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Low-precision GPU kernels were being tested with one fixed tolerance, and numoracle derives the acceptance region per element instead

AspireAI community · arXiv (numoracle)
Low-precision GPU kernels are usually checked against a reference with hand-picked absolute and relative tolerances, but legitimate numerical error varies with the input, the format and the precision plan. numoracle instead derives per-element acceptance regions from precision-annotated reference programs, with a calculus that tracks shared rounding errors, provenance-ordered products, block-scaled quantizers and calibrated math-library errors. Across 13 Triton operators from Liger-Kernel, Unsloth and vLLM on two GPU generations, it produced no false alarm across 33,960 correct-kernel and behaviour-preserving-variant runs per GPU, and on an RTX PRO 6000 it killed 116 of 124 effective mutants against 59-83 for four fixed-tolerance baselines. The authors are explicit about the limits: soundness is conditional on stated rounding, hardware, domain and implementation assumptions, and a fixed-input mode is needed to drop the zero-mean rounding assumption.
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