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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