الملخص
Post-training quantization (PTQ) methods in the GPTQ family minimize a layer-wise reconstruction error on a uniform grid whose scale must be chosen; the common max-based choice degrades sharply at low bit-widths. We study how sensitive this objective is to the scale. For a layer with i.i.d. Gaussian weights and calibration activations of sufficiently large effective rank, we prove that, as the width grows, the normalized round-to-nearest loss converges with high probability, uniformly over all scales, to the mean-squared error of a uniform quantizer applied to a standard Gaussian; we verify the effective-rank condition for wide, randomly initialized MLPs with odd Lipschitz activations and isotropic Gaussian calibration data. The limiting objective has a unique nondegenerate minimizer, whose scale decreases strictly with the number of levels and whose curvature with respect to relative scale errors decays approximately exponentially with the bit-width. GPTQ experiments on five LLMs show the same trend: the scale rule changes perplexity substantially at 2--3 bits and negligibly from 6 bits on, and a local measure of GPTQ scale sensitivity decreases with bit-width in line with the Gaussian curvature. The Gaussian-optimal scale fails on raw weights; after Hadamard incoherence processing it matches the best searched rule at 3 bits and above without any search, but remains clearly worse at 2 bits.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
von Berg, J., Datres, M., Kneißl, C., & Kutyniok, G. (2026). Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape. https://omanscience.com/ar/articles/scale-sensitivity-in-low-bit-post-training-quantization-curvature-of-the-quantization-error-landscape
MLA 9
von Berg, Jonas, et al. "Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape." https://omanscience.com/ar/articles/scale-sensitivity-in-low-bit-post-training-quantization-curvature-of-the-quantization-error-landscape.
شيكاغو (المؤلف–التاريخ)
von Berg, Jonas, Massimiliano Datres, Carlo Kneißl, and Gitta Kutyniok. 2026. "Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape." https://omanscience.com/ar/articles/scale-sensitivity-in-low-bit-post-training-quantization-curvature-of-the-quantization-error-landscape.
هارفارد
von Berg, J., Datres, M., Kneißl, C. and Kutyniok, G. (2026) 'Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape', Available at: https://omanscience.com/ar/articles/scale-sensitivity-in-low-bit-post-training-quantization-curvature-of-the-quantization-error-landscape.
فانكوفر
von Berg J, Datres M, Kneißl C, Kutyniok G. Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape. https://omanscience.com/ar/articles/scale-sensitivity-in-low-bit-post-training-quantization-curvature-of-the-quantization-error-landscape
IEEE
J. von Berg, M. Datres, C. Kneißl, and G. Kutyniok, "Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape," https://omanscience.com/ar/articles/scale-sensitivity-in-low-bit-post-training-quantization-curvature-of-the-quantization-error-landscape.