.3\% prevalence for Vilification) rather than suppressing predictions entirely, which is further validated by the non-zero macro-F1 scores.

\section{Conclusion}

In this work, we presented our system for the POLAR 2026 shared task  on multilingual manifestation identification of polarization in social media. 
Our approach integrates transformer-based encoders with controlled oversampling, Adaptive Focal Loss, and label-wise threshold optimization within a One-vs-Rest framework, explicitly designed to address severe class imbalance and label sparsity.

On the validation set, the One-vs-Rest framework achieved a macro-F1 of 0.50 for English and 0.20 for Hausa. On the official test set, the system obtained macro-F1 scores of 0.464 for English and 0.192 for Hausa, demonstrating stable behavior across both languages despite the severe class sparsity of the Hausa setting.

Future work will explore hybrid strategies combining label-wise optimization with structured modeling of label dependencies, enhanced cross-lingual transfer techniques for low-resource languages such as Hausa, access to larger models and GPUs and additional data collection.


\section{Limitations}
Our study has three main limitations. First, the free Google Colab environment 
prevented us from exploring larger transformer models or extensive hyperparameter 
tuning. Second, the small and highly imbalanced Hausa dataset limits 
generalization for rare manifestations. Finally, results rely on a single run 
(seed = 42), though our stratified K-fold threshold optimization demonstrated 
stable convergence, supporting the reliability of the reported metrics.

% \newpage
\section*{Acknowledgments}

We would like to thank Shamsuddeen Hassan Muhammad 
and Idris Abdulmumin for their course on Natural 
Language Processing, which provided the foundation 
for this work, and for their encouragement to 
participate in the POLAR 2026 shared task competition.
\bibliography{custom}
\appendix


\section{Appendix}
\label{sec:appendix}


\subsection{Subtask 3: Manifestation Identification}

The third subtask \citep{naseem-etal-2026-polar} focuses on identifying the rhetorical and linguistic manifestations of polarization in social media posts. Each instance can be associated with one or more labels, including , Vilification, Dehumanization, Extreme Language, Lack of Empathy, and Invalidation \citep{naseem2026polarbenchmarkmultilingualmulticultural}
.This subtask is formulated as a multi-label classification problem, aiming to capture how polarized opinions are expressed rather than just whether they exist.

\begin{table}[t]
\centering
\footnotesize
\setlength{\tabcolsep}{3pt}
\begin{tabular}{llcc}
\toprule
{Label 1} & {Label 2} & {EN} & {HA} \\
\midrule
vilification & extreme\_language      & 3.70e-271 & 2.76e-04 \\
stereotype & vilification             & 1.04e-168 & 5.59e-02 \\
vilification & dehumanization         & 8.80e-147 & 4.44e-01 \\
vilification & invalidation           & 4.91e-143 & 1.00e+00$^\dagger$ \\
extreme\_language & invalidation      & 2.44e-124 & 1.64e-02 \\
vilification & lack\_of\_empathy      & 6.90e-124 & 1.00e+00$^\dagger$ \\
stereotype & extreme\_language        & 1.57e-122 & 8.82e-16 \\
extreme\_language & lack\_of\_empathy & 2.85e-120 & 1.11e-01 \\
stereotype & dehumanization           & 1.29e-113 & 6.89e-02 \\
dehumanization & extreme\_language    & 2.61e-100 & 5.81e-23 \\
stereotype & invalidation             & 3.06e-76  & 6.57e-02 \\
dehumanization & lack\_of\_empathy    & 1.05e-71  & 1.03e-03 \\
lack\_of\_empathy & invalidation      & 8.57e-68  & 1.00e+00$^\dagger$ \\
dehumanization & invalidation         & 1.22e-56  & 1.00e+00$^\dagger$ \\
stereotype & lack\_of\_empathy        & 6.46e-56  & 2.85e-04 \\
\bottomrule
\end{tabular}
\caption{P-values of pairwise $\chi^2$ independence tests for
manifestation labels in English (EN) and Hausa (HA).
$^\dagger$Values of 1.00 indicate zero observed co-occurrence
in the Hausa dataset; the $\chi^2$ statistic is undefined for
these pairs, which are treated as independent.}
\label{tab:chi2_pvalues_manifestation}
\end{table}

