## 4 Experimental Evaluation
### Experiment Analysis
According to Equation (12), where \(L_{\text{hybrid}}\) denotes the loss function across different languages or tasks and \(\alpha\) represents the weighting coefficient, the model adapts better to various linguistic features when \(\alpha\) is balanced. The strength of hybrid data lies in its ability to help the model learn from both the source and target languages by optimizing this loss function, thus explaining why LightChatGLM can more effectively capture the correlation between these languages in a mixed-data setting, ultimately leading to better translation performance. Conversely, in non-hybrid scenarios, the model may only optimize a single loss function, leading to insufficient learning. Furthermore, the model's poor performance in single-language scenarios could be attributed to overfitting, where it learns the idiosyncrasies of a specific dataset but lacks the generalization capability to handle other contexts. To quantify this, let translation accuracy be defined as \(Acc(D,\theta)\), where \(D\) represents the dataset, and \(\theta\) denotes the model parameters. The accuracy rate \(Acc(D_{\text{mix}},\theta)\) for the mixed-data scenario can be expressed as  
\[Acc(D_{\text{mix}},\theta)=\frac{1}{N_{\text{mix}}}\sum_{i=1}^{N_{\text{mix}} }P(T_{i}|S_{i},\theta), \tag{14}\]  
where \(T_{i}\) is the target language sentence, \(S_{i}\) is the source language sentence, \(N_{\text{mix}}\) is the number of samples in the mixed dataset, and \(P(T_{i}|S_{i},\theta)\) represents the probability of a correct translation given the model parameters \(\theta\). Due to the diversity of the mixed data, \(Acc(D_{\text{mix}},\theta)\) tends to be higher. In contrast, the translation accuracy \(Acc(D_{\text{single}},\theta)\) in single-language scenarios may exhibit greater variability:  
\[Acc(D_{\text{single}},\theta)=\frac{1}{N_{\text{single}}}\sum_{i=1}^{N_{ \text{single}}}P(T_{i}|S_{i},\theta), \tag{15}\]  
where \(N_{\text{single}}\) represents the number of samples in a single-language dataset. In such cases, the model may struggle to capture the diversity present in a mixed dataset, leading to fluctuating performance. In order to enhance the cross-linguistic capabilities of teacher models, LightChatGLM employs a hybrid data-based fine-tuning approach. This method involves randomly mixing annotated data from both the source and target languages, followed by fine-tuning the teacher model on the hybrid dataset while continuing knowledge distillation on downstream tasks. This process aims to yield student models with superior performance. Figure 5 illustrates the average results of Chinese-English bilingual migration experiments conducted using three different fine-tuning methods on WMT 2020, UM-Corpus, and Ai Challenger. Here, the English training set serves as the source-language-labeled corpus, and the Chinese validation set acts as the target-language-labeled corpus. From Figure 5, it is evident that the performance of fine-tuning solely using the source language yields the poorest results. This can be attributed to the absence of target annotation language, leading to the diminished generalization ability of the fine-tuned model. Conversely, the fine-tuning method incorporating the target annotation language and hybrid annotation language demonstrates improved performance results. To evaluate the effectiveness of the hybrid data fine-tuning method in more complex tasks, we selected two high-resource datasets, WMT 2020 and UM-Corpus, and two low-resource datasets, IWSLT 17 and XGLUE 20. We applied three fine-tuning strategies: (1) fine-tuning using only high-resource language data (high fine-tuning), (2) fine-tuning using only low-resource language data (low fine-tuning), and (3) hybrid data fine-tuning, which incorporates data from both high- and low-resource languages.