# A Lightweight Module for Feature Fusion Based on Their Dimensions
## 3 Materials and Methods
### \(\varphi\)Net  
\(\varphi\)Net is a novel network architecture, which is inspired by classic networks such as U-Net [41], GhostNet [40] and MobileNetV2 [17]. In \(\varphi\)Net, the up-convolution operation from U-Net [41] is adopted in this work, and we introduce \(\varphi\)unit to enable cross-level feature fusion. \(\varphi\)unit is one of the basic units of \(\varphi\)Net, which fuses the high-dimensional feature information and low-dimensional feature information extracted by the bottleneck group. The fused feature information comprises both abstract information from high-dimensional convolution and superficial information from low-dimensional convolution. Specifically, we fuse the two feature maps by cross-stitching them following the channel order. By this way, each pixel position in the fused feature map possesses feature representations from both the current and the previous levels. Furthermore, this study also takes into account the phenomenon of excessive redundant feature information in the extracted feature images [40]. By meticulously designing the network structure and feature selection strategy, \(\varphi\)Net can generate low-cost redundant features with lower cost and improve the overall performance. Additionally, the bottleneck structure from MobileNetV2 is also employed in this work to further increase the representation power and convergence speed of \(\varphi\)Net. A network called \(\varphi\)Net, which integrates the strengths of U-Net, GhostNet and MobileNetV2, is built in this study. By using key techniques such as up-convolution, feature fusion and residual structure, \(\varphi\)Net can achieve excellent performance in image processing tasks. The structure and organization of the related network is displayed in Table 1.  
This paper uses the bottleneck module in Mobinetv2 to extract basic feature information, and adjusts the feature depth and size according to the dimension change rule and network actual characteristics of Mobinetv2. The network construction strategy is as  
Figure 2: Explains cross concatenation in the proposed unit. follows: first, use one convolution layer and three bottleneck layers to obtain the shallowest feature of the original image; second, use multiple bottleneck structures to extract high-dimensional abstract features from low-dimensional features; then, use the \(\varphi\)unit proposed in this paper to fuse the extracted features twice; finally, convert all fused image features into final classification information. This study proposes a novel network \(\varphi\)Net, which can fully capture the feature space and logical feature continuity. The overview of the network structure is shown in Figure 3. The network structure used in this study constructs the low-dimensional and high-dimensional representations of the basic features through the downsampling layer and the feature extraction layer, respectively, after performing the basic feature extraction on the original image. Next, the high-dimensional features obtained are upsampled to narrow the gap with the low-dimensional features, and a downsampling operation is also carried out, which serves as one of the input contents for the next feature fusion. The function of \(\varphi\)unit is to fuse the processed high-dimensional and low-dimensional features and pass them to the next layer, so as to achieve the goal of retaining the high-dimensional abstract features while alleviating the problem of low-dimensional feature loss caused by the network depth increase. This process is executed twice in total, and the detailed proof is given in Section 4.2. Finally, in order to integrate the global features and prepare for the prediction task, the final fused features are subjected to a final feature extraction, and then input to the classification module to complete the classification task. The effectiveness of the network is verified by a series of comparative experiments in Section 4.3.