WEBVTT

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An unused input gets a gradient. In M L X gather matrix

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multiplication, sorted repeated indices reproduce this error

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on the C P U.

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Both outputs select the first input. Their sum needs gradient

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eight, zero. The original sorted path returns three, five. The

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forward outputs are correct.

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In a small quadratic example, one update raises loss from

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eight to eleven point two eight one two five. The corrected

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update lowers it to six point one two five.

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Two backward methods enable an optimization without its

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required conditions. Repeated left indices and left

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broadcasting violate those conditions. A synthetic slice test

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also reads its own initialized backing tail.

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The local C plus plus repair passes six hundred twenty six

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checks across sixty nine scenarios. The original fails seventy

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one checks. Affine quantized gradients are included.

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These are F P thirty two C P U tests with a partial rebuild.

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Some half precision calls hit an unsupported fallback after

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this patch. Full model impact remains untested. Report and

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logs are linked.