## 3 Proposed Method
### Convolutional Cross-Substitution Transformer Module
#### 3.2.1 Convolutional Cross-Substitution Attention Block  
The convolutional cross-substitution attention block, which serves as the core component of this study, seeks to effectively synthesize the advantages of CNNs and Transformers. This integration facilitates the efficient extraction and processing of hyperspectral image features while simultaneously reducing computational complexity and maintaining robust global representational capacity. Consequently, the optimization process emphasizes two critical aspects. During the projection phase, convolutional projections are utilized to replace traditional linear projections for the representations of the query (\(Q\)), key (\(K\)), and value (\(V\)). This enhancement aids in capturing local contextual features during global interactions and promotes effective integration of CNN and Transformer mechanisms. In the attention computation phase, a cross-substitution strategy is implemented to streamline the model's complexity. This strategy not only preserves global representational capacity but also enhances overall computational efficiency. The specific approach is elaborated as follows. During the projection phase, instead of employing conventional self-attention modules, depthwise separable convolutions are utilized to perform the projection operations for local feature extraction. As illustrated in the upper portion of Figure 4, this study implements depthwise separable convolutions with a kernel size of \(3\times 3\) for spatial feature projection, while for the spectral dimension, depthwise separable convolutions with a kernel size of \(1\times 1\times 7\) are employed for spectral feature projection. Notably, in comparison to conventional convolutions, depthwise separable convolutions significantly reduce computational costs. For instance, considering a token with dimensions \(N\times d\), where \(N\) denotes the number of tokens to be processed and \(d\) represents the channel dimension of each token with a convolution kernel size \(K\times K\), the parameter count in standard convolution would be \(d\times(K\times K)\times d\), resulting in a computational load of \(O(d\times(K\times K)\times d\times N)\) FLOPs. Conversely, with depthwise separable convolution (which consists of depthwise and pointwise convolutions), the parameter count is reduced to \((K\times K)\times d+d^{2}\), leading to a computational load of \(O((K\times K)\times d\times N+d\times N\times d)\) FLOPs. To further minimize computational demands, our approach involves sharing the query vectors \(Q\) and value vectors \(V\). However, to mitigate potential model instability arising from identical \(Q\) and \(V\) values, pooling values \(Q_{pool}\) for query vectors \(Q\) and pooling values \(K_{pool}\) for key vectors \(K\) are cross-substituted to ensure differentiation in the actual calculations. As shown in Equations (8) and (9), the query vectors \(Q\) and key vectors \(K\) are derived through depthwise separable convolution, followed by max pooling to obtain their respective pooling values, denoted as \(Q_{pool}\) and \(K_{pool}\). \[Q =V=DWConv_{1}(x) Q_{pool} =Pooling(Q) \tag{8}\] \[K =DWConv_{1}(x) K_{pool} =Pooling(K) \tag{9}\]  
In the attention computation phase, as illustrated in the lower portion of Figure 4, \(Q_{pool}\) and \(K_{pool}\) are employed to cross-substitute the input \(Q\) and \(K\) during attention calculations, delineated across two distinct stages. Furthermore, a nested lightweight attention mechanism is incorporated to minimize computational load while mitigating the loss of essential global information. In the first stage of attention computation, \(Q_{pool}\) is utilized as a substitute for the original query vector \(Q\), while the original \(Q\) is treated as the value vector \(V\) within the attention framework. Specifically, attention is computed among  
Figure 3: Convolutional cross-substitution transformer module. \(Q_{pool}\), \(K\), and \(Q\) to produce the aggregated global feature representations \(V_{ant}\), as indicated in Equation (10).