Proves that for bounded n, there exist MV embeddings with m vectors each whose Chamfer matrix requires single-vector dimension D = (ε² m)^Ω(1/ε) to approximate within ε, separating MV from SV expressiveness.
Efficient multi-vector dense retrieval using bit vectors.arXiv preprint arXiv:2404.02805,
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Multi-Vector Embeddings are Provably More Expressive than Single Vector Embeddings
Proves that for bounded n, there exist MV embeddings with m vectors each whose Chamfer matrix requires single-vector dimension D = (ε² m)^Ω(1/ε) to approximate within ε, separating MV from SV expressiveness.