← Lab
stochround
confirmedC++ · CPUSystems & data structuresJuly 9, 2026
the question
What's the third fix for bf16 accumulation, and is it unbiased?
what came out
Stochastic rounding -- and it's the only unbiased one. Round-to-nearest summing ones freezes at 256 forever (a bf16 weight can't learn a sub-ulp gradient); SR tracks the true sum, noisy per run but unbiased in the mean. Deterministic runs verified bit-for-bit across two languages.
method & receipts
- Result: confirmed
- Pre-registered — the prediction was written down and committed before the run.
→ read the code and re-run it
github.com/v-code01/stochround