Ricci flow is a curvature-guided diffusion process that deforms space by shrinking regions of high positive curvature and expanding those with negative curvature. Similarly, discrete Ricci flow on weighted graphs modifies edge weights by shrinking edges with positive Ricci curvature and stretching those with negative Ricci curvature, effectively increasing the separation between clusters. Inspired by these two cornerstone works, we propose a geometry-based RAG reranker enhancement procedure called Ricci-Filtration. By modeling the input query and initial retrieved chunks as a network, where the input query and chunks serve as nodes and embedding-based pairwise relations define an initial graph, Ricci-Filtration leverages discrete curvature and Ricci flow to evaluate the structural importance of each chunk with respect to the user query. The system first filters the initial chunks based on their geometric curvature relative to the query; then, a reranker processes the remaining chunks to enhance generative performance. We theoretically prove that normalized discrete Ricci flow can detect community structures by identifying distinct asymptotic behaviors in edge weights. This supports the removal of ``noisy'' document chunks characterized by large weights and negative Ricci curvature relative to the query node. Extensive experiments confirm that Ricci-Filtration outperforms several baseline reranking methods in accuracy, precision, recall, and F1 scores. Furthermore, ablation studies demonstrate that the Ricci-Filtration generally outperforms the baseline under various settings, highlighting the framework's robustness across different architectures.

翻译：[里奇流是一种曲率引导的扩散过程，通过收缩高正曲率区域并拉伸负曲率区域来形变空间。类似地，加权图上的离散里奇流通过收缩具有正里奇曲率的边与拉伸具有负里奇曲率的边来修改边权重，有效增加了簇间的分离度。受这两项奠基性工作启发，我们提出了一种基于几何的检索增强生成重排序器增强方法，称为"里奇流滤波"。通过将输入查询与初始检索块建模为网络（其中查询与块作为节点，基于嵌入的成对关系定义初始图），里奇流滤波利用离散曲率与里奇流评估每个块相对于用户查询的结构重要性。系统首先根据各块的几何曲率（相对查询的）过滤初始块；随后，重排序器处理剩余块以增强生成性能。我们理论上证明了归一化离散里奇流可通过识别边权重的不同渐近行为来检测社区结构，这支持了移除相对查询节点具有大权重与负里奇曲率的"噪声"文档块。大量实验证实了里奇流滤波在准确率、精确率、召回率与F1分数上优于多种基线重排序方法。此外，消融研究表明，里奇流滤波在不同设置下普遍优于基线，凸显了该框架在不同架构下的鲁棒性。]