← Lab
normfootgun
mixedC++ · CPUSystems & data structuresJuly 9, 2026
the question
Is RMSNorm actually more numerically stable than LayerNorm?
what came out
Real but conditional. RMSNorm wins big under naive bf16 accumulation (its target is well-conditioned; LayerNorm's variance isn't) and it can't express the one-pass cancellation footgun -- but a correctly fp32-accumulated two-pass LayerNorm ties it. An implementation gap, not a law.
method & receipts
- Result: mixed
- Pre-registered — the prediction was written down and committed before the run.
→ read the code and re-run it
github.com/v-code01/normfootgun