# Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning

arXiv: https://arxiv.org/abs/2208.11580 · HTML: https://mlsanity.com/paper/2208.11580/

## Key facts

- Cited by 322 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 24 Aug 2022.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [AMC: AutoML for Model Compression and Acceleration on Mobile Devices](https://mlsanity.com/paper/1802.03494/) (2018)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [Accelerating Sparse Deep Neural Networks](https://mlsanity.com/paper/2104.08378/) (2021)
- [Learning to Prune Deep Neural Networks via Layer-wise Optimal Brain Surgeon](https://mlsanity.com/paper/1705.07565/) (2017)
- [MLPerf Inference Benchmark](https://mlsanity.com/paper/1911.02549/) (2019)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [Learning N:M Fine-grained Structured Sparse Neural Networks From Scratch](https://mlsanity.com/paper/2102.04010/) (2021)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [Group Fisher Pruning for Practical Network Compression](https://mlsanity.com/paper/2108.00708/) (2021)
- [The Optimal BERT Surgeon: Scalable and Accurate Second-Order Pruning for Large Language Models](https://mlsanity.com/paper/2203.07259/) (2022)
- [Accelerated Sparse Neural Training: A Provable and Efficient Method to Find N:M Transposable Masks](https://mlsanity.com/paper/2102.08124/) (2021)
- [EigenDamage: Structured Pruning in the Kronecker-Factored Eigenbasis](https://mlsanity.com/paper/1905.05934/) (2019)
- [Loss Aware Post-training Quantization](https://mlsanity.com/paper/1911.07190/) (2019)
- [Fast Sparse ConvNets](https://mlsanity.com/paper/1911.09723/) (2019)
- [M-FAC: Efficient Matrix-Free Approximations of Second-Order Information](https://mlsanity.com/paper/2107.03356/) (2021)

## Built on by (most cited first, 30 of 322)

- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [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)
- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [Efficient Large Language Models: A Survey](https://mlsanity.com/paper/2312.03863/) (2023)
- [BiLLM: Pushing the Limit of Post-Training Quantization for LLMs](https://mlsanity.com/paper/2402.04291/) (2024)
- [OWQ: Outlier-Aware Weight Quantization for Efficient Fine-Tuning and Inference of Large Language Models](https://mlsanity.com/paper/2306.02272/) (2023)
- [SLEB: Streamlining LLMs through Redundancy Verification and Elimination of Transformer Blocks](https://mlsanity.com/paper/2402.09025/) (2024)
- [A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validation](https://mlsanity.com/paper/2305.11391/) (2023)
- [LQ-LoRA: Low-rank Plus Quantized Matrix Decomposition for Efficient Language Model Finetuning](https://mlsanity.com/paper/2311.12023/) (2023)
- [A Survey of Resource-efficient LLM and Multimodal Foundation Models](https://mlsanity.com/paper/2401.08092/) (2024)
- [GPTVQ: The Blessing of Dimensionality for LLM Quantization](https://mlsanity.com/paper/2402.15319/) (2024)
- [ZeroQuant-V2: Exploring Post-training Quantization in LLMs from Comprehensive Study to Low Rank Compensation](https://mlsanity.com/paper/2303.08302/) (2023)
- [Dynamic Context Pruning for Efficient and Interpretable Autoregressive Transformers](https://mlsanity.com/paper/2305.15805/) (2023)
- [AffineQuant: Affine Transformation Quantization for Large Language Models](https://mlsanity.com/paper/2403.12544/) (2024)
- [Model Compression and Efficient Inference for Large Language Models: A Survey](https://mlsanity.com/paper/2402.09748/) (2024)
- [SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2405.14917/) (2024)
- [GPTAQ: Efficient Finetuning-Free Quantization for Asymmetric Calibration](https://mlsanity.com/paper/2504.02692/) (2025)
- [On the Impact of Calibration Data in Post-training Quantization and Pruning](https://mlsanity.com/paper/2311.09755/) (2023)
- [Decoding Compressed Trust: Scrutinizing the Trustworthiness of Efficient LLMs Under Compression](https://mlsanity.com/paper/2403.15447/) (2024)
- [Model Tailor: Mitigating Catastrophic Forgetting in Multi-modal Large Language Models](https://mlsanity.com/paper/2402.12048/) (2024)
- [Optimize Weight Rounding via Signed Gradient Descent for the Quantization of LLMs](https://mlsanity.com/paper/2309.05516/) (2023)
- [ZipLM: Inference-Aware Structured Pruning of Language Models](https://mlsanity.com/paper/2302.04089/) (2023)

## Abstract (arXiv)

We consider the problem of model compression for deep neural networks (DNNs) in the challenging one-shot/post-training setting, in which we are given an accurate trained model, and must compress it without any retraining, based only on a small amount of calibration input data. This problem has become popular in view of the emerging software and hardware support for executing models compressed via pruning and/or quantization with speedup, and well-performing solutions have been proposed independently for both compression approaches. In this paper, we introduce a new compression framework which covers both weight pruning and quantization in a unified setting, is time- and space-efficient, and considerably improves upon the practical performance of existing post-training methods. At the technical level, our approach is based on an exact and efficient realization of the classical Optimal Brain Surgeon (OBS) framework of [LeCun, Denker, and Solla, 1990] extended to also cover weight quantization at the scale of modern DNNs. From the practical perspective, our experimental results show that it can improve significantly upon the compression-accuracy trade-offs of existing post-training methods, and that it can enable the accurate compound application of both pruning and quantization in a post-training setting.