# DenseShift: Towards Accurate and Efficient Low-Bit Power-of-Two Quantization

arXiv: https://arxiv.org/abs/2208.09708 · HTML: https://mlsanity.com/paper/2208.09708/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 48 references that are in the map.
- First posted on arXiv 20 Aug 2022.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Trained Ternary Quantization](https://mlsanity.com/paper/1612.01064/) (2016)
- [Ternary Weight Networks](https://mlsanity.com/paper/1605.04711/) (2016)
- [Speech Model Pre-training for End-to-End Spoken Language Understanding](https://mlsanity.com/paper/1904.03670/) (2019)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [Forward and Backward Information Retention for Accurate Binary Neural Networks](https://mlsanity.com/paper/1909.10788/) (2019)
- [Towards Accurate Binary Convolutional Neural Network](https://mlsanity.com/paper/1711.11294/) (2017)
- [Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks](https://mlsanity.com/paper/1909.13144/) (2019)
- [Overcoming Oscillations in Quantization-Aware Training](https://mlsanity.com/paper/2203.11086/) (2022)
- [Deep Learning with Low Precision by Half-wave Gaussian Quantization](https://mlsanity.com/paper/1702.00953/) (2017)
- [Convolutional Neural Networks using Logarithmic Data Representation](https://mlsanity.com/paper/1603.01025/) (2016)
- [AdderNet: Do We Really Need Multiplications in Deep Learning?](https://mlsanity.com/paper/1912.13200/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons](https://mlsanity.com/paper/1305.2982/) (2013)
- [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)
- [Learning Discrete Weights Using the Local Reparameterization Trick](https://mlsanity.com/paper/1710.07739/) (2017)
- [Power-of-Two Quantization for Low Bitwidth and Hardware Compliant Neural Networks](https://mlsanity.com/paper/2203.05025/) (2022)

## Built on by (most cited first, 5 of 5)

- [ShiftAddLLM: Accelerating Pretrained LLMs via Post-Training Multiplication-Less Reparameterization](https://mlsanity.com/paper/2406.05981/) (2024)
- [PoTPTQ: A Two-step Power-of-Two Post-training for LLMs](https://mlsanity.com/paper/2507.11959/) (2025)
- [Rescaling-Aware Training for Efficient Deployment of Deep Learning Models on Full-Integer Hardware](https://mlsanity.com/paper/2510.11484/) (2025)
- [PoTAcc: A Pipeline for End-to-End Acceleration of Power-of-Two Quantized DNNs](https://mlsanity.com/paper/2605.06082/) (2026)
- [Threshold Neuron: A Brain-inspired Artificial Neuron for Efficient On-device Inference](https://mlsanity.com/paper/2412.13902/) (2024)

## Abstract (arXiv)

Efficiently deploying deep neural networks on low-resource edge devices is challenging due to their ever-increasing resource requirements. To address this issue, researchers have proposed multiplication-free neural networks, such as Power-of-Two quantization, or also known as Shift networks, which aim to reduce memory usage and simplify computation. However, existing low-bit Shift networks are not as accurate as their full-precision counterparts, typically suffering from limited weight range encoding schemes and quantization loss. In this paper, we propose the DenseShift network, which significantly improves the accuracy of Shift networks, achieving competitive performance to full-precision networks for vision and speech applications. In addition, we introduce a method to deploy an efficient DenseShift network using non-quantized floating-point activations, while obtaining 1.6X speed-up over existing methods. To achieve this, we demonstrate that zero-weight values in low-bit Shift networks do not contribute to model capacity and negatively impact inference computation. To address this issue, we propose a zero-free shifting mechanism that simplifies inference and increases model capacity. We further propose a sign-scale decomposition design to enhance training efficiency and a low-variance random initialization strategy to improve the model's transfer learning performance. Our extensive experiments on various computer vision and speech tasks demonstrate that DenseShift outperforms existing low-bit multiplication-free networks and achieves competitive performance compared to full-precision networks. Furthermore, our proposed approach exhibits strong transfer learning performance without a drop in accuracy. Our code was released on GitHub.