# BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction

arXiv: https://arxiv.org/abs/2102.05426 · HTML: https://mlsanity.com/paper/2102.05426/

## Key facts

- Cited by 479 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 41 references that are in the map.
- First posted on arXiv 10 Feb 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [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)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Single Path One-Shot Neural Architecture Search with Uniform Sampling](https://mlsanity.com/paper/1904.00420/) (2019)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [Model compression via distillation and quantization](https://mlsanity.com/paper/1802.05668/) (2018)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Learning to Prune Deep Neural Networks via Layer-wise Optimal Brain Surgeon](https://mlsanity.com/paper/1705.07565/) (2017)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks](https://mlsanity.com/paper/1909.13144/) (2019)
- [Practical Gauss-Newton Optimisation for Deep Learning](https://mlsanity.com/paper/1706.03662/) (2017)
- [Bit Fusion: Bit-Level Dynamically Composable Architecture for Accelerating Deep Neural Networks](https://mlsanity.com/paper/1712.01507/) (2017)
- [Loss Aware Post-training Quantization](https://mlsanity.com/paper/1911.07190/) (2019)
- [Faster gaze prediction with dense networks and Fisher pruning](https://mlsanity.com/paper/1801.05787/) (2018)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)
- [Generalization Error in Deep Learning](https://mlsanity.com/paper/1808.01174/) (2018)

## Built on by (most cited first, 30 of 479)

- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [Outlier Suppression: Pushing the Limit of Low-bit Transformer Language Models](https://mlsanity.com/paper/2209.13325/) (2022)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [BiLLM: Pushing the Limit of Post-Training Quantization for LLMs](https://mlsanity.com/paper/2402.04291/) (2024)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [RPTQ: Reorder-based Post-training Quantization for Large Language Models](https://mlsanity.com/paper/2304.01089/) (2023)
- [ViDiT-Q: Efficient and Accurate Quantization of Diffusion Transformers for Image and Video Generation](https://mlsanity.com/paper/2406.02540/) (2024)
- [OWQ: Outlier-Aware Weight Quantization for Efficient Fine-Tuning and Inference of Large Language Models](https://mlsanity.com/paper/2306.02272/) (2023)
- [Q-DiT: Accurate Post-Training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2406.17343/) (2024)
- [ZipCache: Accurate and Efficient KV Cache Quantization with Salient Token Identification](https://mlsanity.com/paper/2405.14256/) (2024)
- [FP8 Quantization: The Power of the Exponent](https://mlsanity.com/paper/2208.09225/) (2022)
- [COIN++: Neural Compression Across Modalities](https://mlsanity.com/paper/2201.12904/) (2022)
- [Temporal Dynamic Quantization for Diffusion Models](https://mlsanity.com/paper/2306.02316/) (2023)

## Abstract (arXiv)

We study the challenging task of neural network quantization without end-to-end retraining, called Post-training Quantization (PTQ). PTQ usually requires a small subset of training data but produces less powerful quantized models than Quantization-Aware Training (QAT). In this work, we propose a novel PTQ framework, dubbed BRECQ, which pushes the limits of bitwidth in PTQ down to INT2 for the first time. BRECQ leverages the basic building blocks in neural networks and reconstructs them one-by-one. In a comprehensive theoretical study of the second-order error, we show that BRECQ achieves a good balance between cross-layer dependency and generalization error. To further employ the power of quantization, the mixed precision technique is incorporated in our framework by approximating the inter-layer and intra-layer sensitivity. Extensive experiments on various handcrafted and searched neural architectures are conducted for both image classification and object detection tasks. And for the first time we prove that, without bells and whistles, PTQ can attain 4-bit ResNet and MobileNetV2 comparable with QAT and enjoy 240 times faster production of quantized models. Codes are available at https://github.com/yhhhli/BRECQ.