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

arXiv: https://arxiv.org/abs/2508.04853 · HTML: https://mlsanity.com/paper/2508.04853/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 30 of 32)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [A Thorough Examination of Decoding Methods in the Era of LLMs](https://mlsanity.com/paper/2402.06925/) (2024)
- [Training Transformers with 4-bit Integers](https://mlsanity.com/paper/2306.11987/) (2023)
- [A Survey on Model Compression and Acceleration for Pretrained Language Models](https://mlsanity.com/paper/2202.07105/) (2022)
- [Post-training Quantization for Neural Networks with Provable Guarantees](https://mlsanity.com/paper/2201.11113/) (2022)
- [MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantization](https://mlsanity.com/paper/2406.00800/) (2024)
- [Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization](https://mlsanity.com/paper/2505.11695/) (2025)
- [Discrepancy Minimization via a Self-Balancing Walk](https://mlsanity.com/paper/2006.14009/) (2020)
- [A Greedy Algorithm for Quantizing Neural Networks](https://mlsanity.com/paper/2010.15979/) (2020)
- [QERA: an Analytical Framework for Quantization Error Reconstruction](https://mlsanity.com/paper/2410.06040/) (2024)
- [FrameQuant: Flexible Low-Bit Quantization for Transformers](https://mlsanity.com/paper/2403.06082/) (2024)
- [Improving Quantization with Post-Training Model Expansion](https://mlsanity.com/paper/2503.17513/) (2025)

## Built on by (most cited first, 16 of 16)

- [Pushing the Limits of Block Rotations in Post-Training Quantization](https://mlsanity.com/paper/2601.22347/) (2026)
- [WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantization](https://mlsanity.com/paper/2603.04956/) (2026)
- [High-Rate Quantized Matrix Multiplication II](https://mlsanity.com/paper/2605.13768/) (2026)
- [Beacon: Post-Training Quantization with Integrated Grid Selection](https://mlsanity.com/paper/2508.20293/) (2025)
- [Optimal Post-Training Quantization Scales and Where to Find Them](https://mlsanity.com/paper/2606.10890/) (2026)
- [BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models](https://mlsanity.com/paper/2602.04163/) (2026)
- [Correspondence Between Ising Machines and Neural Networks](https://mlsanity.com/paper/2511.00746/) (2025)
- [GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation](https://mlsanity.com/paper/2606.01412/) (2026)
- [Signed Symmetric Quantization for Few-Bit Integers](https://mlsanity.com/paper/2607.08779/) (2026)
- [When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation](https://mlsanity.com/paper/2607.23390/) (2026)
- [FastKron: Efficient Quantization with Kronecker-Factored Hessians](https://mlsanity.com/paper/2608.06291/) (2026)
- [Transforms for LLM Quantization: The Great Inversion and Format Co-Design](https://mlsanity.com/paper/2608.25188/) (2026)
- [WaterKron and FlipFlop Hessian: Information-Theoretically Grounded Quantization with Kronecker-factored Hessians](https://mlsanity.com/paper/2609.14706/) (2026)
- [Predicting Quantization Price for Selecting PTQ Configurations Before Deployment](https://mlsanity.com/paper/2609.28270/) (2026)
- [Generalization behavior of OPTQ and the role of regularization](https://mlsanity.com/paper/2609.31560/) (2026)
- [When Does Compensating Inherited Quantization Error Help? Mean-Square Guarantees for Layer-Wise Quantization and Their Limits](https://mlsanity.com/paper/2610.16020/) (2026)

## Abstract (arXiv)

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.