Ricci-Filtration: Boosting Retrieval-Augmented Generation Reranking for Question-Answering Tasks with Discrete Ricci Flow

TMLR Paper9742 Authors

Abstract:

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 provide a stylized theoretical analysis showing that normalized discrete Ricci flow can separate edge types on idealized community graphs, offering support for the post-flow filtering mechanism while not implying guarantees on arbitrary embedding-derived retrieval graphs. Experiments across QA benchmarks show that Ricci-Filtration improves several settings, especially SQuADv2 and selected MultiHop-RAG query types, while also revealing limitations on harder connected multi-hop reasoning tasks. Ablation studies characterize sensitivity to graph-construction thresholds, flow iterations, embeddings, rerankers, and a simple K-means filtering baseline.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Xuming_Hu1

Submission Number: 9742