## 3 Methods
### Procedure
\begin{table}
\begin{tabular}{l c c l} \hline \hline
**Data Split** & **Claims** & **Languages** & **Pre-3 Languages** \\ \hline Train & 19,079 & 13 & Portuguese, Indonesian, Arabic \\ Development & 2535 & 12 & Portuguese, Indonesian, Arabic \\ In-domain (Test1) & 3826 & 12 & Portuguese, Indonesian, Arabic \\ Out-of-domain (Test2) & 2368 & 4 & Indonesian, Turkish, Portuguese \\ Zero-shot (Test3) & 3381 & 12 & Albanian, Bengali, Russian \\ \hline \hline \end{tabular}
\end{table} 
Table 1: X-Fact dataset details. X-FACT contains three challenges sets, namely, in-domain test (Test1), out-of-domain test (Test2), and zero-shot test (Test3). Each set consists of multilingual claims and pieces of evidence, whereby language numbers and pre-three languages are counted. weights are randomly initialized and gradually optimized in iteration. Furthermore, the class label number is 7, which is consistent with the number of task categories. Next, regarding the training of the model, we optimize the model via the AdamW optimizer for the best performance, in which the initial learning rate is \(1.95\times 10^{-5}\), and the learning rate warm-up steps are set to 10% of the total training steps. In addition, the maximum batch size is 8 and the train epoch number is 10. Once each epoch training is completed, we evaluate the model performance and save the model once. All our models were run with four random seeds (seed = [1; 2; 3; 4]). Lastly, for the experimental environment, all algorithm codes are developed based on the PyTorch framework, which is run on the NVIDIA GeForce RTX 3090 machine (24 GB VRAM) with a GPU accelerator. Furthermore, the average training time of our model is about 160 min. The experiments can be sped up with distributed data-parallel training via multiple GPUs on multiple computing machines. ### Overall Performance

We compare our methods with the following several models, including top-performing models reported with the X-FACT dataset [9], and homogeneous models retrieved on the same dataset [42]. * **Majority. ** The model directly generates classification results based on the majority label of the dataset distribution, i.e., Mostly False. * **Claim-Only. ** The model is only inputted with the textual claim, basically treating the task as a multi-class problem. * **Attn-EA. ** The procedure is emulated by developing an attention-based evidence aggregation model that operates on evidence documents retrieved from web searches with the claim using Google. * **Graph-EA. ** The framework for claim verification utilizes the BERT sentence encoder, the evidence reasoning network, and an evidence aggregator to encode, propagate, and aggregate information from multiple pieces of evidence. **Common and Different Aspects. ** In addition to the Majority model, which is calculated based on statistical methods, other models are designed based on the common architecture of a deep neural network, which leverages the mbert model to encode the claims and pieces of evidence. The core distinction between other models is the downstream network structure of the basic semantic encoder. Furthermore, the different network modules can be modeled to extract different features, which determines the final performance superiority of multilingual claim verification. **Metadata Augmenting. ** As far as metadata augmenting is concerned, to strengthen the model performance, the above models mainly adopt the scheme whereby the input is increased with additional metadata, and is represented as a sequence of the key-value form. In detail, the metadata includes the language, website name, claimant, claim date, and review date. If a certain field is not available for a claim, the value is set by none. Unlike the previous scheme, we only embed the metadata of language and language family for augmenting performances. Table 2 reports the performance of our model and other models under the same evaluation conditions. Compared with the above models, PEINet has achieved state-of-the-art scores.