标题： 可证明的训练后量化：OPTQ和Qronos的理论分析 显示英文标题

标题： Provable Post-Training Quantization: Theoretical Analysis of OPTQ and Qronos

摘要： 后训练量化（PTQ）已成为减少现代深度神经网络，包括大型语言模型（LLMs）的内存和计算成本的关键工具。 在PTQ算法中，OPTQ框架——也称为GPTQ——由于其计算效率和强大的经验性能而成为一种领先的 方法。 然而，尽管被广泛采用，OPTQ缺乏严格的定量理论保证。 本文首次为OPTQ的确定性和随机变体以及Qronos——一种最近相关的最先进的PTQ算法——提供了定量误差界限。 我们分析了OPTQ的迭代过程如何引起量化误差，并推导出依赖于校准数据和OPTQ使用的正则化参数的非渐近2-范数误差界限。 我们的分析为几个实际设计选择提供了理论依据，包括广泛使用的按降序范数排序特征的启发式方法，以及选择正则化参数的指导。 对于随机变体，我们建立了更强的无穷范数误差界限，这可以控制所需的量化字母表，并且对下游层和非线性特别有用。 最后，我们将分析扩展到Qronos，为它的确定性和随机变体提供了新的理论界限，有助于解释其经验优势。 显示英文摘要

摘要： Post-training quantization (PTQ) has become a crucial tool for reducing the memory and compute costs of modern deep neural networks, including large language models (LLMs). Among PTQ algorithms, the OPTQ framework-also known as GPTQ-has emerged as a leading method due to its computational efficiency and strong empirical performance. Despite its widespread adoption, however, OPTQ lacks rigorous quantitative theoretical guarantees. This paper presents the first quantitative error bounds for both deterministic and stochastic variants of OPTQ, as well as for Qronos, a recent related state-of-the-art PTQ algorithm. We analyze how OPTQ's iterative procedure induces quantization error and derive non-asymptotic 2-norm error bounds that depend explicitly on the calibration data and a regularization parameter that OPTQ uses. Our analysis provides theoretical justification for several practical design choices, including the widely used heuristic of ordering features by decreasing norm, as well as guidance for selecting the regularization parameter. For the stochastic variant, we establish stronger infinity-norm error bounds, which enable control over the required quantization alphabet and are particularly useful for downstream layers and nonlinearities. Finally, we extend our analysis to Qronos, providing new theoretical bounds, for both its deterministic and stochastic variants, that help explain its empirical advantages.