# MUVERA: Multi-Vector Retrieval via Fixed Dimensional Encodings

arXiv: https://arxiv.org/abs/2405.19504 · HTML: https://mlsanity.com/paper/2405.19504/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2024.

## Built on by (most cited first, 30 of 32)

- [MetaEmbed: Scaling Multimodal Retrieval at Test-Time with Flexible Late Interaction](https://mlsanity.com/paper/2509.18095/) (2025)
- [Llama Nemoretriever Colembed: Top-Performing Text-Image Retrieval Model](https://mlsanity.com/paper/2507.05513/) (2025)
- [DocPruner: A Storage-Efficient Framework for Multi-Vector Visual Document Retrieval via Adaptive Patch-Level Embedding Pruning](https://mlsanity.com/paper/2509.23883/) (2025)
- [Efficient Constant-Space Multi-Vector Retrieval](https://mlsanity.com/paper/2504.01818/) (2025)
- [Nemotron ColEmbed V2: Top-Performing Late Interaction Embedding Models for Visual Document Retrieval](https://mlsanity.com/paper/2602.03992/) (2026)
- [CausalEmbed: Auto-Regressive Multi-Vector Generation in Latent Space for Visual Document Embedding](https://mlsanity.com/paper/2601.21262/) (2026)
- [Beyond the Grid: Layout-Informed Multi-Vector Retrieval with Parsed Visual Document Representations](https://mlsanity.com/paper/2603.01666/) (2026)
- [Retrieval Needs Multivectors: An Exponential Separation](https://mlsanity.com/paper/2608.21494/) (2026)
- [Towards Lossless Token Pruning in Late-Interaction Retrieval Models](https://mlsanity.com/paper/2504.12778/) (2025)
- [Global-to-Local or Local-to-Global? Enhancing Image Retrieval with Efficient Local Search and Effective Global Re-ranking](https://mlsanity.com/paper/2509.04351/) (2025)
- [Simple Projection Variants Improve ColBERT Performance](https://mlsanity.com/paper/2510.12327/) (2025)
- [IRPAPERS: A Visual Document Benchmark for Scientific Retrieval and Question Answering](https://mlsanity.com/paper/2602.17687/) (2026)
- [LIR: The First Workshop on Late Interaction and Multi Vector Retrieval @ ECIR 2026](https://mlsanity.com/paper/2511.00444/) (2025)
- [Graph Memory: A Structured and Interpretable Framework for Modality-Agnostic Embedding-Based Inference](https://mlsanity.com/paper/2511.14961/) (2025)
- [TurkColBERT: A Benchmark of Dense and Late-Interaction Models for Turkish Information Retrieval](https://mlsanity.com/paper/2511.16528/) (2025)
- [LLM-Oriented Information Retrieval: A Denoising-First Perspective](https://mlsanity.com/paper/2605.00505/) (2026)
- [No More K-means: Single-Stage Sparse Coding for Efficient Multi-Vector Retrieval](https://mlsanity.com/paper/2605.30120/) (2026)
- [Distance Adaptive Beam Search for Provably Accurate Graph-Based Nearest Neighbor Search](https://mlsanity.com/paper/2505.15636/) (2025)
- [Query Generation Pipeline with Enhanced Answerability Assessment for Financial Information Retrieval](https://mlsanity.com/paper/2511.05000/) (2025)
- [Breaking the Curse of Dimensionality: On the Stability of Modern Vector Retrieval](https://mlsanity.com/paper/2512.12458/) (2025)
- [Chamfer-Linkage for Hierarchical Agglomerative Clustering](https://mlsanity.com/paper/2602.10444/) (2026)
- [The Virtuous Cycle: AI-Powered Vector Search and Vector Search-Augmented AI](https://mlsanity.com/paper/2603.09347/) (2026)
- [Text Corpora as Concept Fields: Black-Box Hallucination and Novelty Measurement](https://mlsanity.com/paper/2605.05103/) (2026)
- [TechRAG: Evidence-Gated Multimodal Agentic RAG for Technical Literature Reasoning](https://mlsanity.com/paper/2606.01613/) (2026)
- [CAMI: Cost-Aware Agent-Guided Multi-Indexing for Semantic Retrieval](https://mlsanity.com/paper/2606.28365/) (2026)
- [ANNLib: A Development Framework for Efficient Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2607.17582/) (2026)
- [MosaicJoin: Compact Semantic Sketches for Value-Level Join Discovery](https://mlsanity.com/paper/2607.21781/) (2026)
- [MoganColBERT-TR: A Late-Interaction Multi-Vector Retrieval Model for Turkish](https://mlsanity.com/paper/2608.26344/) (2026)
- [NeoMME: A Single-Tower Multimodal-Native Multilingual Foundation Encoder for Efficient Fine-Tuning and Inference](https://mlsanity.com/paper/2609.01657/) (2026)
- [ColNanoVDR: Document-Free Query Distillation for Multi-Vector Visual Document Retrieval via Optimal Transport](https://mlsanity.com/paper/2609.34899/) (2026)

## Abstract (arXiv)

Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding x ∈ ℝd per data-point, allowing for fast retrieval via highly optimized maximum inner product search (MIPS) algorithms. Recently, beginning with the landmark ColBERT paper, multi-vector models, which produce a set of embedding per data point, have achieved markedly superior performance for IR tasks. Unfortunately, using these models for IR is computationally expensive due to the increased complexity of multi-vector retrieval and scoring. In this paper, we introduce MUVERA (MUlti-VEctor Retrieval Algorithm), a retrieval mechanism which reduces multi-vector similarity search to single-vector similarity search. This enables the usage of off-the-shelf MIPS solvers for multi-vector retrieval. MUVERA asymmetrically generates Fixed Dimensional Encodings (FDEs) of queries and documents, which are vectors whose inner product approximates multi-vector similarity. We prove that FDEs give high-quality ε-approximations, thus providing the first single-vector proxy for multi-vector similarity with theoretical guarantees. Empirically, we find that FDEs achieve the same recall as prior state-of-the-art heuristics while retrieving 2-5× fewer candidates. Compared to prior state of the art implementations, MUVERA achieves consistently good end-to-end recall and latency across a diverse set of the BEIR retrieval datasets, achieving an average of 10% improved recall with 90% lower latency.