# Power-of-Two Quantization for Low Bitwidth and Hardware Compliant Neural Networks

arXiv: https://arxiv.org/abs/2203.05025 · HTML: https://mlsanity.com/paper/2203.05025/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 9 Mar 2022.

## Builds on (most cited first, 4 of 4)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Convolutional Neural Networks using Logarithmic Data Representation](https://mlsanity.com/paper/1603.01025/) (2016)
- [DeepShift: Towards Multiplication-Less Neural Networks](https://mlsanity.com/paper/1905.13298/) (2019)
- [ShiftAddNet: A Hardware-Inspired Deep Network](https://mlsanity.com/paper/2010.12785/) (2020)

## Built on by (most cited first, 26 of 26)

- [A Practical Mixed Precision Algorithm for Post-Training Quantization](https://mlsanity.com/paper/2302.05397/) (2023)
- [Memory-Efficient Fine-Tuning for Quantized Diffusion Model](https://mlsanity.com/paper/2401.04339/) (2024)
- [Reducing Computational Complexity of Neural Networks in Optical Channel Equalization: From Concepts to Implementation](https://mlsanity.com/paper/2208.12866/) (2022)
- [Custom Gradient Estimators are Straight-Through Estimators in Disguise](https://mlsanity.com/paper/2405.05171/) (2024)
- [DenseShift: Towards Accurate and Efficient Low-Bit Power-of-Two Quantization](https://mlsanity.com/paper/2208.09708/) (2022)
- [Energy Efficient Hardware Acceleration of Neural Networks with Power-of-Two Quantisation](https://mlsanity.com/paper/2209.15257/) (2022)
- [A Performance Analysis of You Only Look Once Models for Deployment on Constrained Computational Edge Devices in Drone Applications](https://mlsanity.com/paper/2502.15737/) (2025)
- [PoTPTQ: A Two-step Power-of-Two Post-training for LLMs](https://mlsanity.com/paper/2507.11959/) (2025)
- [Low-Precision Streaming PCA](https://mlsanity.com/paper/2510.22440/) (2025)
- [PowerYOLO: Mixed Precision Model for Hardware Efficient Object Detection with Event Data](https://mlsanity.com/paper/2407.08272/) (2024)
- [Computational Complexity Evaluation of Neural Network Applications in Signal Processing](https://mlsanity.com/paper/2206.12191/) (2022)
- [Accelerating PoT Quantization on Edge Devices](https://mlsanity.com/paper/2409.20403/) (2024)
- [Where and How to Enhance: Discovering Bit-Width Contribution for Mixed Precision Quantization](https://mlsanity.com/paper/2508.03002/) (2025)
- [Rescaling-Aware Training for Efficient Deployment of Deep Learning Models on Full-Integer Hardware](https://mlsanity.com/paper/2510.11484/) (2025)
- [Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.03345/) (2026)
- [PoTAcc: A Pipeline for End-to-End Acceleration of Power-of-Two Quantized DNNs](https://mlsanity.com/paper/2605.06082/) (2026)
- [Super Efficient Neural Network for Compression Artifacts Reduction and Super Resolution](https://mlsanity.com/paper/2401.14641/) (2024)
- [Power-of-Two (PoT) Weights in Large Language Models (LLMs)](https://mlsanity.com/paper/2506.00315/) (2025)
- [A Selective Quantization Tuner for ONNX Models](https://mlsanity.com/paper/2507.12196/) (2025)
- [Fibbinary-Based Compression and Quantization for Efficient Neural Radio Receivers](https://mlsanity.com/paper/2511.01921/) (2025)
- [Power-of-Two Quantization-Aware-Training (PoT-QAT) in Large Language Models (LLMs)](https://mlsanity.com/paper/2601.02298/) (2026)
- [Benford's Law as a Distributional Prior for Post-Training Quantization of Large Language Models](https://mlsanity.com/paper/2602.00165/) (2026)
- [GRAU: Generic Reconfigurable Activation Unit Design for Neural Network Hardware Accelerators](https://mlsanity.com/paper/2602.22352/) (2026)
- [ShiftLIF: Efficient Multi-Level Spiking Neurons with Power-of-Two Quantization](https://mlsanity.com/paper/2605.01866/) (2026)
- [ViM-Q: Scalable Algorithm-Hardware Co-Design for Vision Mamba Model Inference on FPGA](https://mlsanity.com/paper/2605.01935/) (2026)
- [LogbQuant: Quantizing Language Models in Logarithmic Space](https://mlsanity.com/paper/2607.01127/) (2026)

## Abstract (arXiv)

Deploying Deep Neural Networks in low-power embedded devices for real time-constrained applications requires optimization of memory and computational complexity of the networks, usually by quantizing the weights. Most of the existing works employ linear quantization which causes considerable degradation in accuracy for weight bit widths lower than 8. Since the distribution of weights is usually non-uniform (with most weights concentrated around zero), other methods, such as logarithmic quantization, are more suitable as they are able to preserve the shape of the weight distribution more precise. Moreover, using base-2 logarithmic representation allows optimizing the multiplication by replacing it with bit shifting. In this paper, we explore non-linear quantization techniques for exploiting lower bit precision and identify favorable hardware implementation options. We developed the Quantization Aware Training (QAT) algorithm that allowed training of low bit width Power-of-Two (PoT) networks and achieved accuracies on par with state-of-the-art floating point models for different tasks. We explored PoT weight encoding techniques and investigated hardware designs of MAC units for three different quantization schemes - uniform, PoT and Additive-PoT (APoT) - to show the increased efficiency when using the proposed approach. Eventually, the experiments showed that for low bit width precision, non-uniform quantization performs better than uniform, and at the same time, PoT quantization vastly reduces the computational complexity of the neural network.