## 5 Results and Discussion
### Experiment with Balanced Softmax  
In order to prove the effectiveness of the improved model after using the balanced softmax function, we compare with the current mainstream models. Table 4 shows the recognition results of the Kazakh language dataset under different models. From the results in Table 4, it can be seen that the performance results of BLSTM-CTC are not as good as the recognition results of the traditional DNN-HMM model, with a 15.1% difference in results. The Transformer model, on the other hand, using a multi-head self-attention mechanism, results in a good pair of results compared to the first two, with a relative decrease in the word error rate of 0.85% and 15.95%. The Conformer model enhances the Transformer's learning of local features by using a convolutional module, and its recognition results achieve a good result compared to the Transformer; the result is reduced by 2.49%. The model with the balanced softmax function has a decrease compared to the baseline model, with a 0.15% decrease in the word error rate. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **WER** \\ \hline DNN-HMM [13] & 13.7\% \\ BLSTM-CTC [13] & 28.8\% \\ Transformer-CTC & 12.85\% \\ Conformer no CTC & 15.38\% \\ Baseline (Conformer-CTC) & 10.36\% \\ Baseline + balanced softmax & 10.21\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison experiments between the Conformer model using balanced softmax and other models. Figure 4: Training loss of different rank values of Conformer model and baseline model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Size** & **\(\Delta\)Size** & **\(\Delta\)WER** \\ \hline Baseline (Conformer-CTC) & 182 MB & 0 & 0 \\ Baseline + low rank (r = 128) & 182 MB & 0 & 0.03 \\ Baseline + low rank (r = 64) & 168.5 MB & \(-\)13.5 MB & \(-\)0.49\% \\ Baseline + low rank (r = 32) & 161.8 MB & \(-\)20.2 MB & \(-\)0.64\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: We used Conformer as the baseline model and then compared the decomposition results of different rank sizes. The reason for this is that adding a penalty factor can reduce the penalty for low-frequency words, enhance the model's learning of low-frequency words, and thus improve the overall recognition performance. Table 5 gives the comparative recognition results of some low-frequency words after using the penalty factor. For example, in the Kazakh test dataset, the word \(\text{Keeeekrep}\) (translated as: pieces) appears with a frequency of one, which is a low-frequency word. When the training model does not use the penalty factor, the word is incorrectly recognized as \(\text{Keekrep}\), while when the model uses the improved method, the word is correctly recognized. The loss of the training process of the model is shown in Figure 5. It can be seen that using CTC as an auxiliary function in the multi-task learning approach can accelerate the convergence of the model and speed up the training, reduce the loss value in the model training, and improve the recognition effect of the model. To verify the effect of setting different sizes of penalty factors on the model recognition results, we use Conformer as the baseline model and conduct comparative experiments with models using different sizes of penalty factors. From Table 6, it can be seen that adding the penalty factor can effectively improve the recognition effect; compared with the baseline model, the penalty factor causes the word error rate to decrease by 0.15%. However, the penalty factor cannot be set too large, otherwise the recognition accuracy will be reduced. Figure 5: The train loss with and without CTC as an auxiliary task. \begin{table}
\begin{tabular}{c c c c c} \hline
**Word in KSC** & **Translation * & \begin{tabular}{c} **Number of** \\ **Appearances** \\ \end{tabular}  & **Baseline** & \ \begin{tabular}{c} **Use balanced** \\ **softmax** \\ \end{tabular}