## 3 Methods
### Linear Correlation Attention Module  
The backbone is based on the Generalized Efficient Layer Aggregation Network (GELAN) from the YOLOv9 model; it is shown in Figure 2. GELAN employs a modular design that integrates advanced convolution operations, feature fusion, and down-sampling strategies, ensuring efficient feature extraction and fusion across different scales, thereby enhancing feature extraction capabilities. RepNCSPELAN4 is a deep learning module that combines the ideas of CSP (cross-stage partial) and ELAN (Efficient Layer Aggregation Network), designed to enhance the efficiency of feature extraction and fusion, particularly in handling complex and multi-scale visual tasks. This module optimizes the network's expressiveness and computational efficiency through multiple bottleneck structures (such as RepNCSP) and efficient convolution operations. As a core submodule, RepNCSP effectively extracts multi-level feature information and enhances the model's performance across different scales by utilizing cross-stage partial connections and feature fusion. In the workflow of RepNCSPELAN4, the input is first passed through a \(1\times 1\) convolution layer for channel conversion, followed by feature extraction and processing through multiple RepNCSP modules. Subsequently, the processed features are fused through concatenation and down-sampling, improving the model's performance in complex visual tasks. Ultimately, RepNCSPELAN4 efficiently extracts multi-level feature information and provides more accurate feature representations for specific tasks. To better adapt to underwater instance segmentation tasks, we introduce a Linear Correlation Attention (LCA) module, which captures linear correlations between features to enhance the model's ability to handle lighting variations and color differences in complex underwater environments [29; 30]. With this design, the backbone generates rich feature representations with consistent semantic information, providing a solid foundation for subsequent detection and segmentation tasks. In instance segmentation tasks, the diversity in object shapes and sizes, especially the significant differences among objects of the same category, demands extremely high precision and robustness from segmentation algorithms. Non-local attention mechanisms [31] assist models in capturing important contextual information by accounting for long-range dependencies across different positions in the feature map. However, this mechanism relies on dot-product operations to compute the similarity between feature vectors, focusing primarily on the angular relationship between vectors while failing to fully capture the linear correlations between features. This limitation is particularly pronounced in underwater environments. Due to the absorption and scattering effects of water, objects of the same category can exhibit significant color differences at various depths. For example, fish of the same species may show different hues and brightness levels due to changes in lighting underwater. These variations result in inconsistent feature representations of the same objects within images, thereby impacting the performance of segmentation algorithms. To address these challenges, we propose the Linear Correlation Attention (LCA) module, which replaces the traditional dot-product operation with Pearson correlation coefficients. This approach better captures the linear correlations between features, helping  
Figure 2: The architecture of GELAN backbone network. the model maintain semantic consistency when processing objects of the same category. Even in complex underwater scenes, where object colors change due to light scattering and absorption, Pearson correlation coefficients are more effective than dot-product similarity in unifying these variations into consistent target features. By accurately capturing the relationships between features, the LCA module enhances the model's ability to extract semantically relevant features in complex environments, ensuring consistent target representation.