## 3 Framework
### Relation-Aware Document-Context Filter
#### 3.3.1 Stage I: Important-Sentence Filtering  
Following [8], we first compute bridge entity importance scores through three co-occurrence conditions but add a fourth relation keyword score.  
**1. Direct co-occurrence score \(s_{1}(e^{b})\)**:  
\[s_{1}(e^{b})=\begin{cases}1,&\text{if }\Gamma_{1}(e^{b})\\ 0,&\text{otherwise}\end{cases} \tag{4}\]  
**2. Indirect co-occurrence score \(s_{2}(e^{b})\)**:  
\[s_{2}(e^{b})=\begin{cases}\sum_{e^{\rho}\in E_{i}^{b}}I(e^{\rho})\cdot\delta( \Gamma_{1}(e^{\rho})),&\text{if }\Gamma_{2}(e^{b})\\ 0,&\text{otherwise}\end{cases} \tag{5}\]  
where  
* \(I(e^{\rho})=1\) if \(e^{\rho}\) co-occurs with \(e^{b}\) in sentences;
* \(\delta(\Gamma_{1}(e^{\rho}))\) is an indicator function (1 if \(e^{\rho}\) satisfies \(\Gamma_{1}\), else 0).
* **3. Potential co-occurrence score \(s_{3}(e^{b})\)**: \[s_{3}(e^{b})=\begin{cases}\left|\{p_{j}\,|\,e^{b}\in E_{j}^{b}\}\right|_{,}& \text{if }\Gamma_{3}(e^{b})\\ 0,&\text{otherwise}\end{cases}\] (6)  
**4. Relation keyword similarity score \(s_{4}(e^{b})\)**:  
To incorporate relation-specific information into our filtering process, we propose a novel relation keyword similarity score:  
\[s_{4}(e^{b})=\max_{s\in S(e^{b})}\max_{r\in R_{\text{end}}}\text{sim}(s,r) \tag{7}\]  
where\(S(e^{b})\) is the set of sentences containing bridge entity \(e^{b}\);
* \(R_{\text{cand}}\) is a set of candidate relation descriptions;
* \(\text{sim}(s,r)\) measures the semantic similarity between sentence \(s\) and relation description \(r\).  
**Relation description generation:** The relation descriptions in \(R_{\text{cand}}\) can be obtained through multiple approaches: (1) _Schema-derived descriptions_ from dataset relation schemas (e.g., CodRED's predefined relation types like \"owned by\"; \"entity A is owned or controlled by entity B\"); (2) _Manual descriptions_ crafted by domain experts based on linguistic and semantic knowledge; or (3) _LLM-generated descriptions_ using large language models such as Llama3.1 to generate diverse paraphrases and contextual variations. While different generation methods may yield varying performance impacts, our current implementation uses schema-derived descriptions as they provide consistent and standardized relation semantics. A comprehensive comparison of these description generation approaches represents an important direction for future work.  
To obtain \(R_{\text{cand}}\), we first extract sentences containing the target entities \(e^{h}\) and \(e^{l}\), combine them as input to a BERT + MLP classifier, and select the top-N predicted relation types. We then compute the cosine similarity between the word2 vec embeddings of sentence keywords and relation type terms to derive the similarity score.  
**Total score formula:**  
\[\text{score}(e^{b})=\alpha s_{1}(e^{b})+\beta s_{2}(e^{b})+\gamma s_{3}(e^{b}) +\delta s_{4}(e^{b}) \tag{8}\]  
with default hyperparameters \(\alpha=0.1\), \(\beta=0.01\), \(\gamma=0.001\), and \(\delta=0.05\) reflecting higher weights for direct co-occurrence while giving substantial weight to relation-specific information. This prioritizes \"more direct associations are more important\" by reducing long reasoning chains and cross-document noise, while ensuring relation-specific context is adequately represented.  
\[g^{s}=\sum_{e^{b}\in E^{b}_{s}}\text{score}(e^{b}) \tag{9}\]  
The top \(K\) high-score sentences are retained (default \(K=16\)), forming candidate set \(S=\{s_{1},s_{2},\ldots,s_{K}\}\).