GPTQ: Rounding with the Hessian
An interactive live film: two weights, the layer error as a tilted bowl over the quantization grid; rounding to nearest against GPTQ's round-compensate-round, and the reader drags the weights and turns the bowl.
Narration
To quantize a layer, GPTQ keeps its output close to the original: the error is the squared norm of X times the change in the weights. Here are two weights, and that error drawn as a bowl over them, with its bottom at the full precision weights w.
The dots on the floor are the only values the weights may take after quantization: a grid.
The rest of the narration is in the book's Companion.
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Preview1:43The Derivative of the Matrix InverseChapter 11
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Preview1:32Taylor Expansion, One Term at a TimeChapter 11
Preview1:30Second-Order Taylor: Where the Quadratic Model Can Be TrustedChapter 11
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