# No More K-means: Single-Stage Sparse Coding for Efficient Multi-Vector Retrieval

arXiv: https://arxiv.org/abs/2605.30120 · HTML: https://mlsanity.com/paper/2605.30120/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 67 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 30 of 51)

- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [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)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)
- [Improving Text Embeddings with Large Language Models](https://mlsanity.com/paper/2401.00368/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [SPLADE: Sparse Lexical and Expansion Model for First Stage Ranking](https://mlsanity.com/paper/2107.05720/) (2021)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [CLIMATE-FEVER: A Dataset for Verification of Real-World Climate Claims](https://mlsanity.com/paper/2012.00614/) (2020)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [jina-embeddings-v3: Multilingual Embeddings With Task LoRA](https://mlsanity.com/paper/2409.10173/) (2024)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [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)
- [On the Theoretical Limitations of Embedding-Based Retrieval](https://mlsanity.com/paper/2508.21038/) (2025)
- [PLAID: An Efficient Engine for Late Interaction Retrieval](https://mlsanity.com/paper/2205.09707/) (2022)
- [Llama-Embed-Nemotron-8B: A Universal Text Embedding Model for Multilingual and Cross-Lingual Tasks](https://mlsanity.com/paper/2511.07025/) (2025)
- [KaLM-Embedding-V2: Superior Training Techniques and Data Inspire A Versatile Embedding Model](https://mlsanity.com/paper/2506.20923/) (2025)
- [MUVERA: Multi-Vector Retrieval via Fixed Dimensional Encodings](https://mlsanity.com/paper/2405.19504/) (2024)
- [Counting Ability of Large Language Models and Impact of Tokenization](https://mlsanity.com/paper/2410.19730/) (2024)

## Built on by (most cited first, 1 of 1)

- [When LLM Meets Tree Search: A Systematic View of Inference as Search in Large Language Models](https://mlsanity.com/paper/2608.30395/) (2026)

## Abstract (arXiv)

Multi-vector retrieval (MVR) models, exemplified by ColBERT, have established new benchmarks in retrieval accuracy by preserving fine-grained token-level interactions. However, this granularity imposes prohibitive storage and retrieval efficiency bottlenecks: to manage the immense memory footprint and computational overhead of billion-scale token vectors, state-of-the-art systems are forced to rely on aggressive dimension reduction and complex clustering (e.g., K-means). This compromise introduces two critical limitations: excessive indexing latency of clustering large-scale corpora and semantic information loss inherent to compression. In this paper, we propose Single-stage Sparse Retrieval (SSR}, a paradigm shift that replaces expensive clustering with efficient sparse coding. Instead of compressing features into low-dimensional dense vectors, we utilize Sparse Autoencoder (SAE) to project token embeddings into a high-dimensional but highly sparse representation. This transformation enables us to bypass vector clustering entirely and leverage inverted indexing for precise, high-throughput retrieval. Extensive experiments on the BEIR benchmark demonstrate that SSR achieves a "trifecta" of improvements: it reduces indexing time by 15x compared to ColBERTv2, halves retrieval latency, and simultaneously improves retrieval performance over leading baselines.