## 3 Method
### Feature Encoding Network
Here, \(B\) signifies the data dimension of each point and is set to 9, including coordinates \(x\), \(y\), \(z\), reflectivity \(r\), distance to the arithmetic mean of all points inside the pillar \(x_{r}\), \(x_{r}\), \(x_{r}\), and the offset to the center of the pillar's \(X\)-\(Y\) plane \(x_{p}\), \(y_{p}\). \(P\) denotes the count of non-empty pillars in each sample, and \(N\) represents the number of points within each pillar. Subsequently, a simplified version of PointNet (a linear layer with 64 output channels followed by BatchNorm [28] and ReLU [29]) is employed to generate a high-dimension feature metric (\(C\), \(P\), \(N\)), followed by a max pooling in the \(N\) dimension, generating a tensor of size (\(C\), \(P\)) [15]. This tensor, referred to as the feature matrix \(F\), will be input into the CPA module subsequently. 2. CPA module  
After converting the point clouds into tensors, the CPA module is employed to enhance the feature association among points within the pillar. Since the self-attention mechanism [23] can effectively establish contextual information association, it is introduced here. Ultimately, the features of points within the pillar are strengthened. Figure 4 illustrates the principle of the CPA module. As shown in Figure 4, the input for the CPA module is feature metric \(F\). According to [15], \(F\) is sent into a Multilayer Perceptron (MLP) layer to obtain matrices \(Q\) (query), \(K\) (Key), and \(V\) (value), as shown in Equations (6)-(8). Then, \(Q\), \(K\), and \(V\) are input into  
Figure 4: Schematic diagram of CPA module. It consists of a self-attention module and residual connection, which are used to establish feature associations among points within a pillar. Equation (9) to obtain attention weight matrix \(\mathbf{A}\). \(d_{q}\), \(d_{k}\), and \(d_{v}\) in the following equation represent the dimensions of \(\mathbf{Q}\), \(\mathbf{K}\), and \(\mathbf{V}\), respectively. \[\mathbf{Q} =\mathrm{MLP}_{\mathrm{Q}}(\mathbf{F}),\mathbf{Q}\in\mathbb{R}^{C\times d_{q}} \tag{6}\] \[\mathbf{K} =\mathrm{MLP}_{\mathrm{K}}(\mathbf{F}),\mathbf{K}\in\mathbb{R}^{C\times d _{k}}\] (7) \[\mathbf{V} =\mathrm{MLP}_{\mathrm{V}}(\mathbf{F}),\mathbf{V}\in\mathbb{R}^{C\times d _{v}}\] (8) \[\mathbf{A} =softmax\left(\frac{\mathbf{Q}\mathbf{K}^{\mathrm{T}}}{\sqrt{d_{k}}} \right)\mathbf{V},\mathbf{A}\in\mathbb{R}^{C\times C} \tag{9}\]  
Then, MLP is used to restore \(\mathbf{A}\) to the original dimension \(P\) and obtain the self-attention feature \(\mathbf{F}^{\prime}\), as shown in Equation (10). \[\mathbf{F}^{\prime}=\mathrm{MLP}(\mathbf{A}),\mathbf{F}^{\prime}\in\mathbb{R}^{C\times P} \tag{10}\]  
Because the self-attention might increase the complexity of the model, it might not outperform Convolutional Neural Networks (CNNs) on small-scale datasets. To circumvent this issue, residual connection is employed. This connection adds the original feature \(\mathbf{F}\) to the self-attention feature \(\mathbf{F}^{\prime}\), as shown in Equation (11). As a result, the correlation between points within local spaces is enhanced to improve the network's recognition capability. \[\mathbf{F}^{\prime}=\mathbf{F}^{\prime}+\mathbf{F},\mathbf{F}^{\prime}\in\mathbb{R}^{C\times P} \tag{11}\]  
Because the improved self-attention can enhance the feature correlation within each pillar, it can thus enhance robustness against sparse points. As shown in Figure 2, the enhanced features obtained from the CPA module are redistributed to their original positions based on the pillar index, resulting in a 2D pseudo image [15]. As shown in Figure 1, the pseudo image is then input into the Detection Neck to further extract features, after which the Detection Head obtains the detection result.