# Multi-Vector Retrieval as Sparse Alignment

arXiv: https://arxiv.org/abs/2211.01267 · HTML: https://mlsanity.com/paper/2211.01267/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 29 of 29)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [RocketQA: An Optimized Training Approach to Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2010.08191/) (2020)
- [SPLADE: Sparse Lexical and Expansion Model for First Stage Ranking](https://mlsanity.com/paper/2107.05720/) (2021)
- [Promptagator: Few-shot Dense Retrieval From 8 Examples](https://mlsanity.com/paper/2209.11755/) (2022)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Sparse, Dense, and Attentional Representations for Text Retrieval](https://mlsanity.com/paper/2005.00181/) (2020)
- [Simple Entity-Centric Questions Challenge Dense Retrievers](https://mlsanity.com/paper/2109.08535/) (2021)
- [SPLADE v2: Sparse Lexical and Expansion Model for Information Retrieval](https://mlsanity.com/paper/2109.10086/) (2021)
- [COIL: Revisit Exact Lexical Match in Information Retrieval with Contextualized Inverted List](https://mlsanity.com/paper/2104.07186/) (2021)
- [Adversarial Retriever-Ranker for dense text retrieval](https://mlsanity.com/paper/2110.03611/) (2021)
- [Dialog Inpainting: Turning Documents into Dialogs](https://mlsanity.com/paper/2205.09073/) (2022)
- [Neural Data Augmentation via Example Extrapolation](https://mlsanity.com/paper/2102.01335/) (2021)
- [Domain-matched Pre-training Tasks for Dense Retrieval](https://mlsanity.com/paper/2107.13602/) (2021)
- [SPARTA: Efficient Open-Domain Question Answering via Sparse Transformer Matching Retrieval](https://mlsanity.com/paper/2009.13013/) (2020)
- [Phrase Retrieval Learns Passage Retrieval, Too](https://mlsanity.com/paper/2109.08133/) (2021)
- [Introducing Neural Bag of Whole-Words with ColBERTer: Contextualized Late Interactions using Enhanced Reduction](https://mlsanity.com/paper/2203.13088/) (2022)

## Built on by (most cited first, 12 of 12)

- [CoLT5: Faster Long-Range Transformers with Conditional Computation](https://mlsanity.com/paper/2303.09752/) (2023)
- [Rethinking the Role of Token Retrieval in Multi-Vector Retrieval](https://mlsanity.com/paper/2304.01982/) (2023)
- [Fast, Differentiable and Sparse Top-k: a Convex Analysis Perspective](https://mlsanity.com/paper/2302.01425/) (2023)
- [CITADEL: Conditional Token Interaction via Dynamic Lexical Routing for Efficient and Effective Multi-Vector Retrieval](https://mlsanity.com/paper/2211.10411/) (2022)
- [Visual Late Chunking: An Empirical Study of Contextual Chunking for Efficient Visual Document Retrieval](https://mlsanity.com/paper/2604.10167/) (2026)
- [Efficient Document Ranking with Learnable Late Interactions](https://mlsanity.com/paper/2406.17968/) (2024)
- [Improving Dual-Encoder Training through Dynamic Indexes for Negative Mining](https://mlsanity.com/paper/2303.15311/) (2023)
- [POQD: Performance-Oriented Query Decomposer for Multi-vector retrieval](https://mlsanity.com/paper/2505.19189/) (2025)
- [Beyond the Grid: Layout-Informed Multi-Vector Retrieval with Parsed Visual Document Representations](https://mlsanity.com/paper/2603.01666/) (2026)
- [Differentiable Knapsack and Top-k Operators via Dynamic Programming](https://mlsanity.com/paper/2601.21775/) (2026)
- [No More K-means: Single-Stage Sparse Coding for Efficient Multi-Vector Retrieval](https://mlsanity.com/paper/2605.30120/) (2026)
- [DeCAL Tokenwise Compression](https://mlsanity.com/paper/2508.08514/) (2025)

## Abstract (arXiv)

Multi-vector retrieval models improve over single-vector dual encoders on many information retrieval tasks. In this paper, we cast the multi-vector retrieval problem as sparse alignment between query and document tokens. We propose AligneR, a novel multi-vector retrieval model that learns sparsified pairwise alignments between query and document tokens (e.g. `dog' vs. `puppy') and per-token unary saliences reflecting their relative importance for retrieval. We show that controlling the sparsity of pairwise token alignments often brings significant performance gains. While most factoid questions focusing on a specific part of a document require a smaller number of alignments, others requiring a broader understanding of a document favor a larger number of alignments. Unary saliences, on the other hand, decide whether a token ever needs to be aligned with others for retrieval (e.g. `kind' from `kind of currency is used in new zealand}'). With sparsified unary saliences, we are able to prune a large number of query and document token vectors and improve the efficiency of multi-vector retrieval. We learn the sparse unary saliences with entropy-regularized linear programming, which outperforms other methods to achieve sparsity. In a zero-shot setting, AligneR scores 51.1 points nDCG@10, achieving a new retriever-only state-of-the-art on 13 tasks in the BEIR benchmark. In addition, adapting pairwise alignments with a few examples (<= 8) further improves the performance up to 15.7 points nDCG@10 for argument retrieval tasks. The unary saliences of AligneR helps us to keep only 20% of the document token representations with minimal performance loss. We further show that our model often produces interpretable alignments and significantly improves its performance when initialized from larger language models.