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Predicting Quantization Price for Selecting PTQ Configurations Before Deployment
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Formulates weight-space PTQ as pre-deployment configuration selection and prices candidate layer-output error covariances via a forward-KL quadratic term, yielding a trace-based budgeted selector.
Problem
Weight-space PTQ must choose formats, granularities, quantizer families, transformations, and bits before the completed quantized model reveals its output-distribution drift; existing proxies score only parts of this decision.
Approach
Treat each admissible layer configuration as an error generator with deployment cost; forward KL at the full-precision reference cancels the first-order term, so the drift is priced by a quadratic form of candidate-induced layer-output error covariance weighted by reference output curvature. A trace reduction gives a calibration-time price table used in a budgeted selector.
Key results
- Realized layer-output price correlates with measured KL drift at rho=0.9470 on OPT-125M and 0.9249 on Qwen3-0.6B.
- Implemented trace price keeps near-equal alignment with KL drift (rho=0.9483 OPT-125M, 0.9438 Qwen3-0.6B).
- On Llama-3.2-1B bit allocation at 3.0 average bits, the price-guided selector reaches avg 51.24 and PPL 12.22 in 579 s versus HIGGS 12.50 PPL / 813 s and AMQ 11635 s with PPL 11.05.
Surprising findings
- AMQ achieves the lowest WikiText2 perplexity (11.05) in bit allocation, beating the price-guided selector, though the selector is far faster and has higher average task accuracy.
- Random granularity selection yields PPL 23313 on Llama-3.2-1B, far worse than fixed group-128.
Limitations
- Price is a local quadratic approximation valid only in low-bit-nonlocality, moment-stable, curvature-aligned regimes; the paper states that other regimes are outside scope.
- Trace reduction relies on approximately isotropic candidate covariance; diagonal and imatrix-style proxies drop factors that may vary across candidates.
- Evaluation is limited to small models (0.125B to 1B) and weight-only PTQ; activation quantization is excluded from the main selector.
Experimental setup
Datasets: WikiText2
Benchmarks: WikiText2 BoolQ TruthfulQA PIQA WinoGrande WiC
Metrics: perplexity accuracy average accuracy selection time correlation with KL drift
Baselines: HIGGS AMQ CALM-CKA Fixed Group-128 Random Selection
Builds on: GPTQ HAWQ-V3 HIGGS AMQ QuaRot
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