mlsanityData to 7 Oct 2026

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

arXiv 2508.04853 ↗First posted 6 Aug 2025cs.LG cs.AI cs.ITcited by 13

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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.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 32 of its 44 references that are in the map. First posted on arXiv 6 Aug 2025.

Builds on

32 of 44 references.

References · 32

  1. 2024The Llama 3 Herd of Modelscited by 14,192
  2. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,838
  3. 2017Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inferencecited by 1,548
  4. 2022SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Modelscited by 1,338
  5. 2023AWQ: Activation-aware Weight Quantization for LLM Compression and Accelerationcited by 1,234
  6. 2023SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shotcited by 1,090
  7. 2021A Survey of Quantization Methods for Efficient Neural Network Inferencecited by 798
  8. 2020Up or Down? Adaptive Rounding for Post-Training Quantizationcited by 600
  9. 2024QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMscited by 598
  10. 2022ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformerscited by 517
  11. 2024SpinQuant: LLM quantization with learned rotationscited by 446
  12. 2023OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Modelscited by 403
20 more
  1. 2023QuIP: 2-Bit Quantization of Large Language Models With Guaranteescited by 397
  2. 2024QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebookscited by 354
  3. 2019Data-Free Quantization Through Weight Equalization and Bias Correctioncited by 328
  4. 2022Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruningcited by 317
  5. 2023A Survey on Model Compression for Large Language Modelscited by 263
  6. 2024Extreme Compression of Large Language Models via Additive Quantizationcited by 223
  7. 2021The Low-Rank Simplicity Bias in Deep Networkscited by 150
  8. 2024A Thorough Examination of Decoding Methods in the Era of LLMscited by 112
  9. 2023Training Transformers with 4-bit Integerscited by 58
  10. 2022A Survey on Model Compression and Acceleration for Pretrained Language Modelscited by 45
  11. 2022Post-training Quantization for Neural Networks with Provable Guaranteescited by 32
  12. 2024MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantizationcited by 26
  13. 2025Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantizationcited by 24
  14. 2020Discrepancy Minimization via a Self-Balancing Walkcited by 22
  15. 2020A Greedy Algorithm for Quantizing Neural Networkscited by 21
  16. 2024QERA: an Analytical Framework for Quantization Error Reconstructioncited by 21
  17. 2024FrameQuant: Flexible Low-Bit Quantization for Transformerscited by 17
  18. 2025Improving Quantization with Post-Training Model Expansioncited by 4
  19. 2024Unified Stochastic Framework for Neural Network Quantization and Pruningcited by 3
  20. 2025Theoretical Guarantees for Low-Rank Compression of Deep Neural Networkscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 11.

13 papers.

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  1. 2026Pushing the Limits of Block Rotations in Post-Training Quantizationcited by 9
  2. 2026WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantizationcited by 5
  3. 2025Beacon: Post-Training Quantization with Integrated Grid Selectioncited by 3
  4. 2026High-Rate Quantized Matrix Multiplication IIcited by 2
  5. 2025Correspondence Between Ising Machines and Neural Networkscited by 1
  6. 2026BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Modelscited by 1
  7. 2026GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptationcited by 1
  8. 2026Optimal Post-Training Quantization Scales and Where to Find Themcited by 1
  9. 2026FastKron: Efficient Quantization with Kronecker-Factored Hessianscited by 1
  10. 2026Signed Symmetric Quantization for Few-Bit Integerscited by 0
  11. 2026WaterKron and FlipFlop Hessian: Information-Theoretically Grounded Quantization with Kronecker-factored Hessianscited by 0
  12. 2026Predicting Quantization Price for Selecting PTQ Configurations Before Deploymentcited by 0
1 more
  1. 2026Generalization behavior of OPTQ and the role of regularizationcited by 0