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

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 $17.8 \text{--} 22.0\times$ less memory than three separately trained QINCo2 indices, and $1.89 \text{--} 2.02\times$ less than a lean shared-model steelman. The saving is not free: per-rate QINCo2 is $0.026 \text{--} 0.107$ NDCG 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 $420\times$ 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.