## 3 DAMP-YOLO Network
### Deformable CSP Bottleneck  
When the traditional convolution layer performs convolution calculation on images in visual recognition and detection tasks, it will select input features according to the preset rectangular grid structure for convolution calculation (for example, a convolution module with a convolution kernel of \(3\times 3\) will select eight neighboring pixels of the current pixel), which cannot cope with the geometric transformation of the image well. At the same time, the traditional convolutional layer is performed in a small local receptive field, ignoring some distant information. Therefore, the traditional convolutional layer is limited to unknown geometric transformations. The ability to model geometric transformations mainly comes from many data enhancements, more model parameters, and some artificially designed modules(such as short-distance translation and invariant max-pooling layers). Figure 4: The structure diagram of the DAMP-YOLO network, mainly consisting of a Conv module, DCB module, ATA module, SPPF module, and a Detect module. Deformable convolution [36] introduces an offset into the traditional convolution operation. It gives each input feature point selected by the convolution layer an offset so that the convolution will focus on selecting the input feature during the training process. In the effective information area, different convolutional layers will focus on different image geometric transformations, thereby improving the robustness of the model to image geometric transformations. As illustrated in Figure 5, let the input feature map be \(X\in R^{H\times W\times C}\) and the output feature map be \(Y\in R^{H\times W\times D}\), where \(H\) and \(W\) represent the height and width of the feature map, respectively, and \(C\) and \(D\) represent the input feature map and output feature map, respectively, for the number of channels. The operation of deformable convolution can be expressed as  
\[Y[h,w,d]=\sum_{c=1}^{C}\sum_{i=1}^{I_{h}}\sum_{j=1}^{I_{w}}W_{c,i,j,d}*X[h+i-1, w+j-1,c] \tag{1}\]  
where \(h,w,d\) denote the pixel co-ordinates and channel co-ordinates on the output feature map, respectively. \(I_{h}\) and \(I_{w}\) represent the offset range of the convolution kernel in height and width, respectively, \(W_{c,i,j,d}\) represent the weight of the convolution kernel, and the sign \"*\" represents the convolution operation. In contrast to traditional convolution, deformable convolution needs to consider the offset of each pixel when operating, so the offset needs to be added to the convolution kernel. The following mathematical formula can calculate these offsets:  
\[Offset_{i,j}=\frac{1}{N}\sum_{n=1}^{N}Grad_{i,j,n} \tag{2}\]  
Among them, \(Offset_{i,j}\) represents the offset of the convolution kernel at the position (i, j), \(Grad_{i,j,n}\) represents the gradient of the loss function to the nth pixel on the output feature map, and \(N\) represents the pixel on the output feature map quantity. For the abovementioned, we proposed DCB modules that combine the advantages of C2f, ELAN, and deformable convolution. The DCB module structure is shown in Figure 6. The input features are initially processed through the first convolutional layer to extract the preliminary features. The output of this layer is then split into two branches: the main gradient flow and the subgradient flow. The main gradient flow is further processed through deformable convolutional bottleneck layers to extract deeper features. Similar to the first layer, the output of each deformable convolutional bottleneck layer is split into two branches, with the main gradient flow serving as the input for the next layer. Figure 5: Schematic diagram of 3 \(\times\) 3 deformable convolution structure. After passing through N deformable convolutional bottlenecks, the last main gradient flow is concatenated with all subgradient flows and fed into the second convolutional layer to produce the final fused features.