# Post-Training Piecewise Linear Quantization for Deep Neural Networks

arXiv: https://arxiv.org/abs/2002.00104 · HTML: https://mlsanity.com/paper/2002.00104/

## Key facts

- Cited by 79 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 30 of 79)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [BiLLM: Pushing the Limit of Post-Training Quantization for LLMs](https://mlsanity.com/paper/2402.04291/) (2024)
- [Q-ViT: Accurate and Fully Quantized Low-bit Vision Transformer](https://mlsanity.com/paper/2210.06707/) (2022)
- [PD-Quant: Post-Training Quantization based on Prediction Difference Metric](https://mlsanity.com/paper/2212.07048/) (2022)
- [Towards Accurate Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2303.14341/) (2023)
- [A Comprehensive Survey on Model Quantization for Deep Neural Networks in Image Classification](https://mlsanity.com/paper/2205.07877/) (2022)
- [VS-Quant: Per-vector Scaled Quantization for Accurate Low-Precision Neural Network Inference](https://mlsanity.com/paper/2102.04503/) (2021)
- [LLM-Powered Hierarchical Language Agent for Real-time Human-AI Coordination](https://mlsanity.com/paper/2312.15224/) (2023)
- [Towards Accurate Post-training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.18723/) (2023)
- [IntraQ: Learning Synthetic Images with Intra-Class Heterogeneity for Zero-Shot Network Quantization](https://mlsanity.com/paper/2111.09136/) (2021)
- [Towards Efficient Post-training Quantization of Pre-trained Language Models](https://mlsanity.com/paper/2109.15082/) (2021)
- [Edge-Cloud Polarization and Collaboration: A Comprehensive Survey for AI](https://mlsanity.com/paper/2111.06061/) (2021)
- [Post-training Quantization for Neural Networks with Provable Guarantees](https://mlsanity.com/paper/2201.11113/) (2022)
- [Applications and Techniques for Fast Machine Learning in Science](https://mlsanity.com/paper/2110.13041/) (2021)
- [F8Net: Fixed-Point 8-bit Only Multiplication for Network Quantization](https://mlsanity.com/paper/2202.05239/) (2022)
- [Instance-Aware Group Quantization for Vision Transformers](https://mlsanity.com/paper/2404.00928/) (2024)
- [Q-DETR: An Efficient Low-Bit Quantized Detection Transformer](https://mlsanity.com/paper/2304.00253/) (2023)
- [Vision Transformers on the Edge: A Comprehensive Survey of Model Compression and Acceleration Strategies](https://mlsanity.com/paper/2503.02891/) (2025)
- [Towards Accurate Post-Training Quantization of Vision Transformers via Error Reduction](https://mlsanity.com/paper/2407.06794/) (2024)
- [PowerQuant: Automorphism Search for Non-Uniform Quantization](https://mlsanity.com/paper/2301.09858/) (2023)
- [Post-Training Sparsity-Aware Quantization](https://mlsanity.com/paper/2105.11010/) (2021)
- [Data Quality-aware Mixed-precision Quantization via Hybrid Reinforcement Learning](https://mlsanity.com/paper/2302.04453/) (2023)
- [Quantization Variation: A New Perspective on Training Transformers with Low-Bit Precision](https://mlsanity.com/paper/2307.00331/) (2023)
- [Digital-SC: Digital Semantic Communication with Adaptive Network Split and Learned Non-Linear Quantization](https://mlsanity.com/paper/2305.13553/) (2023)
- [SPIQ: Data-Free Per-Channel Static Input Quantization](https://mlsanity.com/paper/2203.14642/) (2022)
- [Robust Machine Unlearning for Quantized Neural Networks via Adaptive Gradient Reweighting with Similar Labels](https://mlsanity.com/paper/2503.13917/) (2025)
- [HPTQ: Hardware-Friendly Post Training Quantization](https://mlsanity.com/paper/2109.09113/) (2021)
- [Fine-grained Data Distribution Alignment for Post-Training Quantization](https://mlsanity.com/paper/2109.04186/) (2021)

## Abstract (arXiv)

Quantization plays an important role in the energy-efficient deployment of deep neural networks on resource-limited devices. Post-training quantization is highly desirable since it does not require retraining or access to the full training dataset. The well-established uniform scheme for post-training quantization achieves satisfactory results by converting neural networks from full-precision to 8-bit fixed-point integers. However, it suffers from significant performance degradation when quantizing to lower bit-widths. In this paper, we propose a piecewise linear quantization (PWLQ) scheme to enable accurate approximation for tensor values that have bell-shaped distributions with long tails. Our approach breaks the entire quantization range into non-overlapping regions for each tensor, with each region being assigned an equal number of quantization levels. Optimal breakpoints that divide the entire range are found by minimizing the quantization error. Compared to state-of-the-art post-training quantization methods, experimental results show that our proposed method achieves superior performance on image classification, semantic segmentation, and object detection with minor overhead.