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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