## 2 Related Studies
### SimAM Module  
SimAM [32] is a parameter-free and efficient three-dimensional attention. According to the importance of information carried by neurons in various regions, different attention is allocated, making the network prioritize crucial features within the target district, thereby enhancing the feature representation of the target. Different from traditional methods, the 3D weights obtained by the module are directly calculated using a specific energy function, and no additional subnetworks are needed to generate them. The analytical solution defined by the function can infer the 3D weights for the current neuron. It is worth explaining that the existing attention module treats all neurons of the same dimension equally. This module distributes an exclusive weight to individual neurons while simultaneously considering the importance of both channel and spatial dimensions, which is more in line with the characteristics of human attention. In addition, the SimAM module has been embedded into some classical network structures to verify its generalization in disparate tasks.  
In visual neuroscience, neurons carrying different amounts of information activate in diverse ways, and the way to find neurons carrying more important information is to determine whether the target neuron and surrounding neurons are linearly separable. Linear separability can be achieved by minimizing the energy function formulation. First, the energy function after introducing the regularization term is described as follows:  
\[e_{t}(w_{t},b_{t},y,x_{i})=\frac{1}{M-1}\sum_{i=1}^{M-1}(-1-(w_{t}x_{i}+b_{t}) )^{2}+(1-(w_{t}t+b_{t}))^{2}+\lambda w_{t}^{2} \tag{5}\]  
where \(t\) and \(x_{i}\) are the target and surrounding neurons of the input feature \(X=R^{C\times H\times W}\) in a single channel, respectively; \(M=H\times W\) represents the quantity of neurons within that channel; and \(i\) denotes the index of the spatial location. \(w_{t}\) and \(b_{t}\) are the weight and bias transforms.  
Secondly, the specific forms of the analytical solutions of \(w_{t}\) and \(b_{t}\) are defined using Equations (6) and (7).  
\[w_{t}=-\frac{2(t-\mu_{t})}{(t-\mu_{t})^{2}+2\sigma_{t}^{2}+2\lambda} \tag{6}\]  
\[b_{t}=-\frac{1}{2}(t+\mu_{t})w_{t} \tag{7}\]  
where \(\mu_{t}=\frac{1}{M-1}\sum_{i=1}^{M-1}x_{i}\) and \(\sigma_{t}^{2}=\frac{1}{M-1}\sum_{i}^{M-1}(x_{i}-\mu_{t})^{2}\) represent the mean and variance of every neuron except \(t\), respectively. Then, the minimum energy can be calculated as follows:  
\[e_{t}^{*}=\frac{4(\hat{\sigma}^{2}+\lambda)}{(t-\hat{\mu})^{2}+2\hat{\sigma}^{ 2}+2\lambda} \tag{8}\]  
Here, \(\hat{\mu}=\frac{1}{M}\sum_{i=1}^{M}x_{i}\) and \(\hat{\sigma}^{2}=\frac{1}{M}\sum_{i}^{M}(x_{i}-\hat{\mu})^{2}\). Equation (5) shows that the lower the energy, the more pronounced the distinction between the target neuron and other neurons, so the significance of the target neuron may be represented using \(\frac{1}{\hat{e}_{t}^{2}}\). At this point, we use \(\mathbf{E}\) to define \(e_{t}^{*}\) across all channels and spatial dimensions, and then we apply the _sigmoid_ to \(\frac{1}{\mathbf{E}}\) as the 3D weight and multiply it by the original input feature.  
\[\mathbf{\widetilde{X}}=sigmoid(\frac{1}{\mathbf{E}})\odot\mathbf{X} \tag{9}\]  
Figure 1: MCA network structure.