# Universal Adder Neural Networks

arXiv: https://arxiv.org/abs/2105.14202 · HTML: https://mlsanity.com/paper/2105.14202/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 55 references that are in the map.
- First posted on arXiv 29 May 2021.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [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)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [GhostNet: More Features from Cheap Operations](https://mlsanity.com/paper/1911.11907/) (2019)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Network Trimming: A Data-Driven Neuron Pruning Approach towards Efficient Deep Architectures](https://mlsanity.com/paper/1607.03250/) (2016)
- [Quantization Networks](https://mlsanity.com/paper/1911.09464/) (2019)
- [Deep Learning with Low Precision by Half-wave Gaussian Quantization](https://mlsanity.com/paper/1702.00953/) (2017)
- [Shift: A Zero FLOP, Zero Parameter Alternative to Spatial Convolutions](https://mlsanity.com/paper/1711.08141/) (2017)
- [AdderNet: Do We Really Need Multiplications in Deep Learning?](https://mlsanity.com/paper/1912.13200/) (2019)
- [Triple Wins: Boosting Accuracy, Robustness and Efficiency Together by Enabling Input-Adaptive Inference](https://mlsanity.com/paper/2002.10025/) (2020)
- [E2-Train: Training State-of-the-art CNNs with Over 80% Energy Savings](https://mlsanity.com/paper/1910.13349/) (2019)
- [Kervolutional Neural Networks](https://mlsanity.com/paper/1904.03955/) (2019)
- [Perturbative Neural Networks](https://mlsanity.com/paper/1806.01817/) (2018)

## Built on by (most cited first, 1 of 1)

- [VanillaNet: the Power of Minimalism in Deep Learning](https://mlsanity.com/paper/2305.12972/) (2023)

## Abstract (arXiv)

Compared with cheap addition operation, multiplication operation is of much higher computation complexity. The widely-used convolutions in deep neural networks are exactly cross-correlation to measure the similarity between input feature and convolution filters, which involves massive multiplications between float values. In this paper, we present adder networks (AdderNets) to trade these massive multiplications in deep neural networks, especially convolutional neural networks (CNNs), for much cheaper additions to reduce computation costs. In AdderNets, we take the ℓ1-norm distance between filters and input feature as the output response. We first develop a theoretical foundation for AdderNets, by showing that both the single hidden layer AdderNet and the width-bounded deep AdderNet with ReLU activation functions are universal function approximators. An approximation bound for AdderNets with a single hidden layer is also presented. We further analyze the influence of this new similarity measure on the optimization of neural network and develop a special training scheme for AdderNets. Based on the gradient magnitude, an adaptive learning rate strategy is proposed to enhance the training procedure of AdderNets. AdderNets can achieve a 75.7% Top-1 accuracy and a 92.3% Top-5 accuracy using ResNet-50 on the ImageNet dataset without any multiplication in the convolutional layer.