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Equation 18 · Part 9 · How a Model Actually Gets Small Enough to Run on a Phone

Symbol X

W′=arg min⁡∥W′∥0≤k∥WX−W′X∥22W' = \operatorname*{arg\,min}_{\|W'\|_0 \le k} \|WX - W'X\|_2^2
XX

What this part means

X is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

X is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

SparseGPT poses pruning as a per-layer reconstruction problem. For a layer with weight matrix W and a small calibration set of activations X , it looks for a sparse replacement W' that keeps that layer’s output as close as possible to the original: W′=arg min⁡∥W′∥0≤k∥WX−W′X∥22W' = \operatorname*{arg\,min}_{\|W'\|_0 \le k} \|WX - W'X\|_2^2. Rather than solving this by retraining, Frantar and Alistarh adapt a closed-form update derived from the layer’s second-order (Hessian) information, in the spirit of…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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