Rotation rescues prefix truncation (Matryoshka-like)

Perf record: 027-rotation-rescues-prefix.json. Cohere v3, 1M × 1024, cosine, Granite box. --quant binary --scan-bits N --rotate 2 --batch 16.

The idea

014 found prefix truncation cheap on QPS but costly on recall, because Cohere isn't Matryoshka-trained — the first N raw dims aren't the most informative. 026's rotation spreads each vector's information evenly across all dims. So a prefix of the rotated vector is effectively a random projection to N dims (each output dim mixes all D inputs), not a drop of (D−N) raw dims. Hypothesis: rotation should make truncation lose much less recall.

Result — rotation helps more the more you truncate

Compare the full-bit gain from 026: only +0.27 pts at 1024/C=1000. The rotation's benefit grows as you truncate harder — exactly the hypothesis. QPS is unchanged (rotation is free).

Conclusions

1. Rotation fixes 014's limitation. Prefix truncation was a recall-lossy lever on Cohere; with rotation it's far gentler. 768-bit rot×2 → 0.983 recall @ 923 QPS — 014 needed C=2000 to approach that recall and only hit ~517 QPS. The prefix lever is now genuinely useful at high recall, not just below 0.97.
2. The effect compounds with truncation depth (+4.6 pts at 512 vs +0.27 at 1024), because the more dims you drop, the more it matters that the kept ones are balanced. This is the practical realization of the Matryoshka idea without a Matryoshka-trained model — a random rotation buys most of the benefit for free.
3. This reshapes the Pareto frontier (mapped next): rotation + prefix + tiling should push the recall↔QPS curve out beyond the non-rotated 018 frontier.

Caveats

• Still cosine/Cohere; the absolute recall at 512-bit (0.93) is below the full-bit 0.997, so prefix remains a recall trade — just a much better one with rotation.
• tile=16, reps=4, CV < 0.5%.