## 3 MPBCNER Model
### GAT-Based Boundary Information Fusion Layer  
The graph attention network (GAT) is a neural network model that has been specifically designed to process graph-structured data. It introduces an attention mechanism that enables the model to assign different weights to the neighboring nodes of each node during graph data processing. This mechanism facilitates the enhanced capture of the complex relationships between nodes and the local structures within the graph data, thereby improving the model's ability to understand and represent the intricate patterns present in the data. While PLM is capable of effectively extracting contextual features, its ability to capture boundary information features within the input text is limited. To address this, the present paper proposes employing GAT to extract features based on the internal dependency relationships present in the input text. This approach involves mining the word and character dependency relationships within the text to extract the boundary features of entities. Consequently, this enhances the accuracy of entity recognition. In this study, a sequence of Chinese text is treated as a graph-structured network, with each character in the sequence considered a node in the graph. In particular, we use DDParser [42] to obtain the dependencies of the input sequence and then construct a directed graph based on the dependencies, where the directed edges point to the center word of a given word, and the directed edges are labeled with the specific type of dependency, and the words located at the beginning of the directed edges depend on the words located at the end of the directed edges in some kind of dependency relationship. For a Chinese text sequence \"(Bank of Beijing opens branch in Guangxi)\", the syntactic dependency relationship graph is shown in Figure 2.  
In this sentence, \"(Bank of Chinese)\" is a qualifying modifier for \"(Bank of Chinese)\", \"(Bank of Chinese)\" and \"(Bank of Chinese)\" have a subject-predicate relationship, \"(Bank of Chinese)\" and \"(Bank of Chinese)\" are in a verb-object relationship, etc. Since the model in this paper is character-based, each character in a word has the same dependency relationship with the word. Meanwhile, to retain the feature information of the node itself, it is assumed that each word is related to itself. Each node in the graph will have a ring pointing to itself. According to the dependency relationship between nodes, the elements at the corresponding positions in the dependency matrix are set to 1, and the remaining elements are set to 0. According to the above rules, the dependency matrix of the input sequence is constructed. In a directed graph, nodes that have a dependency relationship with entities reflect the existence of the entities to a certain extent. Meanwhile, directed edges containing dependency information can assist in distinguishing entity boundaries and identifying the categories of entities. To more clearly extract features related to boundary information between entities, we built a GAT to capture dependencies between words. Firstly, a linear transformation is done on the input features of each node to map the feature dimension from \(F\) to \(F^{\prime}\):  
\[Wh_{i}\in\mathbb{R}^{F^{\prime}} \tag{4}\]  
Figure 2: Example of a syntactic dependency diagram. where \(W\in\mathbb{R}^{F^{\prime}\times F}\) is sharing weight matrices. \(h_{i}\) is the original feature vector of node \(i\). Then, the attention coefficient \(e^{ij}\) indicates the importance of node \(j\) to node \(i\):  
\[ \begin{split} e^{ij}&=att\big{(}Wh_{i},Wh_{j}\big{)} \\ &=LeakReLU(\overset{\rightarrow}{a}^{T}[Wh_{i}\parallel Wh_{j}] \big{)}\end{split}  \tag{5}\]  
where \(att(\cdot,\cdot)\) is the attention function, implemented by a single-layer feedforward neural network. \(\overset{\rightarrow}{a}\) is the weight vector. In order to compare the importance of different neighboring nodes, the \(soft\)max function is used to normalize all attention coefficients:  
\[