# Post-training Quantization for Neural Networks with Provable Guarantees

arXiv: https://arxiv.org/abs/2201.11113 · HTML: https://mlsanity.com/paper/2201.11113/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [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)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [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)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [Improving Neural Network Quantization without Retraining using Outlier Channel Splitting](https://mlsanity.com/paper/1901.09504/) (2019)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)
- [Generative Low-bitwidth Data Free Quantization](https://mlsanity.com/paper/2003.03603/) (2020)
- [Post-Training Piecewise Linear Quantization for Deep Neural Networks](https://mlsanity.com/paper/2002.00104/) (2020)
- [A Survey on Methods and Theories of Quantized Neural Networks](https://mlsanity.com/paper/1808.04752/) (2018)
- [An Overview of Neural Network Compression](https://mlsanity.com/paper/2006.03669/) (2020)
- [Zero-shot Adversarial Quantization](https://mlsanity.com/paper/2103.15263/) (2021)
- [A Greedy Algorithm for Quantizing Neural Networks](https://mlsanity.com/paper/2010.15979/) (2020)
- [Quantization for Rapid Deployment of Deep Neural Networks](https://mlsanity.com/paper/1810.05488/) (2018)

## Built on by (most cited first, 30 of 33)

- [Microscaling Data Formats for Deep Learning](https://mlsanity.com/paper/2310.10537/) (2023)
- [MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantization](https://mlsanity.com/paper/2406.00800/) (2024)
- [Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization](https://mlsanity.com/paper/2505.11695/) (2025)
- [Provable Post-Training Quantization: Theoretical Analysis of OPTQ and Qronos](https://mlsanity.com/paper/2508.04853/) (2025)
- [COMQ: A Backpropagation-Free Algorithm for Post-Training Quantization](https://mlsanity.com/paper/2403.07134/) (2024)
- [A simple approach for quantizing neural networks](https://mlsanity.com/paper/2209.03487/) (2022)
- [Accumulator-Aware Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2409.17092/) (2024)
- [A Comprehensive Review and a Taxonomy of Edge Machine Learning: Requirements, Paradigms, and Techniques](https://mlsanity.com/paper/2302.08571/) (2023)
- [Exploring Extreme Quantization in Spiking Language Models](https://mlsanity.com/paper/2405.02543/) (2024)
- [A Rescaling-Invariant Lipschitz Bound Based on Path-Metrics for Modern ReLU Network Parameterizations](https://mlsanity.com/paper/2405.15006/) (2024)
- [Resource Efficient Neural Networks Using Hessian Based Pruning](https://mlsanity.com/paper/2306.07030/) (2023)
- [Hyper-Compression: Model Compression via Hyperfunction](https://mlsanity.com/paper/2409.00592/) (2024)
- [Unified Stochastic Framework for Neural Network Quantization and Pruning](https://mlsanity.com/paper/2412.18184/) (2024)
- [Theoretical Guarantees for Low-Rank Compression of Deep Neural Networks](https://mlsanity.com/paper/2502.02766/) (2025)
- [AWP: Activation-Aware Weight Pruning and Quantization with Projected Gradient Descent](https://mlsanity.com/paper/2506.10205/) (2025)
- [Beacon: Post-Training Quantization with Integrated Grid Selection](https://mlsanity.com/paper/2508.20293/) (2025)
- [Post-Training Quantization for Audio Diffusion Transformers](https://mlsanity.com/paper/2510.00313/) (2025)
- [CEG4N: Counter-Example Guided Neural Network Quantization Refinement](https://mlsanity.com/paper/2207.04231/) (2022)
- [Frame Quantization of Neural Networks](https://mlsanity.com/paper/2404.08131/) (2024)
- [Verification of Bit-Flip Attacks against Quantized Neural Networks](https://mlsanity.com/paper/2502.16286/) (2025)
- [Rotation Invariant Quantization for Model Compression](https://mlsanity.com/paper/2303.03106/) (2023)
- [Quantized Distillation: Optimizing Driver Activity Recognition Models for Resource-Constrained Environments](https://mlsanity.com/paper/2311.05970/) (2023)
- [Error Diffusion: Post Training Quantization with Block-Scaled Number Formats for Neural Networks](https://mlsanity.com/paper/2410.11203/) (2024)
- [Efficient Quantization-Aware Training on Segment Anything Model in Medical Images and Its Deployment](https://mlsanity.com/paper/2412.11186/) (2024)
- [ACT360: An Efficient 360-Degree Action Detection and Summarization Framework for Mission-Critical Training and Debriefing](https://mlsanity.com/paper/2503.12852/) (2025)
- [The Hidden Costs of Translation Accuracy: Distillation, Quantization, and Environmental Impact](https://mlsanity.com/paper/2509.23990/) (2025)
- [Theoretical Compression Bounds for Wide Multilayer Perceptrons](https://mlsanity.com/paper/2512.06288/) (2025)
- [TTQ: Activation-Aware Test-Time Quantization to Accelerate LLM Inference On The Fly](https://mlsanity.com/paper/2603.19296/) (2026)
- [GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation](https://mlsanity.com/paper/2606.01412/) (2026)
- [SPFQ: A Stochastic Algorithm and Its Error Analysis for Neural Network Quantization](https://mlsanity.com/paper/2309.10975/) (2023)

## Abstract (arXiv)

While neural networks have been remarkably successful in a wide array of applications, implementing them in resource-constrained hardware remains an area of intense research. By replacing the weights of a neural network with quantized (e.g., 4-bit, or binary) counterparts, massive savings in computation cost, memory, and power consumption are attained. To that end, we generalize a post-training neural-network quantization method, GPFQ, that is based on a greedy path-following mechanism. Among other things, we propose modifications to promote sparsity of the weights, and rigorously analyze the associated error. Additionally, our error analysis expands the results of previous work on GPFQ to handle general quantization alphabets, showing that for quantizing a single-layer network, the relative square error essentially decays linearly in the number of weights -- i.e., level of over-parametrization. Our result holds across a range of input distributions and for both fully-connected and convolutional architectures thereby also extending previous results. To empirically evaluate the method, we quantize several common architectures with few bits per weight, and test them on ImageNet, showing only minor loss of accuracy compared to unquantized models. We also demonstrate that standard modifications, such as bias correction and mixed precision quantization, further improve accuracy.