# Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization

arXiv: https://arxiv.org/abs/2505.11695 · HTML: https://mlsanity.com/paper/2505.11695/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 47 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 30 of 33)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [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)
- [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)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [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)
- [Why do LLMs attend to the first token?](https://mlsanity.com/paper/2504.02732/) (2025)
- [OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting](https://mlsanity.com/paper/2501.13987/) (2025)
- [QTIP: Quantization with Trellises and Incoherence Processing](https://mlsanity.com/paper/2406.11235/) (2024)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [GPTAQ: Efficient Finetuning-Free Quantization for Asymmetric Calibration](https://mlsanity.com/paper/2504.02692/) (2025)
- [Optimize Weight Rounding via Signed Gradient Descent for the Quantization of LLMs](https://mlsanity.com/paper/2309.05516/) (2023)
- [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)
- [A Greedy Algorithm for Quantizing Neural Networks](https://mlsanity.com/paper/2010.15979/) (2020)

## Built on by (most cited first, 28 of 28)

- [Provable Post-Training Quantization: Theoretical Analysis of OPTQ and Qronos](https://mlsanity.com/paper/2508.04853/) (2025)
- [Pushing the Limits of Block Rotations in Post-Training Quantization](https://mlsanity.com/paper/2601.22347/) (2026)
- [The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm](https://mlsanity.com/paper/2508.01077/) (2025)
- [WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantization](https://mlsanity.com/paper/2603.04956/) (2026)
- [LPCD: Unified Framework from Layer-Wise to Submodule Quantization](https://mlsanity.com/paper/2512.01546/) (2025)
- [HARP: Hadamard-Preconditioned Adaptive Rotation Processor for Extreme LLM Quantization](https://mlsanity.com/paper/2605.29843/) (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)
- [Understanding Calibration and Truncation Error Propagation in Training-Free Low-Rank Compression for LLMs](https://mlsanity.com/paper/2608.08506/) (2026)
- [SoftWater: Class-Aware Rate Allocation for Softmax Quantization](https://mlsanity.com/paper/2608.12026/) (2026)
- [GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation](https://mlsanity.com/paper/2606.01412/) (2026)
- [OffQ: Taming Structured Outliers in LLM Quantization by Offsetting](https://mlsanity.com/paper/2606.07116/) (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)
- [Why Does Post-Training Quantization Work?](https://mlsanity.com/paper/2609.11716/) (2026)
- [Post-Training Quantization of Generative and Discriminative LSTM Text Classifiers: A Study of Calibration, Class Balance, and Robustness](https://mlsanity.com/paper/2507.09687/) (2025)
- [One Qubit Can Beat One Bit: Quantum Advantage for Post-Training Quantization](https://mlsanity.com/paper/2608.05240/) (2026)
- [SchurQuant: Groupwise Discrete Optimization for Layer-Wise LLM Quantization](https://mlsanity.com/paper/2608.15567/) (2026)
- [SandwichQuant: Which Parameters Matter Before and After Quantization?](https://mlsanity.com/paper/2608.24173/) (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)
- [FoldQuantVLA: Native Low-Bit Quantization of Vision-Language-Action Models via Consistent Folding](https://mlsanity.com/paper/2609.24433/) (2026)
- [Generalization behavior of OPTQ and the role of regularization](https://mlsanity.com/paper/2609.31560/) (2026)
- [JARQ: Joint Alternating Refinement for Quantization](https://mlsanity.com/paper/2609.38599/) (2026)
- [CORAL-KV: Compact Cross-Layer Prediction and Residual Coding for Autoregressive Video KV Caches](https://mlsanity.com/paper/2610.12514/) (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)

We introduce Qronos -- a new state-of-the-art post-training quantization algorithm that sequentially rounds and updates neural network weights. Qronos not only explicitly corrects errors due to both weight and activation quantization, but also errors resulting from quantizing previous layers. Our iterative algorithm is based on an interpretable and disciplined optimization framework that subsumes and surpasses existing data-driven approaches. At each step, Qronos alternates between error correction and diffusion via optimal update rules. Importantly, we prove that Qronos admits an efficient implementation that uses the Cholesky decomposition for solving least-squares problems. We also demonstrate that Qronos is compatible with existing transformation techniques such as Hadamard-based incoherence processing and weight-activation scaling equalization, among others. We evaluate Qronos using recent autoregressive language generation models in the Llama3 family; Qronos consistently outperforms previous state-of-the-art adaptive rounding methods when quantizing the weights, activations, and/or KV caches.