# Ricci-Filtration: Boosting Retrieval-Augmented Generation Reranker to Query-Answer Tasks by Discrete Ricci Flow

arXiv: https://arxiv.org/abs/2606.15482 · HTML: https://mlsanity.com/paper/2606.15482/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Generation and context integration, one of 15 directions in Retrieval-augmented generation.
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Placed in

- Retrieval-augmented generation / [Generation and context integration](https://mlsanity.com/rag/generation-and-context-integration/)
- Diffusion models / [Diffusion recommenders](https://mlsanity.com/diffusion/diffusion-recommenders/)

## Builds on (most cited first, 28 of 28)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)
- [Is ChatGPT Good at Search? Investigating Large Language Models as Re-Ranking Agents](https://mlsanity.com/paper/2304.09542/) (2023)
- [MultiHop-RAG: Benchmarking Retrieval-Augmented Generation for Multi-Hop Queries](https://mlsanity.com/paper/2401.15391/) (2024)
- [RankRAG: Unifying Context Ranking with Retrieval-Augmented Generation in LLMs](https://mlsanity.com/paper/2407.02485/) (2024)
- [Evaluation of Retrieval-Augmented Generation: A Survey](https://mlsanity.com/paper/2405.07437/) (2024)
- [Re2G: Retrieve, Rerank, Generate](https://mlsanity.com/paper/2207.06300/) (2022)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [RAG vs. GraphRAG: A Systematic Evaluation and Key Insights](https://mlsanity.com/paper/2502.11371/) (2025)
- [CRUD-RAG: A Comprehensive Chinese Benchmark for Retrieval-Augmented Generation of Large Language Models](https://mlsanity.com/paper/2401.17043/) (2024)
- [Query Focused Abstractive Summarization: Incorporating Query Relevance, Multi-Document Coverage, and Summary Length Constraints into seq2seq Models](https://mlsanity.com/paper/1801.07704/) (2018)
- [Revealing the Numeracy Gap: An Empirical Investigation of Text Embedding Models](https://mlsanity.com/paper/2509.05691/) (2025)

## Abstract (arXiv)

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.