## 2 Materials and Methods
### Modeling Method
#### 2.2.3 Pyramid Pooling of Hollow Space  
Atrous spatial pyramid pooling (ASPP) is a multi-scale feature-extraction strategy that constructs a pyramid of atrous-convolution branches with distinct dilation rates within a convolutional neural network. By substantially enlarging the effective receptive field without a significant increase in parameters, ASPP enables the network to capture contextual information at multiple spatial scales while preserving feature-map resolution, thereby enhancing its ability to recognize objects of varying sizes. Atrous convolution expands the kernel's field of view through sparse sampling, circumventing the detail loss usually caused by downsampling, whereas the parallel multi-branch design endows the model with rich scale awareness. The convolution operations corresponding to the different dilation rates are formally defined in Equations (14)-(16). \[x_{1}=\sigma_{\text{ReLU}}(W_{1}*r_{1}\!\cdot\!x+b_{1}) \tag{14}\]  
\[x_{2}=\sigma_{\text{ReLU}}(W_{2}*r_{2}\!\cdot\!x+b_{2}) \tag{15}\]  
\[x_{3}=\sigma_{\text{ReLU}}(W_{3}*r_{3}\!\cdot\!x+b_{3}) \tag{16}\]  
Among them, \(W_{1},W_{2},W_{3}\) are the weight parameters of different convolutional layers, \(b_{1},b_{2},b_{3}\) are the bias terms, \(r_{1},r_{2},r_{3}\) are the void rates, \(x\) is the input feature sequence, and \(\sigma_{\text{ReLU}}\) is the ReLU activation function. The global-average-pooling branch compresses the input feature map into a global feature vector, refines the channel dimensionality via a \(1\times 1\) convolution, and subsequently restores the spatial resolution through upsampling. This process provides global contextual information, thereby compensating for the limited receptive field of local convolutions. The corresponding mathematical formulations are presented in Equations (17)-(19). \[\overline{x}_{c}=\frac{1}{L}\sum_{i=1}^{L}x_{bic} \tag{17}\]  
\[x_{4}=\sigma_{\text{ReLU}}(W_{4}\!\cdot\!\overline{x}+b_{4}) \tag{18}\]  
\[x_{4}^{\prime}=L_{(1)}\!\cdot\!x_{4}^{T} \tag{19}\]Among them, \(x_{bic}\) represents the value of channel \(c\) at position \(i\) of the Bh batch of the input feature position, \(L\) is the total length of the vector, \(\overline{x}\) is the value of channel \(c\) after compression and \(\overline{x}=[\mathbb{F}_{1},\mathbb{F}_{2},\ldots,\ldots,\mathbb{F}_{c}]\), and \(L_{(1)}\) is the column vector of all 1s. Subsequently, the features extracted from the multi-scale atrous-convolution branches and the global-average-pooling branch are concatenated along the channel dimension and fused via a \(1\times 1\) convolution to realize cross-scale interaction and compression, as formulated in Equations (20) and (21). \[x_{cut}=[x_{1},x_{2},x_{3},x_{4}^{\prime}] \tag{20}\]  
\[y_{out}=\sigma_{\text{ReLU}}(W_{5}\cdot x_{cut}+b_{5}) \tag{21}\]  
Among them, \(x_{out}\) represents the result obtained by concatenating the features obtained by the convolution of different receptive fields with the features obtained by global pooling, and \(y_{out}\) is the cross-scale feature output result after convolution fusion. In the present task, distinct spectral bands in hyperspectral data corresponded to characteristic absorption features of various substances. The ASPP module, with its parallel multi-branch design, concurrently captures local details (small dilation rate), medium- to long-range dependencies (large dilation rate), and global context (pooling branch). The fused multi-scale features enhance the model's robustness to spectral noise and local occlusions, rendering ASPP particularly well-suited to the high spectral dimensionality of hyperspectral data. The ASPP architecture implemented in this study is illustrated in Figure 4, where B denotes the batch size, C is the number of channels, and L is the sequence length. Within the overall framework, the ResNet backbone extracts deep representations via residual connections but may overlook cross-scale contextual information; the ASPP module refines these high-level features at multiple scales.