# MRVQ: One Resident Index for Dimension- and Rate-Elastic Vector Search

arXiv: https://arxiv.org/abs/2610.03651 · HTML: https://mlsanity.com/paper/2610.03651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 15 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 11 of 11)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [C-Pack: Packed Resources For General Chinese Embeddings](https://mlsanity.com/paper/2309.07597/) (2023)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Nomic Embed: Training a Reproducible Long Context Text Embedder](https://mlsanity.com/paper/2402.01613/) (2024)
- [RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2405.12497/) (2024)
- [Residual Quantization with Implicit Neural Codebooks](https://mlsanity.com/paper/2401.14732/) (2024)
- [Practical and Asymptotically Optimal Quantization of High-Dimensional Vectors in Euclidean Space for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2409.09913/) (2024)
- [Matryoshka Quantization](https://mlsanity.com/paper/2502.06786/) (2025)
- [Qinco2: Vector Compression and Search with Improved Implicit Neural Codebooks](https://mlsanity.com/paper/2501.03078/) (2025)
- [AdANNS: A Framework for Adaptive Semantic Search](https://mlsanity.com/paper/2305.19435/) (2023)

## Abstract (arXiv)

Dense-retrieval services must switch among embedding-prefix dimensions and index bit rates as latency, quality, and memory budgets change. Tuning a quantizer separately for each rate gives the best quality, but the retrieval tier then holds several code streams and quantizer states at once. We introduce Matryoshka Residual Vector Quantization (MRVQ), a post-hoc residual quantizer for frozen embeddings. Its maximum-rate code can be truncated two ways: dropping residual stages lowers the rate, and dropping embedding coordinates lowers the dimension. One resident artifact therefore serves every (dimension, rate) pair we evaluate. Across FiQA and NFCorpus, four embedding families, and {4, 8, 16}-byte codes, MRVQ is the lowest-RAM design we evaluate. It uses 17.8-22.0x less memory than three separately trained QINCo2 indices, and 1.89-2.02x less than a lean shared-model steelman. The saving is not free: per-rate QINCo2 is 0.026-0.107 nDCG@10 better on FiQA. But MRVQ beats PQ, OPQ, and AdANNS-OPQ at matched code size. We also evaluate a low-build-cost PCA-scalar design that attains quality comparable to RaBitQ and its extension while fitting 420x faster at the median. Finally, we report two negative results: QINCo2 collapses when trained at high rates, and a ranking-bound hypothesis misses its pre-specified acceptance criteria. MRVQ is therefore a low-memory operating point for elastic retrieval, not a universal quality winner.