## 2 Methods
### Differentiated Multi-Scale Feature Fusion Module (DMF)  
During the multi-scale downsampling process of the image, high-dimensional features often lose fine structural details of small targets, while low-dimensional features have difficulty capturing sufficient global context. To mitigate this problem, this study proposes the differentiated multi-scale feature fusion module (DMF), with its detailed structure shown in Figure 3. The module uses a parallel multi-branch structure to dynamically fuse spatial-spectral features at different scales and applies a feature compensation strategy to achieve complementary enhancement of cross-scale information.  
The multi-scale fusion network begins with the multi-scale feature maps \(\{X_{i},\ i=1,\ 2,\ 3\}\), where \(i\) denotes the spatial resolution index. Each feature map is computed as follows:  
\[X_{Output}\ =\ Depw_{conv2d}\ (Dyfusion(H_{1}(X_{1})+H_{2}(X_{2})+H_{3}(X_{3})), \tag{6}\]  
\[H_{1}(X_{1})=f^{3\times 3}(Pool_{mean}(Depw_{conv2d}(X_{1}))+Pool_{max}(Depw_{ conv2d}(X_{1}))), \tag{7}\]  
where \(H_{1}\) refers to the large-sized feature map, where features are first extracted using the depthwise convolution operation \(Depw_{conv2d}\), followed by dimensionality reduction through a combination of max pooling and average pooling.  
\[H_{2}(X_{2})=f^{1\times 3\times 3}(f^{3\times 1\times 3}(f^{3\times 3\times 1}(X_{2}) )), \tag{8}\]  
For processing horizontal features, feature extraction is achieved by using three different convolutional kernels in parallel (\(3\times 1\times 3\), \(3\times 3\times 1\), and \(1\times 3\times 3\)), effectively enabling joint modeling and preservation of both spectral and spatial information. Specifically, to improve the model's ability to express nonlinear relationships, the GELU (Gaussian Error Linear Unit) activation function is introduced after each convolutional layer. Its  
Figure 3: Illustration of the differentiated multi-scale feature fusion module.  
smooth gradient characteristics, compared to the conventional ReLU function, allow for better retention of detailed information in the feature map.  
\[H_{3}(X_{3})=Nearest(Depw_{conv3d}(X_{3})), \tag{9}\]  
\[Depw_{conv3d}(X)=Reshape(Spcconv(Flatten(f^{3\times 3}(X)))), \tag{10}\]  
\[Spcconv(X)=df^{3}(f^{5}(f^{3}(x))), \tag{11}\]  
For small feature maps, the module combines depthwise separable 3D convolution (\(Depw_{conv3d}\)) with spatial-spectral joint modeling. Spectral convolution kernels of different sizes (\(k_{\rm spec}c_{\rm tral}=[3,\,5]\)) are used to fuse local and global spectral features, and dilated convolutions (dilation = 1) in the spectral domain are applied to expand the receptive field, enabling the network to better capture long-range dependencies across spectral channels. Finally, the dynamic fusion module takes the feature maps from the large, medium, and small scales, processes and spatially aligns them, and then computes their average values to form the \(fusion\_base\).  
The \(Dyfusion\) utilizes a lightweight attention branch, which consists of _AdaptiveAvgPool2d_ layer followed by \(1\times 1\) convolution, to extract global information from \(fusion\_base\) This process generates three weight coefficients that correspond to the response strength of the features at the three scales. The _Sigmoid_ activation function is applied to constrain the weights, and each scale feature is weighted accordingly, enabling dynamic selection and integration of multi-scale information.