## 3 Materials and Methods
### GlobalPointer Decoding Module  
This research utilizes a global pointer network to annotate entities, and the net can treat the start and end positions of entities as a whole, which can distinguish them and offer a more global perspective. The matrix labeling approach of the global pointer network addresses the issues of overlapping triplets and nested entities. A method called Rotary Position Embedding (RoPE) is used to design the scoring matrix using a dot-product attention mechanism and relative position encoding [38]. The RoPE enhances sensitivity to the length and span of entities, making it easier to differentiate between genuine entities. The matrix \([\text{h}_{1},\text{h}_{2},\dots,\text{h}_{n}]\) obtained at the encoding layer undergoes the following transformations:  
\[\text{q}_{i,\alpha}=\text{w}_{\text{q},\alpha}\text{h}_{i}+\text{b}_{\text{q},\alpha}, \tag{2}\]  
\[\text{k}_{i,\alpha}=\text{w}_{\text{k},\alpha}\text{h}_{i}+\text{b}_{\text{k},\alpha} \tag{3}\]  
where \(1\leq i\leq n\), \(\text{w}_{\text{q},\alpha}\) represents the weight parameter of the current linear transformation, \(\text{b}_{\text{q},\alpha}\) is the bias term, \(\text{w}_{\text{k},\alpha}\) represents the weight parameter of the current linear transformation, and \(\text{b}_{\text{k},\alpha}\) is the bias term. The resulting sequences \(\left[\text{q}_{1,\alpha},\text{q}_{2,\alpha},\dots,\text{q}_{n,\alpha}\right]\) and \(\left[\text{k}_{1,\alpha},\text{k}_{2,\alpha},\dots,\text{k}_{n,\alpha}\right]\) are vector sequences used for identifying entities of type \(\alpha\). The scoring function is defined at this point as:  
\[\text{s}_{\alpha}=\text{q}_{i,\alpha}^{\text{T}}\text{k}_{j,\alpha} \tag{4}\]  
\(\text{s}_{\alpha}\) indicates the scoring of a continuous segment from \(i\) to \(j\) as an entity of type \(\alpha\), using the dot product of \(\text{q}_{i,\alpha}\) and \(\text{k}_{i,\alpha}\) as the score for the entity segment. Subsequently, incorporating relative position information involves introducing a transformation matrix \(\text{R}_{i}\) that satisfies the relation \(\text{R}_{i}^{\text{T}}\text{R}_{j}=\text{R}_{j-i}\) and applying it to \(\text{q}\) and \(\text{k}\) to obtain the scoring function infused with relative positions \(\text{s}_{\text{a}}(i,j)\):  
\[\text{s}_{\text{a}}(i,j)=(\text{R}_{i}\text{q}_{i,\alpha})^{\text{T}}\big{(} \text{R}_{j}\text{k}_{j,\alpha}\big{)}=\text{q}_{i,\alpha}^{\text{T}}\text{ R}_{i}^{\text{T}}\text{R}_{j}\text{k}_{j,\alpha}=\text{q}_{i,\alpha}^{\text{T}} \text{R}_{j-i}\text{k}_{j,\alpha} \tag{5}\]  
where \(\text{R}_{i},\text{R}_{j}\) are the transformation matrices used to add the relative position information for the satisfaction relation \(\text{R}_{i}^{\text{T}}\text{R}_{j}=\text{R}_{j-i}\). The task of entity relation extraction entails extracting triples in the form of \(<\)subject, relation, object\(>\), i.e., (s, r, o). However, in practice, it involves extracting quintuples \(<\)subject head, subject tail, relation, object head, object tail\(>\), i.e., (sh, st, r, oh, ot). From a probabilistic graph perspective, it suffices to design a scoring function \(\text{S}(\text{sh},\text{st},\text{r},\text{oh},\text{ot})\) for the quintuples. During training, annotated quintuples are set to be greater than zero, while the remaining ones are less than zero. All quintuples are then enumerated, and the part where the quintuple is greater than zero is outputted. Nevertheless, directly enumerating all quintuples leads to many possibilities.