MUVERA: How a Multi-Vector Set Becomes One Fixed Vector

MUVERA turns a document's whole set of token vectors into a single fixed-length vector you can put in an ordinary ANN index, without any neural encoder in the loop. It works in six steps: a document is ~100 token vectors (a variable-size, unordered set); a SimHash partition of k_sim random hyperplanes splits space into B = 2^k_sim buckets; each bucket is collapsed to one sub-vector (the centroid of the tokens that fell in it, and an empty bucket copies the nearest non-empty one by Hamming distance); each sub-vector is randomly projected down with a JL-style plus/minus-1 matrix; the whole construction is repeated R_reps times with fresh randomness; and the results are concatenated into one fixed vector of dimension B x d_proj x R_reps. The point of the design is that the inner product of two of these Fixed Dimensional Encodings (FDEs) approximates the expensive Chamfer / MaxSim similarity between the original token sets — so a variable-size set becomes a fixed-size vector that drops straight into HNSW, IVF, or DiskANN.