## 3 Methodology
### Construction of Heterogeneous Graph  
We construct a heterogeneous graph G to capture the interactions between sentences and entities, which includes entity, sentence, and document nodes. For a given graph G = (V, E), where V represents the set of nodes and E represents the set of edges. In graph G, the interactions among entities, entities and sentences, and documents and sentences, are all modeled and represented, as shown in Figure 3.  
For an entity node \(e\), its initial embedding \(h_{e}^{(0)}\) is the average pooling value of the word vectors within the entity, specifically represented as \(h_{e}^{(0)}=\underset{j\in e}{\text{Mean}}\{g_{j}\}\), where \(g_{j}\) represents the vector for word j, and the mean denotes the average pooling operation. For a sentence node \(s\), its initial embedding \(h_{s}^{(0)}\) is the maximum pooling value of all the word vectors in the sentence plus the position embedding value of the sentence, specifically represented as \(h_{s}^{(0)}=\underset{j\in s}{\text{Max}}\{g_{j}\}+\text{SentPos}(s)\), where \(\text{Max}\) denotes the maximum pooling operation, and \(\text{SentPos}(s)\) represents the position embedding of the sentence. The document node is jointly represented by the initial embedding vectors of the sentences and entities in the document. The operation involves applying a multi-head attention  
Figure 3: The heterogeneous graph we proposed. Figure 2: The overview of the proposed GNNDRS model, which can be mainly divide into four modules: entity extraction (3.2), construction of heterogeneous graph (3.3), event type detection (3.4), and argument extraction (3.5). mechanism to transform the input sentence embedding vectors and entity embedding vectors into query matrix \(Q\), key matrix \(K\), and value matrix \(V\) through a linear mapping layer. Next, the \(Q\), \(K\), and \(V\) tensors split into m attention heads, where m represents the number of heads. Matrix multiplication and scaling operations are applied to the query and key matrices of each head, resulting in new attention tensors. Then, the softmax function is utilized to weigh the attention tensor and allocate it to the value matrix, generating the final attention-based output tensor. Finally, the output results of the m attention heads are concatenated and passed through a fully connected layer for mapping, generating the embedded features based on attention computation. The multi-head attention mechanism model can be represented by the following formula:  
\[MultiHeadAttention(x)=FC([(Attention(Q,K,V))_{1},\dots,(Attention(Q,K,V))_{m}, \tag{2}\]  
where \(FC\) represents the fully connected layer, \(m\) denotes the number of attention heads, and \(Attention\) denotes the attentional mechanism as follows:  
\[Attention(Q,K,V)=softmax(\frac{QK^{T}}{\sqrt{d_{k}}})V, \tag{3}\]  
where \(d_{k}\) represents the dimensionality of the query vectors. After performing multi-head attention calculations on the initial embedding vectors of sentences, a weighted pooling is applied along the document dimension to obtain the overall sentence-level document vector. As for the initial embedding vectors of entities, the vectors of each word are averaged to create a matrix of equally sized word embedding. Then, multi-head attention calculations are performed on this matrix, and the results are weighted and summed along the document dimension to gain word-level document vectors. Finally, by concatenating these vectors, we get the feature representation of the entire document node. The feature vector representation of the document node is as follows:  
\[DocEmbedding(X_{sent},X_{token})=[Attention(X_{sent}),Attention(X_{token})], \tag{4}\]  
where \(X_{sent}\) consists of all sentence embedding vectors in a document, and matrix \(X_{token}\) consists of all entity embedding vectors in the document. Attention ( ) refer to the multi-head attention operations, and [,] represents the concatenation between the vectors.