← Lab
rmsnorm
confirmedC++ · NEON / Apple M4Systems & data structuresJuly 7, 2026
the question
Is a hand-vectorized RMSNorm faster than a scalar loop, and does it cost accuracy?
what came out
Faster AND more accurate: NEON RMSNorm is ~2x the scalar f32 loop, and its 4-lane tree reduction rounds less than a sequential sum (shown to be the reduction order, not FMA). f32 accumulation error grows with hidden dim; f64 stays flat. Pre-registered, code-reviewed.
method & receipts
- Result: confirmed
- Pre-registered — the prediction was written down and committed before the run.
- Reproducible — one script re-runs the whole thing from scratch.
- Independently reviewed — an adversarial review pass, kept in the repo.
- Machine-readable claims — every reported number, in a checkable file.
- Tested — a correctness/benchmark suite ships alongside the code.
→ read the code and re-run it
github.com/v-code01/rmsnorm