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Equation 18 · Part 12 · How a Model Actually Gets Small Enough to Run on a Phone

subtraction

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

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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 the older Optimal Brain Surgeon method, so that whenever a weight is removed the remaining weights in that row are analytically nudged to compensate for its absence. The result, reported for the GPT-family models tested, is that “large-scale generative pretrained…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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