## 3 Method
### Associated Entity Detection  
The \"Body\" of MER is typically a complicated borderless table structure, comprising various contents. Existing multimodal fusion models fall short of learning the correlation between complex keys, like nested keys, and multiple rows of keys/values. To address this, our paper proposes an associated entity detection model, RIFD-Net. This model treats each test item and its related information as a distinct category, thereby producing the corresponding detection box. The overall architecture is shown in Figure 5.  
In the backbone, the intra-layer feature adjustment module (IFAM), by combining the global information extraction capability of the MLP with the local detail-capturing capability of the learnable residual encoding module, the feature extractor can provide a richer and more discriminative feature representation for the backbone network. This helps enhance the model's adaptability to complex scenes, thereby improving the accuracy of line localization and detection accuracy. The neck employs PANet [40] to extract various level features and fuse them to create a more comprehensive understanding. The head uses a decoupled head [37] separately to predict confidence and regression frames, thereby enhancing the detection accuracy and precision. The RIFD-Net backbone consists of a series of basic convolutional blocks and residual layers, as shown in Figure 6. To minimize noise, the features generated by \(B2\) undergo initial processing via a basic convolution with a kernel size of 7. Subsequent to this, the extracted features are sent to a deep multilayer perceptron (DMLP) and a learnable residual encoding module (LREM). Ultimately, the two outputs pass through a convolution layer with a kernel of size 1 to adjust the output channel to 256. The DMLP consists of a depthwise convolution residual module and a multilayer perceptron residual module, as shown in Figure 7. Depthwise convolution [46] has fewer computational parameters and more efficiency compared to normal convolution. MLP [39] can achieve global information processing. Both modules use residual structures, which help to prevent information loss during information processing. DMLP can detect dense  
Figure 5: Relevant intra-layer fine-tuned detection network (RIFD-Net) architecture. Figure 6: RIFD-Net backbone architecture. \(k\) denotes the convolution kernel size, \(s\) denotes the step size, \(p\) is the padding, and \(c\) denotes the output channel size. \(C3\) is composed of the basic convolution block with a \(k\) of 1, and bottleneck, which consists of the basic convolution block with \(k=1,3\) and optional additive modules. objects by sufficiently integrating global features. The entire process is expressed in Equation (11):  
\[ \begin{split} X^{\prime}&=DW(GN(X))+X\\ F_{1}&=MLP(GN(X^{\prime}))+X^{\prime}\end{split}  \tag{11}\]  
where \(X\) is the output of \(B2\) after smoothing feature processing, \(X^{\prime}\) is the output of the deep convolution module, \(GN\) is GroupNorm, and \(F_{1}\) denotes the output of DMLP. The LREM is constructed based on the encoding layer of the texture encoding network (Deep-TEN) [33], The encoding layer learns both the encoding parameters and the intrinsic dictionary in a supervised learning way. The network structure is shown in Figure 8.  
To break it down, the feature map, \(X\), is fed into an encoding layer with a fixed learned codebook, \(C\). For each input datum, \(x_{i}\), \(i\in[1,N]\), we calculate its residual vector \(r_{ik}=x_{i}-c_{k}\), with each codeword \(ck\), \(k\in[1,K]\) in the dictionary, where \(N\) is the total spatial number of the input features, and \(K\) is the total number of codewords. Then, an attentional weight \(a_{ik}\) is assigned to each codeword, for the \(k\)-th codeword, \(c_{k}\), the attentional weight is denoted as in Equation (12):  
\[\alpha_{ik}=\frac{e^{-s_{k}}||r_{ik}||^{2}}{\sum_{j=1}^{K}e^{-s_{j}}||r_{ij}||^ {2}} \tag{12}\]  
where \(S=\{s_{1},s_{2},\ldots,s_{k}\}\) is a learnable smooth primer.