Figure~\ref{fig:architecture} illustrates the overall pipeline of our system. Given a text and its associated aspect, we encode them as a sentence pair using a multilingual pre-trained encoder, and predict the VA scores via a regression head. Models are trained jointly across all language--domain pairs, and the final predictions are obtained via a development-set-guided adaptive ensemble.
\begin{figure}[ht]
    \centering
    \includegraphics[width=\linewidth]{figure/architecture.png}
    \caption{The architecture of our DimASR system.}
    \label{fig:architecture}
\end{figure}

%----------------------------------------------
\subsection{Data Processing}

The training data is provided in a quadruplet format (\textit{Aspect}, \textit{Category}, \textit{Opinion}, \textit{VA}) shared across all subtasks of Track~A. Since we focus on Subtask~1 (DimASR), we extract only the (\textit{Text}, \textit{Aspect}, \textit{VA}) fields and apply several preprocessing steps before training.

Following the official dataset note that the test set excludes implicit \texttt{NULL} annotations, we remove all training instances where the aspect is \texttt{NULL} to ensure consistency between training and test distributions.
We also discard 3 instances with VA values outside the valid range $[1, 9]$.
For instances with multiple aspect terms, we expand them into independent samples, each paired with the full review text and a single aspect term along with its corresponding VA score.
For instances where multiple opinions are associated with the same aspect, we retain only the VA score corresponding to the first opinion.
%----------------------------------------------

\subsection{Model Architecture}
\label{sec:Model Architecture}

\paragraph{Backbone Encoders.}
We explore three multilingual pre-trained encoders as the backbone: mBERT~\citep{devlin-etal-2019-bert}, XLM-RoBERTa-base, and XLM-RoBERTa-large~\citep{conneau-etal-2020-unsupervised}. These models provide strong cross-lingual representations and are well suited to our multilingual setting. In addition, these models span a range of scales and architectures, allowing us to examine the effect of model size on cross-lingual sentiment regression.

\paragraph{Input Representation.}
The aspect term and review text are encoded as a sentence pair. Depending on the backbone, the tokenizer inserts model-specific special tokens: mBERT formats the input as \texttt{[CLS] aspect [SEP] text [SEP]}, while XLM-RoBERTa uses \texttt{<s> aspect </s></s> text </s>}. All sequences are truncated or padded to a maximum length of 128 tokens.

\paragraph{Regression Head.}
We take the hidden state of the first special token (\texttt{[CLS]} or \texttt{<s>}) as the sentence-level representation.
A dropout layer is applied before a linear projection that maps the hidden representation to two raw output values corresponding to valence and arousal:
%
\vspace{-0.15cm}
\begin{equation}
    \mathbf{h} = \mathrm{Dropout}(\mathbf{e}_{\texttt{[CLS]}}), \quad
    \hat{\mathbf{y}} = \mathbf{W}\mathbf{h} + \mathbf{b},
    \label{eq:head}
\end{equation}
%
where $\mathbf{W} \in \mathbb{R}^{2 \times d}$ and
$\mathbf{b} \in \mathbb{R}^{2}$ are learnable parameters,
and $d$ is the hidden size of the backbone.
The model is trained by minimizing the Mean Squared Error (MSE) loss, which is consistent with the official evaluation metric $\text{RMSE}_{\mathrm{VA}}$ (Equation \ref{eq:rmse_va}).

\paragraph{Bounded Output Transformation.}
The official task defines a valid VA range of $[1, 9]$. 
To align the model's output space with this requirement and enhance training stability, we further apply a sigmoid-based bounded transformation to the raw regression output:
%
\vspace{-0.1cm}
\begin{equation}
    \hat{\mathbf{y}}_{\mathrm{bounded}}
        = \sigma\!\left(\hat{\mathbf{y}}\right) \times 8 + 1,
    \label{eq:sigmoid}
\end{equation}
%
where $\sigma(\cdot)$ denotes the sigmoid function.

This ensures that all predictions are valid at inference time and facilitates smoother convergence during the early stages of training.
During our experiments, we observe that although the transformation stabilizes the training process and yields a consistent overall improvement, its effect varies across individual settings. Therefore, we treat it as a flexible component and include both bounded and unbounded model variants in the candidate pool for the subsequent ensemble stage to leverage their complementary strengths.


% -----------------------------------------------------------
\subsection{Joint Multilingual and Multi-Domain Training}
We adopt a joint multilingual and multi-domain training strategy, pooling data from all language--domain pairs to train a single unified model. Each instance is represented solely by its text--aspect pair, without explicit language or domain indicators. 

Compared with language–domain specific training, which learns independent models for each pair, joint training mitigates overfitting in low-resource settings and encourages the model to learn more generalizable representations that facilitate cross-lingual and cross-domain knowledge transfer \cite{conneau-etal-2020-unsupervised,VanThin03042023}. In particular, for language–domain pairs with limited training instances, the shared encoder is exposed to a substantially larger and more diverse set of sentiment expressions, allowing low-resource pairs to benefit from representations learned from richer languages and domains, thereby compensating for the lack of in-domain supervision.

% -----------------------------------------------------------
\subsection{Model Ensemble}
\label{sec:ensemble}

To reduce prediction variance and improve robustness, we adopt a structured ensemble strategy.

\paragraph{Candidate Pool Construction.}
We evaluate all trained models on the development sets across language--domain pairs and select 7 checkpoints that consistently achieve strong overall performance while collectively covering the top-performing models for each individual pair, forming the candidate pool for ensemble.
All 7 candidates are built on the XLM-RoBERTa-large backbone, but differ in batch size, learning rate, number of training epochs, and whether the sigmoid output constraint (Equation~\ref{eq:sigmoid}) is applied, providing ensemble diversity beyond hyperparameter variation alone. Detailed configurations of the candidate models are provided in Appendix~\ref{app:ensemble_model}.

\paragraph{Ensemble Subset Selection.}
Rather than a naive uniform averaging, we perform an exhaustive search over all possible subsets of size 2 to 7 drawn from the candidate model pool for each language--domain pair independently.
For each subset, predictions are obtained by averaging the valence and arousal outputs of the selected models element-wise.
The subset that achieves the lowest RMSE$_{\mathrm{VA}}$ on the development set is selected as the final ensemble configuration for that specific pair. 
As the optimal subset varies across pairs, this process results in 10 distinct ensemble configurations, which are subsequently applied to the official test sets for final submission. 
The selected optimal subsets for each language--domain pair are reported in Appendix~\ref{app:ensemble_config_pair}.

This exhaustive yet controlled ensemble selection strategy effectively reduces prediction variance and consistently improves performance across all language--domain pairs.