MUVERA: Which Knob Actually Buys Recall (FDE Dimensionality Ablation)

An FDE's size is the product of three knobs — final dimensionality = B x d_proj x R_reps, where B = 2^k_sim SimHash buckets — and this ablation (nfcorpus, ColBERTv2, Recall@100 vs exact top-10) sweeps each knob on its own from the k_sim=5, d_proj=16, r_reps=20 baseline (10,240d, recall around 0.73). The knobs are not interchangeable. r_reps (the number of repetitions) dominates at low dimensionality: recall climbs from 0.25 at r=1 to 0.62 by r=8, so early repetitions are where the recall is bought. d_proj (the per-bucket projection dimension) floors near 16 — pushing it to 64 barely moves the line. k_sim (the number of SimHash hyperplanes) saturates past 5. The practical punchline is in the takeaway strip: because MUVERA always follows tier 1 with an exact rerank, NDCG@10 moves only 0.305 to 0.332 going from 2,560d to 10,240d — a 4x disagreement in FDE size mostly washes out after reranking, so the cheap first-tier index can run far smaller than intuition suggests.