## 3 Method Description
### Multi-Dimensional Labeling Framework Layer
#### 3.2.2 Implementation of the HT-BES Multi-Dimensional Labeling Strategy  
The HT-BES labeling strategy's implementation strategy is as follows: First, all token pairs \((w_{i},w_{j})\) in the input sentence are enumerated in combination with predefined relations \((r_{k})\). Next, the scoring function component calculates the potential score for each triplet combination \((w_{i},r_{k},w_{j})\), generating a scoring matrix. Finally, the scoring matrix is used for  
Figure 4: HT-BES interactive annotation strategy.  
fine-grained classification, and based on the head-tail entity association classification, a relation label classification matrix is generated.  
(1) Scoring Function Component  
In this study, a scoring function was designed based on the HOLE model of knowledge graph embedding technology [41], using a non-linear concatenation projection to evaluate the likelihood of a connection being made between two tokens \((w_{i},w_{j})\) and a specific relation \(r_{k}\). The scoring function is shown in Equation (5):  
\[v_{(w_{i},r_{k},w_{j})}{}_{k=1}^{K}=R^{T}\bigg{(}\sigma\bigg{(}drop\bigg{(}W[e _{i}^{f},e_{j}^{f}]^{T}+b\bigg{)}\bigg{)}\bigg{)} \tag{5}\]  
In the equation, \(v\) is the score vector, \(K\) is the number of predefined relations, \([e_{i}^{f};e_{j}^{f}]\) is the concatenation operation of the vectors for tokens \(i\) and \(j\), and \(drop(.)\) is used to prevent overfitting. \(b\) is the bias, and \(\sigma\) is the activation function LeakyReLU. \(W\in\mathbb{R}^{d_{\epsilon}\times 2d}\) is a trainable weight matrix, where \(d_{\epsilon}\) represents the entity pair feature dimension after projection, and \(2d\) represents the feature dimension after entity pair concatenation. \(R\in\mathbb{R}^{d_{\epsilon}\times K}\) is the relation vector representation matrix, which, like matrix \(W\), is considered a trainable weight. The matrices \(R\) and \(W\) are adaptively learned, allowing the scoring function to dynamically adjust based on the input token features to better evaluate the dependency between token pairs and predefined relations.  
The scoring matrix generated by the scoring function is shown in Figure 1a. The scoring function utilizes a two-layer fully connected network to perform the parallel scoring method, thus reducing the computational complexity of enumerating combinations \((w_{i},r_{k},w_{j})\) from \(L\times K\times L\) to \(L\times 1\times L\). This effectively minimizes redundant computations and improves computational efficiency.  
(2) Fine-Grained Classification Component  
Fine-grained classification aims to assign high-confidence labels to the token pair \((w_{i},w_{j})\) under relation \(r_{k}\) based on the scoring matrix, generating the relation label classification matrix, as shown in Equation (6). This process uses the softmax function to process the score vector \(v_{(w_{i},r_{k},w_{j})}{}_{k=1}^{K}\), converting the original scores into a probability distribution. In using the label types designed in the head-tail entity association classification part of the HT-BES labeling strategy, a fine-grained classification prediction is made for \((w_{i},w_{j})\).  
\[P\Big{(}y_{(w_{i},r_{k},w_{j})}|S\Big{)}=Softmax\Big{(}v_{(w_{i},r_{k},w_{j})} \Big{)} \tag{6}\]  
The fine-grained classification results are shown in Figure 1b. The classification labels are stored in the relation label classification matrix, with different relations being located in different matrices. Each element in the matrix corresponds to the classification result of a token pair and a relation.