Two theorems about the metric, not about the format - #834
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T41 - relative dot-product error cannot see a format destroying a
tensor. When one term dominates a sum, that term governs the
relative error, so a format flushing most weights to zero still
scores well. Measured: at 8 bits under a 4096x outlier, e3m4
scored BEST while zeroing 97.6%, against 2.1% for e4m3.
T42 - a per-tensor scale moves the optimal split toward narrower
exponents, because the scale already covers the range the
exponent bits were being kept for. The ranking reverses between
the unscaled and scaled benchmarks, which is why both are kept.
Citations verified: arXiv:2209.05433 confirmed through the arXiv API
(FP8 Formats for Deep Learning, Micikevicius et al.).
Language audits run locally before pushing this time: RU PASS and EN
PASS over 27 routes each. Last iteration I skipped that and merged a
red audit.
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Two theorems about the metric, not about the format (#834) T41 - relative dot-product error cannot see a format destroying a tensor. When one term dominates a sum, that term governs the relative error, so a format flushing most weights to zero still scores well. Measured: at 8 bits under a 4096x outlier, e3m4 scored BEST while zeroing 97.6%, against 2.1% for e4m3. T42 - a per-tensor scale moves the optimal split toward narrower exponents, because the scale already covers the range the exponent bits were being kept for. The ranking reverses between the unscaled and scaled benchmarks, which is why both are kept. Citations verified: arXiv:2209.05433 confirmed through the arXiv API (FP8 Formats for Deep Learning, Micikevicius et al.). Language audits run locally before pushing this time: RU PASS and EN PASS over 27 routes each. Last iteration I skipped that and merged a red audit.
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Two theorems about the measurement, not about the format — both from trinity-fpga#587.
T41 — relative dot-product error cannot see a format destroying a tensor. When one term dominates a sum, that term governs the relative error. So a format that flushes most of a tensor to zero still scores well:
The first draft of that benchmark reported
e3m4as beating both OCP FP8 splits on exactly this basis. Ranking is now gated at 1% flushed.T42 — a per-tensor scale moves the optimal split toward narrower exponents. The scale already covers the range between tensors, leaving the exponent responsible only for the spread within one. The ranking reverses between the unscaled round-trip benchmark and the scaled dot-product one, which is why both are kept: 16 bits, rule
e6m9at 2.0e-03 againste3m12at 1.7e-04; 32 bits,e12m19at 1.7e-06 againste4m27at 8.1e-09.T42's refusal matters: the optimum is for weights under amax scaling. Activation outliers run ~100× typical and gradients wider still — which is what E5M2's extra exponent is for, and neither was measured.
Citation verified through the arXiv API before publishing:
arXiv:2209.05433, FP8 Formats for Deep Learning, Micikevicius et al.Language audits run locally before pushing:
RU PASS (27 маршрутов),EN PASS (27 маршрутов). Last iteration I skipped that step and merged a red audit.