Predicting Quantization Price for Selecting PTQ Configurations Before Deployment
TL;DR
Weight-space post-training quantization is formulated as pre-deployment configuration selection using priced layer-output error and a trace reduction then yields a calibration-time price table and a budgeted price-guided selector, making fixed-geometry bit allocation a special case rather than the organizing problem.
Abstract
Weight-space post-training quantization (PTQ) must choose finite formats, granularities, quantizer families, transformations, and bits before the completed quantized model reveals its output-distribution drift. Existing PTQ methods predict important pieces of this degradation, including reconstruction error, Hessian sensitivity, transformation effects, and downstream loss, but these pieces are usually scored after fixing the quantization geometry or inside separate configuration families. We formulate weight-space PTQ as pre-deployment configuration selection using priced layer-output error. Each admissible layer configuration is treated as an error generator with a deployment cost, which induces a layer-output error covariance $\boldsymbol{\Sigma}_l(\alpha_l)$, and the full-precision model prices that covariance by downstream curvature, $\widehat{\rho}_l(\alpha_l)=\frac{1}{2}\operatorname{Tr}\left(\widehat{\mathbf{H}}_l\,\widehat{\boldsymbol{\Sigma}}_l(\alpha_l)\right)$. The price follows from full-precision-to-quantized forward KL, whose first-order term cancels at the reference model. It turns reconstruction and diagonal scores into reduced proxies that drop price factors, while finite formats, codebooks, granularities, and equivalent transformations become comparable candidates through the covariances they induce and the costs they pay. A trace reduction then yields a calibration-time price table and a budgeted price-guided selector, making fixed-geometry bit allocation a special case rather than the organizing problem.
