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.

翻译：神经嵌入模型已成为现代信息检索（IR）系统的核心组件。这类模型为每个数据点生成单个嵌入向量 $x \in \mathbb{R}^d$，从而可通过高度优化的最大内积搜索（MIPS）算法实现快速检索。近年来，以具有里程碑意义的 ColBERT 论文为开端，能够为每个数据点生成一组嵌入向量的多向量模型在信息检索任务中取得了显著更优的性能。然而，由于多向量检索与评分复杂度增加，此类模型在信息检索中的计算成本较高。本文提出 MUVERA（多向量检索算法），该检索机制将多向量相似性搜索简化为单向量相似性搜索，使得现成的 MIPS 求解器能够用于多向量检索。MUVERA 通过非对称方式生成查询和文档的固定维度编码（FDE），这些向量其内积可近似多向量相似度。我们证明 FDE 能够提供高质量的 $\epsilon$ 近似，从而首次为多向量相似度提供了具有理论保证的单向量代理。实验表明，FDE 在检索候选数量减少 2-5 倍的情况下，仍能达到与先前最先进启发式方法相同的召回率。相较于现有最优实现方案，MUVERA 在多样化的 BEIR 检索数据集上持续表现出良好的端到端召回率与延迟性能，平均召回率提升 10%，延迟降低 90%。