# Towards Efficient Post-training Quantization of Pre-trained Language Models

arXiv: https://arxiv.org/abs/2109.15082 · HTML: https://mlsanity.com/paper/2109.15082/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 98 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 30 of 59)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Patient Knowledge Distillation for BERT Model Compression](https://mlsanity.com/paper/1908.09355/) (2019)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2106.14156/) (2021)
- [BERT Loses Patience: Fast and Robust Inference with Early Exit](https://mlsanity.com/paper/2006.04152/) (2020)

## Built on by (most cited first, 30 of 39)

- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [Large Language Model Cascades with Mixture of Thoughts Representations for Cost-efficient Reasoning](https://mlsanity.com/paper/2310.03094/) (2023)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)
- [Vision Language Models in Autonomous Driving: A Survey and Outlook](https://mlsanity.com/paper/2310.14414/) (2023)
- [Fly-Swat or Cannon? Cost-Effective Language Model Choice via Meta-Modeling](https://mlsanity.com/paper/2308.06077/) (2023)
- [Towards Accurate Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2303.14341/) (2023)
- [FlexRound: Learnable Rounding based on Element-wise Division for Post-Training Quantization](https://mlsanity.com/paper/2306.00317/) (2023)
- [A Survey on Transformer Compression](https://mlsanity.com/paper/2402.05964/) (2024)
- [ProSparse: Introducing and Enhancing Intrinsic Activation Sparsity within Large Language Models](https://mlsanity.com/paper/2402.13516/) (2024)
- [Efficient Quantization Strategies for Latent Diffusion Models](https://mlsanity.com/paper/2312.05431/) (2023)
- [A Comprehensive Survey of Compression Algorithms for Language Models](https://mlsanity.com/paper/2401.15347/) (2024)
- [LoQT: Low-Rank Adapters for Quantized Pretraining](https://mlsanity.com/paper/2405.16528/) (2024)
- [HW-GPT-Bench: Hardware-Aware Architecture Benchmark for Language Models](https://mlsanity.com/paper/2405.10299/) (2024)
- [The Efficiency vs. Accuracy Trade-off: Optimizing RAG-Enhanced LLM Recommender Systems Using Multi-Head Early Exit](https://mlsanity.com/paper/2501.02173/) (2025)
- [FAIR Enough: How Can We Develop and Assess a FAIR-Compliant Dataset for Large Language Models' Training?](https://mlsanity.com/paper/2401.11033/) (2024)
- [Reducing Computational Complexity of Neural Networks in Optical Channel Equalization: From Concepts to Implementation](https://mlsanity.com/paper/2208.12866/) (2022)
- [Binary and Ternary Natural Language Generation](https://mlsanity.com/paper/2306.01841/) (2023)
- [LO-BCQ: Block Clustered Quantization for 4-bit (W4A4) LLM Inference](https://mlsanity.com/paper/2502.05376/) (2025)
- [Exploring Extreme Quantization in Spiking Language Models](https://mlsanity.com/paper/2405.02543/) (2024)
- [Souper-Model: How Simple Arithmetic Unlocks State-of-the-Art LLM Performance](https://mlsanity.com/paper/2511.13254/) (2025)
- [Low-Rank Compression of Language Models via Differentiable Rank Selection](https://mlsanity.com/paper/2512.13733/) (2025)
- [Augmenting Hessians with Inter-Layer Dependencies for Mixed-Precision Post-Training Quantization](https://mlsanity.com/paper/2306.04879/) (2023)
- [An Analysis on Quantizing Diffusion Transformers](https://mlsanity.com/paper/2406.11100/) (2024)
- [TATAA: Programmable Mixed-Precision Transformer Acceleration with a Transformable Arithmetic Architecture](https://mlsanity.com/paper/2411.03697/) (2024)
- [Zero-Shot Sharpness-Aware Quantization for Pre-trained Language Models](https://mlsanity.com/paper/2310.13315/) (2023)
- [Exploring Post-Training Quantization of Protein Language Models](https://mlsanity.com/paper/2310.19624/) (2023)
- [Herd: Using multiple, smaller LLMs to match the performances of proprietary, large LLMs via an intelligent composer](https://mlsanity.com/paper/2310.19902/) (2023)
- [LCQ: Low-Rank Codebook based Quantization for Large Language Models](https://mlsanity.com/paper/2405.20973/) (2024)

## Abstract (arXiv)

Network quantization has gained increasing attention with the rapid growth of large pre-trained language models~(PLMs). However, most existing quantization methods for PLMs follow quantization-aware training~(QAT) that requires end-to-end training with full access to the entire dataset. Therefore, they suffer from slow training, large memory overhead, and data security issues. In this paper, we study post-training quantization~(PTQ) of PLMs, and propose module-wise quantization error minimization~(MREM), an efficient solution to mitigate these issues. By partitioning the PLM into multiple modules, we minimize the reconstruction error incurred by quantization for each module. In addition, we design a new model parallel training strategy such that each module can be trained locally on separate computing devices without waiting for preceding modules, which brings nearly the theoretical training speed-up (e.g., 4× on 4 GPUs). Experiments on GLUE and SQuAD benchmarks show that our proposed PTQ solution not only performs close to QAT, but also enjoys significant reductions in training time, memory overhead, and data consumption.