## 3 Methods
### Procedure
** We emphatically analyze the performance of different pre-trained multilingual models employed in the framework. Table 6 shows that the model based on mBERT outperforms other similar models. With comparative analysis, the XLM-based model's performance is close to that of the mBERT-based model, and the DistilBERT-based model's overall performance is relatively poor, which is limited to performing direct zero-shot tasks due to the learning mechanism. The results suggest that similar large-scale pre-trained multilingual models can almost achieve the equivalent semantic understanding of the same claims' input, so the core of fact-checking is still an evidence-aware inference. **What are the values of the learned relative weights of the losses in multi-task learning? ** We evaluate the performance of the PEINet model with different loss function calculation frameworks, where different methods correspond to different task weights. In the single-task learning framework, the task weights are set in advance. Under the multi-task learning framework, the relative weights of the losses are automatically generated through iterative training. The results of the contrastive analysis are presented in Table 7, which clearly illustrates the benefit of multi-task learning. Interestingly, what stands out in the table is that the task weight of the fine-grained evidence aggregation loss is higher than that of the prompt loss, which suggests that the verification of most multilingual claims would depend on the evidence chain excavation. **Can we improve performance with data augmentation of English corpus? ** A performance comparison is conducted by augmenting the dataset with 12,311 English claims and retrieved evidences from PolitiFact corpus. Average Micro F1 scores (and standard deviations) of the models are reported over four random runs in Table 8. The result that English data augmentation degrades the models' performances is somewhat counter-intuitive. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Multilingual Model** (**BASE**) & **Dev** & **Test1** & **Test2** & **Test3** \\ \hline DistilBERT & 38.8 (0.7) & 36.1 (0.7) & 16.4 (1.8) & 17.5 (1.0) \\ XLM-Roberta & 40.9 (0.6) & 39.9 (1.0) & **17.4 (1.8)** & 17.9 (1.2) \\ mBERT & 42.9 (0.6) & **42.1 (0.7)** & 17.3 (1.9) & **19.0 (1.1)** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance analysis of different pre-trained multilingual models. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{2}{c}{**Task Weights**} & \multicolumn{2}{c}{**Average Micro F1 Scores**} \\ \cline{2-6}
**Loss Calculation** & \(\lambda_{\text{prompt}}\) & \(\lambda_{\text{regt}}\) & **Test1** & **Test2** & **Test3** \\ \hline
**Prompt weight only** & 1.0 & 0.0 & 36.0 & 15.2 & 13.9 \\
**RGAT weight only** & 0.0 & 1.0 & 38.0 & 15.8 & 17.2 \\
**Unweighted sum of losses** & 0.5 & 0.5 & 39.0 & 16.3 & 15.9 \\
**Approx. optimal weights** & 0.11 & 0.89 & 42.0 & 17.1 & 19.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experiments of quantitative improvement with the multi-task loss. Results are shown from the three test sets. A possible cause proposed by the dataset publishers is that augmenting data almost comes from the political field, and cross-domain tasks increase the difficulty of multilingual fact-checking, especially in the out-of-domain and zero-shot scene. Another significant factor in our observation is that the evaluation criteria between X-Fact dataset and PolitiFact dataset is inconsistent. However, with English data augmentation, different models have different levels of performance degradation, among which, the performance of PEINet is relatively more stable. The results further support the idea that language family embedding strengthens the model transfer learning in the zero-shot scene. ## 6 Conclusions

In the paper, we propose a novel PEINet framework for multilingual fact-checking in the out-of-domain and zero-shot scenes.