# RAPQ: Rescuing Accuracy for Power-of-Two Low-bit Post-training Quantization

arXiv: https://arxiv.org/abs/2204.12322 · HTML: https://mlsanity.com/paper/2204.12322/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 26 Apr 2022.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [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)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [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)
- [Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks](https://mlsanity.com/paper/1909.13144/) (2019)
- [Convolutional Neural Networks using Logarithmic Data Representation](https://mlsanity.com/paper/1603.01025/) (2016)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)
- [Trained Quantization Thresholds for Accurate and Efficient Fixed-Point Inference of Deep Neural Networks](https://mlsanity.com/paper/1903.08066/) (2019)
- [MQBench: Towards Reproducible and Deployable Model Quantization Benchmark](https://mlsanity.com/paper/2111.03759/) (2021)

## Built on by (most cited first, 15 of 15)

- [PD-Quant: Post-Training Quantization based on Prediction Difference Metric](https://mlsanity.com/paper/2212.07048/) (2022)
- [LiDAR-PTQ: Post-Training Quantization for Point Cloud 3D Object Detection](https://mlsanity.com/paper/2401.15865/) (2024)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [EPTQ: Enhanced Post-Training Quantization via Hessian-guided Network-wise Optimization](https://mlsanity.com/paper/2309.11531/) (2023)
- [P2-ViT: Power-of-Two Post-Training Quantization and Acceleration for Fully Quantized Vision Transformer](https://mlsanity.com/paper/2405.19915/) (2024)
- [PoTPTQ: A Two-step Power-of-Two Post-training for LLMs](https://mlsanity.com/paper/2507.11959/) (2025)
- [Improving Post-Training Quantization on Object Detection with Task Loss-Guided Lp Metric](https://mlsanity.com/paper/2304.09785/) (2023)
- [An Edge AI System Based on FPGA Platform for Railway Fault Detection](https://mlsanity.com/paper/2408.15245/) (2024)
- [The Integer Alibi: Localizing Cross-Kernel Divergence in INT8-Quantized LLM Inference](https://mlsanity.com/paper/2608.13756/) (2026)
- [Pack-PTQ: Advancing Post-training Quantization of Neural Networks by Pack-wise Reconstruction](https://mlsanity.com/paper/2505.00259/) (2025)
- [Deterministic LLM Inference Across GPU Kernels: Power-of-Two INT8 Quantization Scales and the Limits of Tolerance-Based Conformance](https://mlsanity.com/paper/2609.00363/) (2026)
- [SIRA: Scaled-Integer Range Analysis for Optimizing FPGA Dataflow Neural Network Accelerators](https://mlsanity.com/paper/2508.21493/) (2025)
- [RPIQ: Residual-Projected Multi-Collaboration Closed-Loop and Single Instance Quantization for Visually Impaired Assistance](https://mlsanity.com/paper/2601.02888/) (2026)
- [ViM-Q: Scalable Algorithm-Hardware Co-Design for Vision Mamba Model Inference on FPGA](https://mlsanity.com/paper/2605.01935/) (2026)
- [Neural Network Quantization by Learning Low-Loss Subspaces](https://mlsanity.com/paper/2606.25087/) (2026)

## Abstract (arXiv)

We introduce a Power-of-Two low-bit post-training quantization(PTQ) method for deep neural network that meets hardware requirements and does not call for long-time retraining. Power-of-Two quantization can convert the multiplication introduced by quantization and dequantization to bit-shift that is adopted by many efficient accelerators. However, the Power-of-Two scale factors have fewer candidate values, which leads to more rounding or clipping errors. We propose a novel Power-of-Two PTQ framework, dubbed RAPQ, which dynamically adjusts the Power-of-Two scales of the whole network instead of statically determining them layer by layer. It can theoretically trade off the rounding error and clipping error of the whole network. Meanwhile, the reconstruction method in RAPQ is based on the BN information of every unit. Extensive experiments on ImageNet prove the excellent performance of our proposed method. Without bells and whistles, RAPQ can reach accuracy of 65% and 48% on ResNet-18 and MobileNetV2 respectively with weight INT2 activation INT4. We are the first to propose the more constrained but hardware-friendly Power-of-Two quantization scheme for low-bit PTQ specially and prove that it can achieve nearly the same accuracy as SOTA PTQ method. The code was released.