Dense-retrieval services must adapt embedding dimension and index bit rate as latency, quality, and memory budgets shift, but maintaining separate quantized indices for each setting is memory-hungry. Matryoshka Residual Vector Quantization (MRVQ) is a post-hoc quantizer for frozen embeddings whose single maximum-rate code can be truncated by dropping residual stages (lower rate) or embedding coordinates (lower dimension). It uses 17.8–22.0x less memory than three separately trained QINCo2 indices while beating PQ and OPQ at matched size, though per-rate QINCo2 is more accurate.
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