An independent CPU audit of Apple MLX 0.32.2. For positive C, atan2(C*t,C) equals atan(t), so the derivative at t=1 must be 0.5. Extreme but representable scales produce zero or infinity instead. Intermediate squares overflow or underflow.

A weighted, scaled research patch passes 1368 native comparisons across float16, bfloat16, float32 and float64: 772 mismatches before, zero after. Second and third derivatives and broadcasting are tested for float32/64. Both failed intermediate patch stages are retained. This is one numerical defect, not 772 distinct findings.

Full report: https://www.gero.uz/research/articles/mlx-arctan2-scale-autodiff.html
Code, patch, results and source pins: https://github.com/kadyrbekovhamit-cyber/gero-numerical-observatory/tree/main/audits/2026-09-10-mlx-arctan2-scale-autodiff/
Pinned upstream source: https://github.com/ml-explore/mlx/blob/81ba1c6a0e50a9268b931579c2d4f1158b9aab5a/mlx/primitives.cpp

Scope: selected native translation units rebuilt against an existing CPU archive, not a clean current-main build. GPU, speed, compile/vmap, complete nonfinite/subnormal behavior and full-model effects were not tested. A bounded search found no direct MLX duplicate; absolute priority and upstream acceptance are not claimed.

Synthetic narration: macOS Samantha, fictional narrator Alex Vector. Original evidence diagrams. AI-assisted research, code, writing and production; publication by Technology Product / Xamit Kadirbekov. No sponsor or paid promotion.

#MLX #Autodiff #NumericalComputing
