For positive C, C/(C*t) equals 1/t. At t=1 its derivative must be −1. Apple MLX 0.32.2 on CPU gives zero or negative infinity at extreme but representable scales. Intermediate multiplication or denominator squaring loses a representable weighted derivative.

A research patch passes 1328 native comparisons: 600 mismatches before, zero after. Another 1886 comparisons pass with the previous inverse-hyperbolic and arctan2 patches together. Higher derivatives and zero gradients are checked for float32/64. Moderate complex64 controls preserve existing behavior; extreme complex stability is not established.

Report: https://www.gero.uz/research/articles/mlx-divide-scale-autodiff.html
Code, patch, logs and exact references: https://github.com/kadyrbekovhamit-cyber/gero-numerical-observatory/tree/main/audits/2026-09-10-mlx-divide-scale-autodiff/
Source: https://github.com/ml-explore/mlx/blob/81ba1c6a0e50a9268b931579c2d4f1158b9aab5a/mlx/primitives.cpp

One numerical defect. Sequential tests, one numerical CPU thread. Selected translation units were rebuilt against an existing CPU archive. GPU, performance, compile/vmap, exhaustive nonfinite/subnormal behavior and full-model impact were not tested. No claim of production readiness, absolute priority or upstream acceptance.

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

#MLX #Autodiff #NumericalComputing
