# Why Does Post-Training Quantization Work?

arXiv: https://arxiv.org/abs/2609.11716 · HTML: https://mlsanity.com/paper/2609.11716/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 48 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Using the Output Embedding to Improve Language Models](https://mlsanity.com/paper/1608.05859/) (2016)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Breaking the Softmax Bottleneck: A High-Rank RNN Language Model](https://mlsanity.com/paper/1711.03953/) (2017)
- [On the Generalization Benefit of Noise in Stochastic Gradient Descent](https://mlsanity.com/paper/2006.15081/) (2020)
- [Quantization Hurts Reasoning? An Empirical Study on Quantized Reasoning Models](https://mlsanity.com/paper/2504.04823/) (2025)
- [GPTAQ: Efficient Finetuning-Free Quantization for Asymmetric Calibration](https://mlsanity.com/paper/2504.02692/) (2025)
- [Spectral Filters, Dark Signals, and Attention Sinks](https://mlsanity.com/paper/2402.09221/) (2024)
- [A Statistical Framework for Low-bitwidth Training of Deep Neural Networks](https://mlsanity.com/paper/2010.14298/) (2020)
- [Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization](https://mlsanity.com/paper/2504.09629/) (2025)
- [CBQ: Cross-Block Quantization for Large Language Models](https://mlsanity.com/paper/2312.07950/) (2023)
- [GuidedQuant: Large Language Model Quantization via Exploiting End Loss Guidance](https://mlsanity.com/paper/2505.07004/) (2025)
- [Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization](https://mlsanity.com/paper/2505.11695/) (2025)
- [Model-Preserving Adaptive Rounding](https://mlsanity.com/paper/2505.22988/) (2025)
- [Quartet II: Accurate LLM Pre-Training in NVFP4 by Improved Unbiased Gradient Estimation](https://mlsanity.com/paper/2601.22813/) (2026)
- [Training Dynamics Impact Post-Training Quantization Robustness](https://mlsanity.com/paper/2510.06213/) (2025)

## Built on by (most cited first, 1 of 1)

- [Depth Laws for the Precision Floor of Trained Neural Networks: Amplification, Residual Scaling, and a Quantization-Aware Training Paradox](https://mlsanity.com/paper/2609.32060/) (2026)

## Abstract (arXiv)

Post-training quantization compresses large language models (LLMs) by storing their weights at reduced precision, and each quantized weight introduces an error into the hidden states. Naively, these errors should accumulate with depth and corrupt next-token prediction; randomly initialized models accumulate these discrepancies rapidly, whereas quantized pretrained models accumulate much less hidden-state error and largely maintain downstream task performance, even though they were never trained with quantization noise. This raises the question we address: why does post-training quantization work? Comparing full-precision and quantized forward passes, we identify two mechanisms that characterize pretrained quantization robustness. First, the error a layer newly introduces tends to oppose the error it inherits from the layer's input. The two cancel partially such that the discrepancy between full-precision and quantized passes grows slowly. This counteracting residual interaction develops during pretraining. Our quantitative analysis identifies it as a major factor slowing hidden-error growth. Second, LM-head geometry preferentially preserves the scores and probabilities of high-ranked tokens, which typically represent the model's most confident predictions. Together, these mechanisms explain why quantization error that passes through numerous layers can still produce only small output changes, and we verify the findings across models and quantization settings.