## 5 Discussion
### Interpretation of Rice Yield Prediction Models  
We employed machine learning and deep learning methods not only to obtain satisfactory yield prediction performance but also to explain the internal mechanism of models. Recently, attention values have been widely used to interpret deep learning models in many fields, such as financial time series prediction [51] and crop yield estimation [55]. First, we applied feature importance to interpret machine learning models. The feature importance analysis showed that NIR\({}_{\text{v}}\) was the most critical feature (Figure 10) since NIRV can better estimate GPP and has great potential in predicting crop yield [19]. Moreover, Srad and Tmax were the crucial factors in the rice yield prediction among four climatic variables (Figure 10). The reason was that they could directly influence rice's photosynthesis and carbon cumulation.  
Second, we analyzed the hidden features to interpret deep learning models using attention weights. The analysis of hidden features provides a new sight to understand the internal working of deep learning models for rice yield prediction. In this study, we applied attention weights and a self-attention weight matrix to interpret AtLSTM and Informer, respectively. The attention weight distributions of AtLSTM illustrated that the reproductive  
Figure 12: Average self–attention weight of the Informer model from 2009 to 2016. Each visual–ized weight matrix represents the averaged weight matrix of all heads of the same encoder layer in the Informer model. The results are the average of all test samples from 2009 to 2016.  
and ripening phases were more important than the vegetation phase (Figure 11). The reason may be that AtLSTM had a recurrent network structure that could store the cumulative information of crop growth with time [34]. In addition, we found that the Informer model had higher attention weights around intervals 5 to 6 (August) and intervals 11 to 12 (November) (Figure 12), which indicated that those periods provided critical information to the later layer of the Informer model. This is because the leaf development and tillering stages (August) before the heading stage of Kharif rice are closely related to rice yield [56], while the flowering and grain-filling stages (November) are sensitive to high temperature and have a great impact on rice yield [57; 58; 59]. The results agreed with the feature importance of machine learning methods, which proved the reliability of our results. The Informer model obtains the later-layer features by calculating the attention weight and weighted summation of earlier-layer features. The results show that the self-attention weights of the Informer model disagreed with the attention weights of the AtLSTM model, which could attribute to the unique structure of these two deep learning methods. The AtLSTM model accumulated the temporal information in the hidden layer by the LSTM cell, resulting in the reproductive phase storing more information than the vegetation phase. Then, the attention weight value of the reproductive phase was higher than the vegetation phase. In contrast, the Informer model acquired temporal dependencies between any two intervals instead of accumulating temporal information over time.