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accumfrontier

confirmedPython · CPUSystems & data structuresJuly 7, 2026

the question

Where does fp16 accumulation break in a length-N reduction?

what came out

Naive fp16 hits 85% error at vocab scale (fp32 stays under 1e-5); the cause is running-sum magnitude, and pairwise or Kahan summation rescue it where the values are representable. Pre-registered, independently verified against a double oracle in NumPy float16.

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/accumfrontier