# CITADEL: Conditional Token Interaction via Dynamic Lexical Routing for Efficient and Effective Multi-Vector Retrieval

arXiv: https://arxiv.org/abs/2211.10411 · HTML: https://mlsanity.com/paper/2211.10411/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 66 references that are in the map.
- First posted on arXiv 18 Nov 2022.

## Builds on (most cited first, 30 of 44)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [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)
- [Reading Wikipedia to Answer Open-Domain Questions](https://mlsanity.com/paper/1704.00051/) (2017)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [SPECTER: Document-level Representation Learning using Citation-informed Transformers](https://mlsanity.com/paper/2004.07180/) (2020)
- [SPLADE: Sparse Lexical and Expansion Model for First Stage Ranking](https://mlsanity.com/paper/2107.05720/) (2021)
- [Efficiently Teaching an Effective Dense Retriever with Balanced Topic Aware Sampling](https://mlsanity.com/paper/2104.06967/) (2021)
- [Sparse, Dense, and Attentional Representations for Text Retrieval](https://mlsanity.com/paper/2005.00181/) (2020)
- [Unsupervised Corpus Aware Language Model Pre-training for Dense Passage Retrieval](https://mlsanity.com/paper/2108.05540/) (2021)
- [Multimodal Contrastive Learning with LIMoE: the Language-Image Mixture of Experts](https://mlsanity.com/paper/2206.02770/) (2022)
- [CLIMATE-FEVER: A Dataset for Verification of Real-World Climate Claims](https://mlsanity.com/paper/2012.00614/) (2020)
- [Overview of the TREC 2020 deep learning track](https://mlsanity.com/paper/2102.07662/) (2021)
- [Condenser: a Pre-training Architecture for Dense Retrieval](https://mlsanity.com/paper/2104.08253/) (2021)
- [Optimizing Dense Retrieval Model Training with Hard Negatives](https://mlsanity.com/paper/2104.08051/) (2021)
- [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)

## Built on by (most cited first, 19 of 19)

- [RA-DIT: Retrieval-Augmented Dual Instruction Tuning](https://mlsanity.com/paper/2310.01352/) (2023)
- [MetaEmbed: Scaling Multimodal Retrieval at Test-Time with Flexible Late Interaction](https://mlsanity.com/paper/2509.18095/) (2025)
- [Rethinking the Role of Token Retrieval in Multi-Vector Retrieval](https://mlsanity.com/paper/2304.01982/) (2023)
- [RuleRAG: Rule-Guided Retrieval-Augmented Generation with Language Models for Question Answering](https://mlsanity.com/paper/2410.22353/) (2024)
- [Sculpting the Vector Space: Towards Efficient Multi-Vector Visual Document Retrieval via Prune-then-Merge Framework](https://mlsanity.com/paper/2602.19549/) (2026)
- [ESPN: Memory-Efficient Multi-Vector Information Retrieval](https://mlsanity.com/paper/2312.05417/) (2023)
- [Generative Retrieval as Multi-Vector Dense Retrieval](https://mlsanity.com/paper/2404.00684/) (2024)
- [Decoding Dense Embeddings: Sparse Autoencoders for Interpreting and Discretizing Dense Retrieval](https://mlsanity.com/paper/2506.00041/) (2025)
- [Hypencoder: Hypernetworks for Information Retrieval](https://mlsanity.com/paper/2502.05364/) (2025)
- [Efficient Document Ranking with Learnable Late Interactions](https://mlsanity.com/paper/2406.17968/) (2024)
- [Moving Beyond Downstream Task Accuracy for Information Retrieval Benchmarking](https://mlsanity.com/paper/2212.01340/) (2022)
- [Distillation for Multilingual Information Retrieval](https://mlsanity.com/paper/2405.00977/) (2024)
- [Towards Lossless Token Pruning in Late-Interaction Retrieval Models](https://mlsanity.com/paper/2504.12778/) (2025)
- [MM-Matryoshka: Towards Budget-Elastic Visual Document Retrieval via a 2D Multimodal Matryoshka Training Framework](https://mlsanity.com/paper/2606.07654/) (2026)
- [Improving Out-of-Distribution Generalization of Neural Rerankers with Contextualized Late Interaction](https://mlsanity.com/paper/2302.06589/) (2023)
- [GEM: A Native Graph-based Index for Multi-Vector Retrieval](https://mlsanity.com/paper/2603.20336/) (2026)
- [MVR-cache: Optimizing Semantic Caching via Multi-Vector Retrieval and Learned Prompt Segmentation](https://mlsanity.com/paper/2605.24914/) (2026)
- [ColBERTSaR: Sparsified ColBERT Index via Product Quantization](https://mlsanity.com/paper/2606.05568/) (2026)
- [Spatial Matryoshka Training for Multi-Granularity Visual Document Retrieval](https://mlsanity.com/paper/2608.29951/) (2026)

## Abstract (arXiv)

Multi-vector retrieval methods combine the merits of sparse (e.g. BM25) and dense (e.g. DPR) retrievers and have achieved state-of-the-art performance on various retrieval tasks. These methods, however, are orders of magnitude slower and need much more space to store their indices compared to their single-vector counterparts. In this paper, we unify different multi-vector retrieval models from a token routing viewpoint and propose conditional token interaction via dynamic lexical routing, namely CITADEL, for efficient and effective multi-vector retrieval. CITADEL learns to route different token vectors to the predicted lexical ``keys'' such that a query token vector only interacts with document token vectors routed to the same key. This design significantly reduces the computation cost while maintaining high accuracy. Notably, CITADEL achieves the same or slightly better performance than the previous state of the art, ColBERT-v2, on both in-domain (MS MARCO) and out-of-domain (BEIR) evaluations, while being nearly 40 times faster. Code and data are available at https://github.com/facebookresearch/dpr-scale.