## 2 Materials and Methods
### Fine-Tuning Transfer Learning (FTTL)  
With the introduction of the Tok-KAN and DLFFSKA modules, the model not only possesses strong nonlinear learning capabilities but also excels in contextual understanding, enabling it to more accurately capture the complex features of landslide regions. However, due to the scarcity of publicly available landslide image datasets, even though the network exhibits superior performance, the insufficient training data may still result in slow model convergence, limited generalization, and low segmentation accuracy.  
Therefore, we introduce FTTL technology [52], which aims to make full use of existing knowledge by adjusting the weights of the base model to adapt to the data characteristics of the target task. Suppose that the parameters of the base model are \(\theta_{\text{pre}}\), which have been pretrained on a large-scale dataset and contain learned general features. The model parameters for the target task are \(\theta_{\text{target}}\), and we expect to fine-tune these parameters to make them more suitable for the characteristics of landslide images. Specifically, the loss function of the fine-tuning process is shown in Equation (12):  
\[\mathcal{L}_{\text{target}}=\mathbb{E}_{(x,y)\sim D_{\text{target}}}\left[ \ell(f_{\theta_{\text{target}}}(x),y)\right] \tag{12}\]  
In fine-tuning, \(\mathcal{L}_{target}\) denotes the target landslide image dataset, \(\mathbb{E}_{(x,y)\sim D_{\text{target}}}\) denotes the expectation of the sample \((x,y)\) of the target dataset, and \(\ell\) is the loss function used to compare the predicted and true values, while \(f_{\theta_{\text{target}}}\) is the output of the target task model.  
To apply FTTL to the landslide image segmentation task, we can freeze certain layers [53] of the base model to preserve the generality of the low-level features. The frozen layers' parameters \(\theta_{\text{freeze}}\) belong to the parameters of the base model \(\theta_{\text{pre}}\), and during training, these parameters remain fixed.  
By freezing the low-level features, we allow the high-level features to adjust according to the characteristics of the landslide images. This strategy ensures that the frozen low-level features capture general image features, such as edges and textures, while the high-level features are optimized to detect specific landslide characteristics, such as the shape and topographical features. This approach not only significantly enhances the model's ability to adapt to landslide features but also improves the model's understanding of the shape, texture, and contextual relationships within the landslide regions.  
In this paper, the base model is first pretrained on a large-scale dataset to learn general features. Next, only the target landslide dataset is trained by freezing the shallow network of the base model to obtain high-level features that are closely related to the task. The training process for the target task can be seen in Equation (13):  
\[\theta_{\text{target}}^{i+1}=\theta_{\text{target}}^{t}-\eta\
abla_{\theta_{ \text{unfreeze}}}\mathcal{L}_{\text{target}} \tag{13}\]  
where \(\theta_{\text{unfreeze}}\) represents the high-level feature parameters that have not been frozen, \(\eta\) is the learning rate, and \(\
abla_{\theta_{\text{unfreeze}}}\mathcal{L}_{\text{target}}\) is the gradient of the target task loss function with respect to the unfrozen parameters. Finally, a model suitable for the landslide segmentation task is constructed based on the fine-tuned target model. The principle and process of FTTL are shown in Figure 4.