\begin{figure}[t]
    \centering
    \includegraphics[width=1\linewidth]{Distribution_target_subtask_3_english_barplot_horizontal_acl.pdf}
    \caption{Distribution of manifestation labels in the English dataset.}
    \label{fig:dist3_en}
\end{figure}
Table~\ref{tab:training_config} summarizes the final configurations for English and Hausa models.
\begin{figure}[t]
    \centering
    \includegraphics[width=1\linewidth]{Distribution_target_subtask_3_hausa_barplot_horizontal_acl.pdf}
    \caption{Distribution of manifestation labels in the Hausa dataset.}
    \label{fig:dist3_hau}
\end{figure}
\begin{table}[t]
\centering
\scriptsize
\resizebox{\columnwidth}{!}{
\begin{tabular}{lcc}
\toprule
 & \textbf{EN} & \textbf{HA} \\
\midrule
Model & RoBERTa-base & Afro-XLM-R-small \\
LR & $1\mathrm{e}{-5}$ & $1\mathrm{e}{-5}$ \\
Batch size & 4 & 4 \\
Grad. Accum. & 1 & 2 \\
Epochs & 5 & 3 \\
Weight decay & 0.01 & 0.01 \\
Max length & 512 & 512 \\
Loss & Focal & Weighted BCE \\
$\gamma$ & 2.0 & -- \\
$\alpha$ & 0.25 & -- \\
Class weight & -- & $N_{\text{neg}}/N_{\text{pos}}$ \\
Oversampling & -- & ratio $> 5$ \\
Threshold search & [0.01--0.99] & [0.01--0.99] \\
\bottomrule
\end{tabular}}
\caption{Final training configurations (EN = English, HA = Hausa).}
\label{tab:training_config}
\end{table}

\subsection{Optimized Decision Thresholds}
Table~\ref{tab:thresholds_comparison} reports the label-wise optimized thresholds for English and Hausa datasets.
\begin{table}[t]
\centering
\footnotesize
\resizebox{\columnwidth}{!}{
\begin{tabular}{lcc}
\toprule
Manifestation & English & Hausa \\
\midrule
Vilification        & 0.18 & 0.990 \\
Extreme Language    & 0.41 & 0.990 \\
Stereotype          & 0.57 & 0.900 \\
Invalidation        & 0.21 & 0.500 \\
Lack of Empathy     & 0.07 & 0.010 \\
Dehumanization      & 0.31 & 0.090 \\
\bottomrule
\end{tabular}
}
\caption{Label-wise optimized thresholds.}
\label{tab:thresholds_comparison}
\end{table}



\subsection{Figures}



\begin{figure}[t]
    \centering
    \includegraphics[width=1\linewidth]{haussount_nuage.png}
    \caption{Thematic Analysis of Bigrams by Hausa Discourse Category}
    \label{fig:placeholder_hausa}
\end{figure}





\begin{figure}[t]
    \centering
    \includegraphics[width=1\linewidth]{FN_rate_analysis_english.png}
    \caption{ FP vs FN rate scatter (English)}
    \label{fig:FP_vs_FN_english}
\end{figure}

\begin{figure}[t]
    \centering
    \includegraphics[width= 1\linewidth]{Fn_rate_Haussa.png}
    \caption{ FP vs FN rate scatter (Hausa)}
    \label{fig:FN_FP_haussa}
\end{figure}

