WEBVTT

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One gradient descent step should lower this loss.

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In Apple’s MLX, it goes up.

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The real loss is hyperbolic cosine, evaluated through complex cosine.

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At one, its derivative should be positive.

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MLX returns a negative derivative.

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The loss rises from 1.543 to 1.557.

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Seven backward rules miss complex conjugation.

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Inverse hyperbolic cosine also has a separate branch error.

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After a local C++ patch, the loss falls.

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All 131 scenarios pass.

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The conjugation class is already known. These are additional tested cases.

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Full-model effects remain unmeasured. Code and sources are linked.