## 1 Introduction  
Strip steel is a vital component of the steel industry, widely used in automobile manufacturing, home appliance production, and construction structures [1]. During manufacturing, strip steel may develop various surface defects, such as scratches, cracks, oxide scales, pits, roll marks, and scabs [2]. These defects not only degrade the appearance but also potentially compromise the mechanical properties and service life of the material [3]. For instance, scratches and cracks can weaken the material's strength, while oxide scales and scabs may negatively impact subsequent processing steps, leading to quality degradation [4]. Therefore, precise and prompt segmentation and the effective addressing of these defects are essential for guaranteeing product quality [5]. Advancements in deep learning have led to remarkable progress in segmenting steel surface defects [6]. For example, [PERSON] et al. [7] proposed the multiscale context segmentation network to segment multiscale defects on strip steel surfaces. Built on Faster R-CNN, the network incorporates a parallel atrous convolution architecture to effectively capture multiscale context and minimize confusion. [PERSON] et al. [8] proposed AFF-Net for strip steel defect segmentation, tackling challenges from size variations, complexity, and diversity. AFF-Net introduces AFF-Block for adaptive feature weighting of segments and Foc-FPN to improve multiscale fusion and semantic balance. As mentioned above, deep learning approaches have made remarkable strides in strip steel surface defect segmentation. However, according to the available information, these approaches have failed to fully recognize a crucial role of edge information in strip steel surface defect segmentation. In fact, in other practical applications, edge information has proven to greatly boost the model's segmentation accuracy. For example, [PERSON] et al. [9] presented CGTD-Net, a dual-branch network utilizing a channel-wise global transformer for strip steel defect segmentation. They enhanced edge information with the SCGA module and optimized feature fusion using the CGT module, improving the accuracy of small or narrow-edge defect segmentation. [PERSON] et al. [10] proposed a model called EMC-UNet to enhance the accuracy of pulmonary nodule segmentation. EMC-UNet utilizes the Sobel operator to enhance edge information, improving the perception of pulmonary nodule boundaries, and employs a multiscale feature extraction module to capture features at different scales. Based on the discussion above, we propose a Differentiable Edge-guided Feature Pyramid Aggregation Network (DEPANet) within an encoder-decoder framework, leveraging edge information from strip steel surface defects to enhance segmentation performance. This edge information inherently exhibits distinctive characteristics, such as intensity discontinuities and boundary contrasts, which can be exploited to guide precise segmentation. The encoder comprises three key components: a backbone network, a Differentiable Edge Feature Pyramid Network (DEFP), and Edge-aware Feature Aggregation Modules (EFAMs). Considering that ResNet possesses both strong feature extraction capabilities and high execution efficiency, we selected ResNet34 [11] as the backbone to extract the overall features of the input image. In contrast, DEFP is proposed to improve the model's ability to extract edge components, consisting of a series of stacked Adaptive Feature Smoothing Filters (AFSFs). Each AFF leverages a learnable Laplacian operator for edge feature extraction and a learnable Gaussian blurring mechanism for feature smoothing and enhancement. The multiple proposed EFAMs are employed to generate edge-enhanced features, with each EFAM designed to integrate the backbone-extracted global features along with the edge components from DEFP at the corresponding level.