# An Analysis of Fusion Functions for Hybrid Retrieval

arXiv: https://arxiv.org/abs/2210.11934 · HTML: https://mlsanity.com/paper/2210.11934/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2022.

## Built on by (most cited first, 30 of 51)

- [Skill Retrieval Augmentation for Agentic AI](https://mlsanity.com/paper/2604.24594/) (2026)
- [RAG-Fusion: a New Take on Retrieval-Augmented Generation](https://mlsanity.com/paper/2402.03367/) (2024)
- [UniMS-RAG: A Unified Multi-source Retrieval-Augmented Generation for Personalized Dialogue Systems](https://mlsanity.com/paper/2401.13256/) (2024)
- [Customized Retrieval Augmented Generation and Benchmarking for EDA Tool Documentation QA](https://mlsanity.com/paper/2407.15353/) (2024)
- [AutoRAG: Automated Framework for optimization of Retrieval Augmented Generation Pipeline](https://mlsanity.com/paper/2410.20878/) (2024)
- [Pneuma: Leveraging LLMs for Tabular Data Representation and Retrieval in an End-to-End System](https://mlsanity.com/paper/2504.09207/) (2025)
- [Guided Query Refinement: Multimodal Hybrid Retrieval with Test-Time Optimization](https://mlsanity.com/paper/2510.05038/) (2025)
- [DAPR: A Benchmark on Document-Aware Passage Retrieval](https://mlsanity.com/paper/2305.13915/) (2023)
- [DAT: Dynamic Alpha Tuning for Hybrid Retrieval in Retrieval-Augmented Generation](https://mlsanity.com/paper/2503.23013/) (2025)
- [HiQA: A Hierarchical Contextual Augmentation RAG for Multi-Documents QA](https://mlsanity.com/paper/2402.01767/) (2024)
- [StatEval: A Comprehensive Benchmark for Large Language Models in Statistics](https://mlsanity.com/paper/2510.09517/) (2025)
- [MedPlan: A Two-Stage RAG-Based System for Personalized Medical Plan Generation](https://mlsanity.com/paper/2503.17900/) (2025)
- [Hybrid Retrieval for Hallucination Mitigation in Large Language Models: A Comparative Analysis](https://mlsanity.com/paper/2504.05324/) (2025)
- [IL-PCSR: Legal Corpus for Prior Case and Statute Retrieval](https://mlsanity.com/paper/2511.00268/) (2025)
- [RAGSmith: A Framework for Finding the Optimal Composition of Retrieval-Augmented Generation Methods Across Datasets](https://mlsanity.com/paper/2511.01386/) (2025)
- [SmartSearch: How Ranking Beats Structure for Conversational Memory Retrieval](https://mlsanity.com/paper/2603.15599/) (2026)
- [Balancing the Blend: An Experimental Analysis of Trade-offs in Hybrid Search](https://mlsanity.com/paper/2508.01405/) (2025)
- [SkillSight: Calibrating Generic Content Bias for Skill Retrieval](https://mlsanity.com/paper/2607.18785/) (2026)
- [Compress, Gather, and Recompute: REFORMing Long-Context Processing in Transformers](https://mlsanity.com/paper/2506.01215/) (2025)
- [Test-time Corpus Feedback: From Retrieval to RAG](https://mlsanity.com/paper/2508.15437/) (2025)
- [TeleOracle: Fine-Tuned Retrieval-Augmented Generation with Long-Context Support for Network](https://mlsanity.com/paper/2411.02617/) (2024)
- [Developing and evaluating a chatbot to support maternal health care](https://mlsanity.com/paper/2603.13168/) (2026)
- [AgentIR: A Workload-Adaptive Cascade Retrieval Substrate for Long-Term Conversational Memory](https://mlsanity.com/paper/2605.25092/) (2026)
- [Know When to Fuse: Investigating Non-English Hybrid Retrieval in the Legal Domain](https://mlsanity.com/paper/2409.01357/) (2024)
- [Content-based 3D Image Retrieval and a ColBERT-inspired Re-ranking for Tumor Flagging and Staging](https://mlsanity.com/paper/2507.17412/) (2025)
- [KG-CQR: Leveraging Structured Relation Representations in Knowledge Graphs for Contextual Query Retrieval](https://mlsanity.com/paper/2508.20417/) (2025)
- [A Reference Architecture for Agentic Hybrid Retrieval in Dataset Search](https://mlsanity.com/paper/2604.16394/) (2026)
- [Conjecture and Inquiry: Quantifying Software Performance Requirements via Interactive Retrieval-Augmented Preference Elicitation](https://mlsanity.com/paper/2604.21380/) (2026)
- [LLM-Oriented Information Retrieval: A Denoising-First Perspective](https://mlsanity.com/paper/2605.00505/) (2026)
- [Bringing Agentic Search to Earth Observation Data Discovery](https://mlsanity.com/paper/2607.02387/) (2026)

## Abstract (arXiv)

We study hybrid search in text retrieval where lexical and semantic search are fused together with the intuition that the two are complementary in how they model relevance. In particular, we examine fusion by a convex combination (CC) of lexical and semantic scores, as well as the Reciprocal Rank Fusion (RRF) method, and identify their advantages and potential pitfalls. Contrary to existing studies, we find RRF to be sensitive to its parameters; that the learning of a CC fusion is generally agnostic to the choice of score normalization; that CC outperforms RRF in in-domain and out-of-domain settings; and finally, that CC is sample efficient, requiring only a small set of training examples to tune its only parameter to a target domain.