## 4 Method
### Event-Trigger Recommendation Backbone  
Consider the training data \((X,E,Y)\), where \(X=\{x_{1},x_{2},\ldots,x_{l}\}\) is the sentence-level text, \(E=\{e_{1},e_{2},\ldots,e_{n}\}\) is the set of event triggers, and \(Y=\{y_{1},y_{2},\ldots,y_{n}\}\) is the event type corresponding to \(E\). Using the pre-trained language model RoBERTa as the encoder, the text \(X\) is input into the pre-trained model to obtain contextual representations \(W=\{w_{1},w_{2},\ldots,w_{l}\}\), where \(w_{i}\in\mathbb{R}^{d}\) denotes the word vector of the i-th word, and \(d\) is the vector dimension. The model treats spans as the smallest unit and generates a candidate span set \(S=\{s_{i}|i=1,2,\ldots,N_{1}\}\) through length- and rule-based filtering. For each candidate span \(s_{i}=\{x_{st_{i}},\ldots,x_{od_{i}}\}=(si_{i},ed_{i})\), we concatenate the word vectors of its head and tail and a length, embedding \(\mathrm{h}_{i}^{\mathrm{length}}\in\mathbb{R}^{d_{w}}\) to obtain its representation \(h_{i}=\left[w_{st_{i}};w_{ed_{i}};h_{i}^{length}\right]\). This representation is then fed into a binary classifier composed of a multi-layer perceptron  
Figure 2: The structure of ICD, which includes a recommendation model, experience replay, contrastive learning, and hierarchical-distillation modules. When learning a new task, it uses the previous model to select replay samples, applies hierarchical-knowledge distillation, and then employs semantic-boundary-smoothing contrastive learning for the new model. MLP1 and a sigmoid activation function to compute and output the confidence score \(p_{i}^{trigger}\) for \(s_{i}\), which is a potential trigger. Footnote 1: [[https://github.com/hugging-learning/](https://github.com/hugging-learning/)]([https://github.com/hugging-learning/](https://github.com/hugging-learning/))  
\[p_{i}^{trigger}=\text{Sigmoid}\Big{(}\text{MLP}^{1}(h_{i})\Big{)}, \tag{1}\]  
The multi-class classifier, composed of a multi-layer perceptron MLP2 and a softmax activation function, calculates and outputs the confidence vector \(\mathbf{p}_{i}^{cent\_type}\in\mathbb{R}^{n+1}\) for span \(s_{i}\), indicating the probability of belonging to each of the predefined event types, where \(n\) represents the total number of event types. \[\mathbf{p}_{i}^{cent\_type}=\text{softmax}\Big{(}\text{MLP}^{2}(h_{i})\Big{)}, \tag{2}\]  
Building on our previous work [1], a semantic-boundary-smoothing approach is employed, which assigns soft labels \(\widetilde{y}_{i}\in[0,1]\) to \(s_{i}\) based on the following three aspects: overlap with the corresponding gold trigger \(e_{i}\), semantic integrity, and part-of-speech information. Specifically, for the overlap score \(f_{1}\), as shown in Formula (3), we use Intersection over Union(IoU) to measure it, where \(|s_{i}\cap e_{i}|\) represents the length of characters in the intersection of the two spans, and \(|s_{i}\cup e_{i}|\) represents the length of characters in their union. In addition, we use pkuseg [35] to provide segmentation and part-of-speech information for the text. For semantic integrity score \(f_{2}\), as shown in Formula (4), if the span \(s_{i}\) is in the segmentation results, it is considered to have complete semantics, scoring 1; otherwise, it scores 0.5. For part-of-speech information \(f_{3}\), as shown inf Formula (5), if the part-of-speech combination of \(s_{i}\) has appeared in the training set, it is deemed reasonable, scoring 1; otherwise, it scores 0.5. Combining these three aspects, the soft label \(\widetilde{y}_{i}\) of \(s_{i}\) is calculated as Formula (6):  
\[f_{1}(s_{i},e_{i})=\text{IoU}(s_{i},e_{i})=\frac{|s_{i}\cap e_{i}|}{|s_{i} \cup e_{i}|} \tag{3}\]  
\[f_{2}(s_{i})=\left\{ \begin{matrix}1,\text{ }s_{i}\text{ is in segmentation results}\\ 0.5,\text{ otherwise}\end{matrix} \right. \tag{4}\]  
\[f_{3}(s_{i})=\left\{ \begin{matrix}1,\text{ }\text{the part of speech of }s_{i}\text{ is reasonable}\\ 0.5,\text{ otherwise}\end{matrix} \right.