@inproceedings{
jayaram2024muvera,
title={{MUVERA}: Multi-Vector Retrieval via Fixed Dimensional Encoding},
author={Rajesh Jayaram and Laxman Dhulipala and Majid Hadian and Jason Lee and Vahab Mirrokni},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=X3ydKRcQr6}
}
Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding $x \in \mathbb{R}^d$ 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 $\epsilon$-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$\times$ 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.
MUVERA: Multi-Vector Retrieval via Fixed Dimensional Encoding
Rajesh Jayaram Laxman Dhulipala Majid Hadian Jason Lee Vahab Mirrokni