## 2 Materials and Methods
### Loss Function Construction
#### 2.1.2 Adaptive Focus Loss Function Construction  
To address the disproportionate ratio of simple to difficult samples, [PERSON] and others introduced a cross-entropy function grounded on Focal Loss (FL). This concept posits that the abundance of simple samples in the dataset, which predominantly govern the total loss, have a negligible influence on model refinement. Therefore, the model should prioritize difficult samples. Accordingly, a focus parameter \(\gamma(\gamma\geq 0)\) is integrated into the loss function to lessen the contribution of simple samples to the total loss. **Definition 4**. : _With \(y_{j}\) and \(p_{j}\) defined as in Definition 1, we state that_  
\[L_{Focal}(p_{i},y_{i})=-|y_{i}-p_{i}|^{\gamma}{y_{i}}^{T}\log(p_{i}) \tag{4}\]  
This Equation embodies the focal loss function. As inferred from Equations (3) and (4), the simpler the sample, the closer \(p_{i}\) is to \(y_{i}\), and the smaller \(|y_{i}-p_{i}|^{\gamma}\), hence the factor \(|y_{i}-p_{i}|^{\gamma}\) serves to diminish the contribution of simple samples while amplifying that of difficult samples. The larger the \(\gamma\) value, the more pronounced this effect becomes [28]. However, considering that meteorological disaster emergency response capability assessments are conducted by experts, a degree of subjectivity is unavoidable. This leads to partial evaluations of the capability profiles of disaster response agencies and the occurrence of mislabeled samples. In this study, these mislabeled samples are termed anomalous samples. Although anomalous samples are not classified as difficult samples, emphasizing them excessively during training can hinder the model from learning the true data distribution efficiently. This not only squanders computational resources and prolongs training time, but also escalates the likelihood of overfitting, showcasing the limitations of Focal Loss. Consequently, this paper proposes an adaptive focal loss function to overcome these issues. **Definition 5**. : _Let \(y_{j}\), \(p_{j}\) be as defined in Definition 1. Then, the adaptive focal loss function is given by_  
\[L_{Adaptive-Focal}(p_{i},y_{i})=-s_{i}{y_{i}}^{T}\log(p_{i}) \tag{5}\]  
_where_  
\[s_{i}^{(e)}=\rho s_{i}^{(e-1)}+(1-\rho)diff_{i}^{(e-1)} \tag{6}\]  
\[diff_{i}^{(e-1)}=\left|\left|y_{i}-p_{i}\right|^{(e-1)}-\left|y_{i}-p_{i}\right| ^{(e-2)}\right| \tag{7}\]  
_Here, \(e\) represents the number of training rounds. \(diff_{i}^{(e-1)}\) denotes the difference in training error between the \(e-1\) th round and the previous round for sample \(i\), with \(diff_{i}^{(0)}=0\)._  
From Definition 5, we observe that \(s_{i}^{(e)}\) represents the accumulated value of diff\({}_{i}\) for sample \(i\) up to the \(e-1\) th training round, indicating the degree of difficulty in classifyingthat sample. When \(e=1,s_{i}^{(0)}=1\). The hyperparameter \(\rho\), ranging between [0,1], controls the adjustment magnitude of \(\text{diff}_{i}^{(e-1)}\) on \(s_{i}^{(e)}\). The smaller the value of \(\rho\), the greater the correction effect exerted by \(\text{diff}_{i}^{(e-1)}\) on \(s_{i}^{(e)}\). It is evident that \(L_{\text{Adaptive-Focal}}\ (p_{i},y_{i})\) at the eighth round is influenced by the accumulated error differences from all previous rounds. If \(\rho=1\), then \(\text{diff}_{i}^{(e-1)}\) will not impact \(s_{i}^{(e)}\), making \(s_{i}\) perpetually equal to 1, which reduces \(L_{\text{Adaptive-Focal}}\ (p_{i},y_{i})\) to \(L_{\text{CE}}(p_{i},y_{i})\). Conversely, if \(\rho=0\) and \(\text{diff}_{i}^{(e-1)}\) remains constantly equal to \(|y_{i}-p_{i}|^{(e-1)}\), then \(L_{\text{Adaptive-Focal}}\ (p_{i},y_{i})\) simplifies to \(L_{\text{Focal}}\ (p_{i},y_{i})\). As the model undergoes more training rounds, \(\text{diff}_{i}^{(e-1)}\) varies continually. If \(\text{diff}_{i}^{(e)}\) stays relatively small over several rounds, it signifies a lack of significant improvement in the model's fit to sample \(i\) during those rounds. This can occur due to two reasons:  
1.