发表机构
Ludwig-Maximilians-Universität München; Munich Center for Machine Learning (MCML); Konrad Zuse School of Excellence in Reliable AI (DAAD)（慕尼黑大学; 慕尼黑机器学习中心; 康拉德·楚泽可靠人工智能卓越学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明低比特后训练量化误差对尺度高度敏感，其极限目标曲率随比特宽度指数衰减，并提出经 Hadamard 处理的高斯最优尺度可在 3 比特以上免搜索匹配最佳规则。
AI 中文摘要
GPTQ 系列的后训练量化（PTQ）方法在均匀网格上最小化逐层重建误差，该网格的尺度必须选择；常见的基于最大值的选法在低比特宽度下会急剧退化。我们研究该目标对尺度的敏感程度。对于具有独立同分布高斯权重且校准激活有效秩足够大的层，我们证明，随着宽度增长，归一化的四舍五入到最近损失以高概率在全部尺度上一致收敛到应用于标准高斯的均匀量化器的均方误差；我们验证了宽随机初始化 MLP（具有奇 Lipschitz 激活和各向同性高斯校准数据）的有效秩条件。极限目标具有唯一的非退化最小化器，其尺度随电平数严格减小，其相对于相对尺度误差的曲率随比特宽度近似指数衰减。在五个 LLM 上的 GPTQ 实验显示相同趋势：尺度规则在 2–3 比特时显著改变困惑度，从 6 比特起影响可忽略，并且 GPTQ 尺度敏感性的局部度量随比特宽度下降，与高斯曲率一致。高斯最优尺度在原始权重上失败；在 Hadamard 非相干处理后，它在 3 比特及以上无需搜索即可匹配最佳搜索规则，但在 2 比特时仍明显较差。
英文摘要
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.
