WEBVTT

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Change only the scale, and a derivative of minus one becomes zero or negative infinity. This is an actual MLX CPU result.

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C divided by C times t equals one over t. The value at one stays one. Its derivative must stay minus one.

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The denominator derivative squares the denominator and multiplies the numerator by a weight. These intermediate operations can break a representable result.

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A research patch chooses the arithmetic order from the operand magnitudes. It keeps values differentiable and preserves the existing complex branch.

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All thirteen hundred twenty eight comparisons pass after repair. Eighteen hundred eighty six additional checks pass with the two earlier patches.

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The archive includes higher derivatives, zero gradients, code and logs. This is one numerical defect. GPU behavior and patch performance remain untested.