## 3 Proposed Method
### Enhancing Feature Extraction with AKConv  
While the YOLOv8 architecture generally excels in generic object detection, its performance in the NEU-DET defect detection task revealed a bottleneck, particularly with crazing and rolled-in scale defects, where mAP values were significantly lower than other categories. This issue primarily stems from the characteristics of these defects; crazing appears as elongated, irregular, and often blurred structures, while rolled-in scale defects exhibit high shape variability. Standard convolutional kernels (e.g., \(3\times 3\) or \(5\times 5\)) with fixed sampling patterns struggle to capture these fine-grained spatial features. To address this, we integrated AKConv modules to replace some convolutional layers within YOLOv8's backbone, thereby enhancing the model's spatial perception flexibility and geometric expression capabilities [27]. AKConv redefines conventional convolution through its dynamic adaptation mechanism, which employs dual control modules to intelligently regulate both kernel geometry and parameter configuration. As shown in Figure 2, this innovative architecture and its operational workflow are comprehensively demonstrated. AKConv receives an input tensor of shape \((C,H,W)\), where \(C\) denotes the number of channels, and \(H\) and \(W\) are spatial dimensions. It introduces a learnable offset prediction module, implemented as a convolution (Convoffset) that outputs \(2N\) channels representing horizontal and vertical offsets \((\Delta x_{i},\Delta y_{i})\) for each of the \(N\) sampling positions. Figure 1: Overall structure of the model. To better understand how AKConv modifies standard convolution, we revisit the original fixed sampling formulation:  
\[\text{Conv}(\mathbf{p}_{0})=\sum_{i}w_{i}\cdot x(\mathbf{p}_{0}+\mathbf{p}_{n}^{i}) \tag{1}\]  
Here, \(\mathbf{p}_{0}\) is the central position, \(\mathbf{p}_{n}^{i}\) denote the predefined offsets of the \(i\)-th kernel element, and \(w_{i}\) denote the learned kernel weights. In AKConv, additional learnable offsets \(\Delta\mathbf{p}^{i}\) are added:  
\[\mathbf{p}^{i}=\mathbf{p}_{0}+\mathbf{p}_{n}^{i}+\Delta\mathbf{p}^{i} \tag{2}\]  
This can also be expressed in terms of coordinates:  
\[(x_{i}^{\prime},y_{i}^{\prime})=(x_{i}+\Delta x_{i},y_{i}+\Delta y_{i}) \tag{3}\]  
Here, \(\Delta x_{i}\) and \(\Delta y_{i}\) implicitly include both the predefined relative offsets \(\mathbf{p}_{n}^{i}\) and the learned dynamic offsets \(\Delta\mathbf{p}^{i}\). Since \(\mathbf{p}^{i}\) may lie between pixel locations, bilinear interpolation is applied:  
\[x(\mathbf{p}^{i})=\sum_{q\in\mathcal{N}(\mathbf{p}^{i})}G(q,\mathbf{p}^{i}) \cdot x(q) \tag{4}\]  
where \(\mathcal{N}(\mathbf{p}^{i})\) includes the four surrounding integer locations, and \(G(q,\mathbf{p}^{i})\) is the interpolation weight. This makes the sampling differentiable, allowing gradients to backpropagate to \(\Delta\mathbf{p}^{i}\), which are trained indirectly via the detection loss \(\mathcal{L}_{\text{det}}\). The adaptively sampled feature map is reshaped and passed through a convolutional block (including normalization and SiLU activation) to produce the final output. This process allows AKConv to dynamically adapt its sampling to better capture irregular or fine-grained features [33]. Figure 2: AKConv structure. The bottom part of the figure demonstrates the coordinate transformation: **Original coordinates:** Fixed sampling positions of the standard convolution kernel, without any offsets. **Offsets:** The trained offset values that refine the original coordinates. **Modified coordinates:** The resultant sampling pattern after offset application. Figure 3 delineates the dynamically adaptive morphological configurations and their parameter polymorphism in AKConv. Figure 4 illustrates a simplified example of AKConv. The left panel shows an image selected from the inclusion dataset, and the right panel displays an image from the rolled-in scale dataset.