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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