\section{The NYCU-NLP System}

As SemEval-2026 Task 9 \cite{naseem-etal-2026-polar} represents the first shared task on online polarization analysis, we design our SLM-based ensemble architecture by drawing on insights from our previous task participations \cite{Lee2024-SemEval24Task2, lin2024-WASSA2024, xu2025-SemEval25Task11}. Figure~\ref{fig:NYCU-NLP_system_architecture} illustrates the overall architecture of the NYCU-NLP system. We first fine-tune three small language models (SLMs) using carefully designed task-specific prompts, and subsequently integrate them through a stacking ensemble framework. Specifically, we train a logistic regression meta-model to aggregate the predictions from multiple fine-tuned SLMs and generate the final outputs for all three subtasks across languages.

\subsection{Small Language Models}
SLMs are lightweight versions of large language models (LLMs), designed to operate efficiently under constrained computational resources while preserving core modeling capabilities. We investigate the effectiveness of the following three SLMs. 

(1) \textbf{Phi-4 (14B)} \cite{abdin2024-Phi4}, developed by Microsoft Research, adopts a training strategy centered on high-quality synthetic data and reasoning-oriented curricula. Despite its relatively moderate scale, Phi-4 achieves strong reasoning performance through optimized training schedules, and post-training techniques such as supervised fine-tuning (SFT)\cite{wei2022-SFT} and Direct Preference Optimization (DPO) \cite{rafailov2023-DPO}.

(2) \textbf{Mistral-small-3.2 (24B)} \cite{Mistral3-small} is a compact language model designed to deliver competitive within a lightweight architecture. It surpasses several larger-scale language models on multiple official benchmarks in instruction following, multilingual understanding, and inference efficiency, demonstrating that carefully optimized small language models can rival, or even outperform substantially larger counterparts.

(3) \textbf{Gemma-3 (27B)} \cite{Kamath-Gemma3}, developed by Google DeepMind, incorporates architectural refinements and advanced post-training techniques to enhance instruction-following and multilingual capabilities. It achieves competitive performance comparable to significantly larger language models across a broad range of language understanding tasks.



\subsection{Instruction Fine-tuning}
We use instruction tuning \cite{wei2022-SFT} in combination with LoRA \cite{hu2021-LoRA} to adapt the three pre-trained SLMs for each subtask. The prompts are designed based on the annotation guidelines provided by the task organizers (see Appendix A). For each subtask, the SLMs are configured to perform the corresponding classification task, including binary polarization detection and multi-label classification for polarization targets and manifestation categories. Each predicted label indicates the presence (1) or absence (0) of the corresponding category.

\subsection{Assembly Mechanism}
To enhance robustness and reduce the variance of individual classifiers, we adopt an ensemble-based aggregation strategy that integrates predictions from three SLMs. Let $M=\{1,2,3\}$ denote the set of base models. Given an input instance x, each SLM produces a binary prediction $\hat{y}_m(x)\in\{0,1\}$, where $m\in M$. 

To further exploit complementarities among the SLMs, we employ a stacking ensemble framework \cite{stacking-ensemble}, in which the meta-model is implemented as a logistic regression classifier. Each SLM outputs a confidence score for the positive class, denoted as $p_m(x) \in[0, 1]$. These three confidence scores serve as meta-level features. Formally, for an instance x, the feature vector is defined as: 

\begin{equation}
\mathbf{z}(x) = [p_1(x), p_2(x), p_3(x)]^\top.
\end{equation}

The meta-model computes the logit value $t(x)$ and applies the sigmoid function to obtain the final predicted probability $\hat{p}(x)$. 
\begin{equation}
t(x) = \mathbf{w}^\top \mathbf{z}(x) + b.
\end{equation}
\begin{equation}
\hat{p}(x) = \sigma\!\big(t(x)\big).
\end{equation}

where $\mathbf{w}$ and $b$ denote the weight vector and bias term learned by the logistic regression meta-classifier, and $\sigma(\cdot)$ is the sigmoid activation function. The final binary prediction is obtained by thresholding the probability: 

\begin{equation}
\hat{y}(x)=
\begin{cases}
1, & \text{if } \hat{p}(x) \ge 0.5,\\
0, & otherwise.
\end{cases}
\end{equation}


\input{Table/Table1-Data-Stat}
\input{Table/Table2-Dev-Results}




\subsection{Task-specific Heuristic Rule}
To improve performance on the \textit{other} category in Subtask 2, we incorporate the prediction from Subtask 1 as an auxiliary signal during inference. Our preliminary analysis indicates that the \textit{other} label is comparatively difficult to learn. In some cases, the Subtask 2 classifier predicts all labels as 0, even when Subtask 1 identifies the instance as polarized (i.e., prediction is 1). 

To enforce cross-task consistency, we introduce a heuristic rule: if Subtask 1 predicts an instance as polarized and all Subtask 2 labels are 0, we assign the \textit{other} label a value of 1. This post-processing strategy recovers missed cases and mitigates false negatives, thereby improving consistency between the two subtasks.

