## 3 Proposed Method
To address this, we propose the LAFM, which enhances the representational capacity of fused features through concatenation and weighted combination, as illustrated in Figure 5. Unlike ASPP's parallel dilated convolutions that statically capture multi-scale context [25], LAFM employs a dynamic weighting mechanism to adaptively adjust fusion strategies based on semantic importance. Specifically, global pooling and convolutional operations generate lightweight weights to refine feature contributions, reducing computational overhead compared to ASPP while maintaining comparable global modeling capabilities. In contrast to SFNet's spatial attention and pyramid pooling [36], which excel in complex background handling but suffer from inference latency, our module prioritizes efficient hierarchical fusion. The concatenation operation merges spatial or channel-level features, while the weighted combination dynamically assigns task-specific importance weights. This design enables LAFM to achieve real-time performance with competitive accuracy on benchmarks, demonstrating superior balance in accuracy-efficiency trade-offs over existing methods. The input features f1 and f2, derived from distinct sources or hierarchical levels, are first concatenated to form fcat. This concatenated feature is then subjected to a linear transformation, involving a matrix multiplication with W followed by the addition of a bias term b1, resulting in Ffeat. A ReLU activation is applied to Ffeat to produce FSR. Through the successive processes of feature fusion and nonlinear activation, the model progressively extracts higher-level feature representations. Each linear transformation and activation function provides a nonlinear mapping, enabling the model to capture intricate relationships and patterns within the data. Subsequently, global average pooling is applied to FSR, yielding a compact feature vector fatten_avg that encapsulates global contextual information. This operation allows the model to focus on the global semantics, enhancing its expressiveness, especially when dealing with multi-scale features. The global feature vector is then subjected to another

Figure 5: Lightweight Adaptive Fusion Module (LAFM). linear transformation using W' and b2, producing f3, which is followed by a ReLU activation to generate f2. Finally, fR2 undergoes a final linear transformation and is passed through a sigmoid function, normalizing the output within the range of [0, 1], which serves as the final output of this module. The formula is presented in Equation (8) as follows:

\[ \begin{gathered}\text{f}_{1}\text{,f}_{2}\in\text{R}^{\text{B} \times\text{C}\times\text{H}\times\text{W}}\\ \text{f}_{\text{cat}}=\text{Concat}(\text{f}_{1}\text{,f}_{2})\\ \text{F}_{\text{feat}}=\text{f}_{\text{cat}}*\text{W}+\text{b}_{1}\\ \text{F}_{\text{R}}=\text{max}\ (0\text{, }\text{F}_{\text{feat}})\\ \text{f}_{\text{atten\_avg}}=\sum_{i=1}^{\text{H}}\sum_{j=1}^{ \text{W}}\text{F}_{\text{R}}/\text{H}\times\text{W}\\ \text{f}_{3}=\text{f}_{\text{atten\_avg}}*\text{W}^{\prime}+\text{b}_{2} \\ \text{f}_{\text{R2}}=\text{max}\ (0\text{, f}_{3})\\ \text{f}_{4}=\text{f}_{\text{R2}}*\text{W}_{3}+\text{b}_{3}\\ \text{f}_{5}=1/\left(1+e^{-f_{R2}\text{ }\text{W}_{3}-\text{b}_{3}}\right)\end{gathered}  \tag{8}\]

The output feature f5 undergoes a linear transformation through the weighted matrices W4 and W5, along with the bias terms b4 and b5, projecting the input feature space into a higher-dimensional space. This process allows for the capture of more intricate dependencies between the features. Subsequently, after passing through a sigmoid activation function, the resulting linear combination is mapped to a range between 0 and 1, ensuring that the transformed values remain within a meaningful range. This operation is a crucial step in maintaining stable learning dynamics. Following this, the new feature weights W1 and W2 are derived from this transformation and are applied to the original input features f1 and f2, enabling dynamic adjustment of the input features.