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

Lixuan Guo, Yifei Wang, Tiansheng Wen, Aosong Feng, Stefanie Jegelka, Chenyu You
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:38400-38425, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-guo26x, title = {No More K-means: Single-Stage Sparse Coding for Efficient Multi-Vector Retrieval}, author = {Guo, Lixuan and Wang, Yifei and Wen, Tiansheng and Feng, Aosong and Jegelka, Stefanie and You, Chenyu}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {38400--38425}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/guo26x/guo26x.pdf}, url = {https://proceedings.mlr.press/v306/guo26x.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T No More K-means: Single-Stage Sparse Coding for Efficient Multi-Vector Retrieval %A Lixuan Guo %A Yifei Wang %A Tiansheng Wen %A Aosong Feng %A Stefanie Jegelka %A Chenyu You %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-guo26x %I PMLR %P 38400--38425 %U https://proceedings.mlr.press/v306/guo26x.html %V 306 %X 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.
APA
Guo, L., Wang, Y., Wen, T., Feng, A., Jegelka, S. & You, C.. (2026). No More K-means: Single-Stage Sparse Coding for Efficient Multi-Vector Retrieval. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:38400-38425 Available from https://proceedings.mlr.press/v306/guo26x.html.

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