\paragraph{Error analysis :Qualitative examples.}

\vspace{0.3cm}

Table~\ref{tab:error_examples} illustrates representative error 
cases for each system. For English, texts discussing political 
or geopolitical topics without explicit hostility such as 
analytical commentary on denazification or culture wars — are 
systematically over-predicted across all six labels, revealing 
that the model conflates politically charged discourse with 
polarization manifestations. Conversely, highly polarized 
short texts such as ``Kamala Harris has the easiest 
job ever'' are entirely missed, suggesting that implicit 
or ironic framing falls below the model's detection threshold. 
For Hausa, the dominant error pattern is label substitution: 
the model predicts plausible but incorrect labels, reflecting 
unstable decision boundaries under low-resource conditions.
\section{Supplemental Figures and Qualitative Analysis}
\label{sec:appendix_figures_error_Analysis}


\begin{figure}[t]
    \centering
    \includegraphics[width=1\linewidth]{nbre_labels_and_error_english.png}
    \caption{Model error rate (English case) by number of gold labels per text}
    \label{fig:error_labelcomplexity_english}
\end{figure}


\begin{figure}[t]
    \centering
    \includegraphics[width=1\linewidth]{relation_between_text_lengthand_model_error_english.png}
    \caption{Error rate of RoBERTa-base (English case) as a function of text length}
    \label{fig:error_rate_vs_text_length_english}
\end{figure}

\begin{figure}[h]
    \centering
    \vspace{-1em}
    \begin{subfigure}{\linewidth}
        \centering
        \includegraphics[width=\linewidth]{Label_complexity_Haussa.png}
        \caption{Model Error Rate (Hausa case) by number of labels in the text}
        \label{fig:error_labelcomplexity_Hausa}
    \end{subfigure}
    \begin{subfigure}{\linewidth}
        \centering
        \includegraphics[width=\linewidth]{error_rate_text_length.png}
        \caption{Error rate of Afro-XLMR-small (Hausa case) as a function of text length}
        \label{fig:error_rate_vs_text_length_Haussa}
    \end{subfigure}
    \caption{Error analysis for the Hausa system.}
    \label{fig:hausa_error_analysis}
\end{figure}
\begin{table}[t]
\centering
\footnotesize
\setlength{\tabcolsep}{2pt}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{p{4.2cm} p{1.5cm} p{1.6cm}}
\toprule
{Text} & {Gold} &{Pred.} \\
\midrule
\multicolumn{3}{l}{{EN — False Positive}} \\[2pt]
``fear and ignorance.. encouraged by populism to push for culture wars.''
& $\emptyset$ 
& all 6 \\[4pt]
\midrule
\multicolumn{3}{l}{{EN — False Negative}} \\[2pt]
``Kamala Harris has the easiest job ever''
& all 6
& $\emptyset$ \\[4pt]
\midrule
\multicolumn{3}{l}{{HA — Label substitution}} \\[2pt]
``Mun aura amarar yai da aidun addinin Islama -- Faransa''
& ext\_lang 
& vilif., stereo., invalid., lack\_emp. \\
\bottomrule
\end{tabular}
\caption{Error cases. $\emptyset$ = no label predicted or expected.
``all 6'' = full manifestation set.}
\label{tab:error_examples}
\end{table}


% =====================
% English (top)
% =====================
\begin{figure*}[t]
    \centering
    \includegraphics[width=\linewidth]{Matrix_confusion_english.png}
    \caption{Confusion matrices for Subtask 3. English shows semantic overlap with vilification.}
    \label{fig:confusion_english}
\end{figure*}


% =====================
% Hausa (bottom)
% =====================
\begin{figure*}[t]
\vspace{-10cm}
    \centering
    \includegraphics[width=\linewidth]{Confusion_matrix_haussa.png}
    \caption{Confusion matrices for Subtask 3. Hausa shows prediction collapse due to sparsity.}
    \label{fig:confusion_hausa}
\end{figure*}
% \begin{figure}[t]
%     \centering
%     \includegraphics[width=1\linewidth]{Confusion_matrix_haussa.png}
%     \caption{Confusion Matrix (Hausa case)}
%     \label{fig:confusion_matrix_Hausa}
% \end{figure}

\end{document}
