## 5 Experiments
### In-Depth Analysis
#### 5.6.4 Analysis of Computational Complexity  
The PyTorch framework performs parallel computations using tensors, and discussing time complexity or space complexity in isolation is not practically meaningful. Therefore, we discuss the overall computational complexity from the perspectives of both the backbone model and the incremental learning methods to assess the required computational resources.  
In terms of the backbone model, traditional span-based models have a high computational cost, as for a text containing n characters, it is theoretically possible to partition it into  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Threshold**} & \multicolumn{2}{c}{**ACE**} & \multicolumn{2}{c}{**DuEE**} \\ \cline{2-5}  & **5-Shot** & **10-Shot** & **5-Shot** & **10-Shot** \\ \hline
0.1 & 89.69 & 91.89 & 68.59 & 71.11 \\
0.2 & **90.39** & **92.49** & **71.48** & **73.12** \\
0.3 & 89.69 & 91.29 & 66.07 & 71.11 \\
0.4 & 87.69 & 86.49 & 63.90 & 71.11 \\
0.5 & 85.59 & 87.69 & 62.46 & 67.37 \\ \hline \hline \end{tabular}
\end{table}
Table 7: _Recall@3_ performance on the final sub-task with different value of threshold \(\beta\).  
Figure 6: _Recall@3_ performance of every sub-task on ACE2005-Chinses and DuEE for extreme scenarios.  
n \(\times\) (n + 1)/2 spans, leading to a computational complexity of \(\mathcal{O}\left(n^{2}\right)\). In contrast, models based on character classification and sequence labeling process each character individually, resulting in a complexity of only \(\mathcal{O}(n)\). Our proposed span-based backbone model reduces the computational complexity to \(\mathcal{O}(nL)\) by limiting the span length \(L\) and punctuation filtering, significantly saving computational resources. Although its complexity is still higher than that of character classification and sequence labeling models, the time difference is acceptable, considering the parallel computing features of PyTorch(1.10.0). It is important to note that this paper focuses on incremental learning methods, and all baseline methods use the same span-based backbone model, so this part of the computational complexity is analyzed only theoretically.  
In terms of incremental learning methods, we set the batch size to 4 and epoch to 30, with other parameters consistent with those in Section 5.2. We report the average time per epoch for different baseline methods trained on the ACE2005-Chinese and DuEE datasets, as shown in Figure 7.  
From the results, we can see that the Joint method, which trains on all data at once, consumes the most time. Our method, ICD, consumes less time compared to the Replay all method, averaging a reduction of 2.24 s, while slightly increasing time compared to other baseline methods, particularly the baseline method EMP, which shows the best overall performance, with an average increase of 2.1 s. This is analyzed to be due to the additional loss introduced by the semantic-boundary smoothing in the contrastive learning module, which brings extra gradient information but also increases the computational load, resulting in a slight increase in model training time. We believe that achieving a significant improvement in recall with such a small time cost is meaningful.