## 5 Results and Analyses
### Main Results
#### 5.1.1 Interpretation and Significance of Performance Metrics  
The achieved performance metrics demonstrate substantial improvements that are significant for the cross-document relation extraction task. **F1 score significance:** The F1 scores of 63.71% (BERT) and 68.42% (RoBERTa) represent substantial improvements over previous state-of-the-art methods. In the context of cross-document relation extraction, these scores are particularly meaningful because (1) the task involves reasoning across multiple documents with extensive noise, making high precision and recall challenging; (2) the CodRED dataset contains 276 diverse relation types, requiring models to discriminate between fine-grained semantic relationships; and (3) previous best-performing models (REIC) achieved only 61.27% (BERT) and 65.02% (RoBERTa), indicating that our improvements of 2.44 and 3.40 percentage points, respectively, represent significant advances in model capability. **AUC performance analysis:** The AUC scores of 64.39% (BERT) and 68.78% (RoBERTa) indicate strong discriminative ability between positive and negative relation instances. These improvements are particularly significant because (1) cross-document tasks typically suffer from class imbalance, with many negative (N/A) instances, making AUC a crucial metric for practical applications; (2) the improvement of 2.90 percentage points over REIC with RoBERTa demonstrates enhanced model calibration and confidence estimation; and (3) AUC values above 65% in this complex multi-document setting indicate that the model \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Backbone**} & \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Dev**} & \multicolumn{4}{c}{**Test**} \\ \cline{3-8}  & & **AUC** & **F1** & **P@500** & **P@1000** & **AUC** & **F1** \\ \hline \multirow{6}{*}{BERT} & Pipeline & 17.45 & 30.54 & 30.60 & 26.70 & 18.94 & 32.29 \\  & End-to-end & 47.94 & 51.26 & 62.80 & 51.00 & 47.46 & 51.02 \\  & ECRIM & 62.96 & 61.43 & 78.40 & 61.80 & 62.17 & 60.80 \\  & Mr. COD & 59.22 & 61.20 & - & - & 61.68 & 62.53 \\  & PILOT & 63.31 & 62.53 & 78.54 & 62.24 & 62.19 & 61.75 \\  & REIC & 64.50 & 63.77 & 78.60 & 63.80 & 62.59 & 61.27 \\  & CLEAR & 66.39 & 65.78 & 79.67 & 64.76 & 64.39 & 63.71 \\ \hline \multirow{6}{*}{RoBERTa} & Pipeline & - & - & - & - & - & - \\  & End-to-end & 56.47 & 57.49 & 72.60 & 57.10 & 56.32 & 56.05 \\  & ECRIM & 59.36 & 61.81 & 79.60 & 61.90 & 62.12 & 63.06 \\ \cline{1-1}  & Mr. COD & - & - & - & - & - & - \\ \cline{1-1}  & PILOT & - & - & - & - & - & - \\ \cline{1-1}  & REIC & 66.41 & 63.47 & 80.20 & 63.50 & 65.88 & 65.02 \\ \cline{1-1}  & CLEAR & 69.02 & 67.29 & 82.21 & 66.69 & 68.78 & 68.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance of different methods on the CodRED dataset. The results are drawn from their original papers. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **F1 Score (\%)** & **AUC Score (\%)** & \(p\)**-Value** \\ \hline \multicolumn{4}{c}{_BERT Backbone_} \\ \hline REIC & 61.27 \(\pm\) 1.82 & 62.59 \(\pm\) 1.95 & - \\ CLEAR & 63.71 \(\pm\) 1.74 & 64.39 \(\pm\) 1.88 & \textless{}0.001 \\
**Improvement** & **+2.44 [1.23, 3.65]** & **+1.80 [0.89, 2.71]** & **t = 3.91** \\ \hline \multicolumn{4}{c}{_RoBERTa Backbone_} \\ \hline REIC & 65.02 \(\pm\) 1.97 & 65.88 \(\pm\) 2.03 & - \\ CLEAR & 68.42 \(\pm\) 1.89 & 68.78 \(\pm\) 1.96 & \textless{}0.001 \\
**Improvement** & **+3.40 [2.18, 4.62]** & **+2.90 [1.94, 3.86]** & **t = 4.23** \\ \hline \hline \end{tabular} Note: 95% confidence intervals in brackets. Effect sizes: Cohen’s d = 0.34 (F1), 0.42 (AUC). Statistical tests: Paired \(t\)-test, df = 1011.  
\end{table} 
Table 3: Statistical significance analysis for CLEAR vs. strongest baselines with 95% confidence intervals. can effectively rank relation candidates, which is essential for real-world knowledge-base construction applications. **Practical implications:** These performance improvements translate to concrete benefits.