# Rotate the ReLU to implicitly sparsify deep networks

arXiv: https://arxiv.org/abs/2206.00488 · HTML: https://mlsanity.com/paper/2206.00488/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 1 Jun 2022.

## Builds on (most cited first, 16 of 16)

- [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)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Seasonal Contrast: Unsupervised Pre-Training from Uncurated Remote Sensing Data](https://mlsanity.com/paper/2103.16607/) (2021)
- [Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations](https://mlsanity.com/paper/1708.02691/) (2017)
- [GluonCV and GluonNLP: Deep Learning in Computer Vision and Natural Language Processing](https://mlsanity.com/paper/1907.04433/) (2019)
- [Millimeter Wave Base Stations with Cameras: Vision Aided Beam and Blockage Prediction](https://mlsanity.com/paper/1911.06255/) (2019)
- [Realizing Neural Decoder at the Edge with Ensembled BNN](https://mlsanity.com/paper/2106.09925/) (2021)

## Abstract (arXiv)

In the era of Deep Neural Network based solutions for a variety of real-life tasks, having a compact and energy-efficient deployable model has become fairly important. Most of the existing deep architectures use Rectifier Linear Unit (ReLU) activation. In this paper, we propose a novel idea of rotating the ReLU activation to give one more degree of freedom to the architecture. We show that this activation wherein the rotation is learned via training results in the elimination of those parameters/filters in the network which are not important for the task. In other words, rotated ReLU seems to be doing implicit sparsification. The slopes of the rotated ReLU activations act as coarse feature extractors and unnecessary features can be eliminated before retraining. Our studies indicate that features always choose to pass through a lesser number of filters in architectures such as ResNet and its variants. Hence, by rotating the ReLU, the weights or the filters that are not necessary are automatically identified and can be dropped thus giving rise to significant savings in memory and computation. Furthermore, in some cases, we also notice that along with saving in memory and computation we also obtain improvement over the reported performance of the corresponding baseline work in the popular datasets such as MNIST, CIFAR-10, CIFAR-100, and SVHN.