## 3 Methods
### Procedure  
In this section, we focus on revealing the model construction and optimization of Algorithm 1 in the training process, which not only includes the input and output data, but also the pre-processing and running process. ``` input : A sample set \(X=\{x_{1},x_{2},\ldots,x_{n}\}\), where \(x_{i}=\{\hat{e_{i}},\hat{e_{1}},\hat{e_{2}},\ldots,\hat{e_{N}}\}\). A corresponding label set \(Y=\{y_{1},y_{2},\ldots y_{n}\}\) output : The new model that will verify the multilingual claim. 1 Set Optimizer AdamW, and Initialize the iterator number iterNum, the batch For better intuitive understanding, the professional function namespace of the Pytorch framework is employed in the pseudocode. As a whole, the inference forecasting of the development and test process can be executed directly based on the model trained by the algorithm. ## 4 Experiments and Results

### Datasets and Evaluation Metrics

We conduct our experiments on the large-scale benchmark dataset X-FACT, which includes 31,189 short claims labeled for veracity by expert fact-checkers and covers 25 typically diverse languages across 12 language families. According to the different rating scales for categorization, the label set is divided into seven labels by fact-checkers: True, Mostly True, Partly True, Mostly False, False, Complicated/Hard to Categorise, and Other. Table 1 shows the statistics of the dataset. Following the evaluation criteria of previous studies, we likewise report average accuracy, macro F1 scores, and standard deviations in the experience with different random seeds. The dataset, shown in the Appendix A.1, provides a challenging multilingual fact-checking evaluation benchmark that measures in-domain classification, out-of-domain generalization, and zero-shot capabilities of the multilingual models. More specifically, the Test1 set contains fact-checks from the same languages and sources as the training set. Second, the out-of-domain test set (Test2) consists of claims from the same languages as the training set but are from a different fact-checking website source. The third test set (Test3) is the zero-shot set, which seeks to measure the cross-lingual transfer abilities of fact-checking systems. Test3 accommodates claims from the new language not contained in the training set. In general, the dataset is specially created to evaluate the various performances of the models that not only solve the difficulty of these multilingual fact-checking sets (Test1), but also fit both source-specific patterns (Test2) and language-specific patterns (Test3). ### Setting

The core details of the model's relevant parameters are provided for better evaluation and reproducibility. Firstly, the hyper-parameter settings of the model architecture are as follows: In the shared encoding layer, the embedding layer of 50 dimensions is randomly initialized to encode the language family feature. For claim-evidence input pairs, all retrieved evidences related to the claim are inputted into the model, totaling five pieces. To maintain uniform input length, the input maximum sequence length is 360 due to constraints on the GPUs memory, where parts longer than the maximum length are truncated, and the shorter sequences are zero-padded. Next, we used the mBART-base model for all of our experiments. This model has 12 layers each with a hidden size of 768, the number of attention heads equal to 12, and the value for dropout in the hidden layer is 0.2. The total number of parameters in this model is 125 million. In the recursive graph attention network, we attempt to stack 0-3 recursive layers and analyze the effect of different layer numbers. Furthermore, the number of multi-attention heads is set to 0, 8, and 16, respectively, for evaluating the evidence aggregating performance. In the classification layer, the dynamic