# A Non-monotonic Smooth Activation Function

arXiv: https://arxiv.org/abs/2310.10126 · HTML: https://mlsanity.com/paper/2310.10126/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (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)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [MosMedData: Chest CT Scans With COVID-19 Related Findings Dataset](https://mlsanity.com/paper/2005.06465/) (2020)
- [Pad'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks](https://mlsanity.com/paper/1907.06732/) (2019)

## Built on by (most cited first, 3 of 3)

- [Zorro: A Flexible and Differentiable Parametric Family of Activation Functions That Extends ReLU and GELU](https://mlsanity.com/paper/2409.19239/) (2024)
- [Robustness as Architecture: Designing IQA Models to Withstand Adversarial Perturbations](https://mlsanity.com/paper/2506.04951/) (2025)
- [Automatic Contouring of Spinal Vertebrae on X-Ray using a Novel Sandwich U-Net Architecture](https://mlsanity.com/paper/2507.09158/) (2025)

## Abstract (arXiv)

Activation functions are crucial in deep learning models since they introduce non-linearity into the networks, allowing them to learn from errors and make adjustments, which is essential for learning complex patterns. The essential purpose of activation functions is to transform unprocessed input signals into significant output activations, promoting information transmission throughout the neural network. In this study, we propose a new activation function called Sqish, which is a non-monotonic and smooth function and an alternative to existing ones. We showed its superiority in classification, object detection, segmentation tasks, and adversarial robustness experiments. We got an 8.21% improvement over ReLU on the CIFAR100 dataset with the ShuffleNet V2 model in the FGSM adversarial attack. We also got a 5.87% improvement over ReLU on image classification on the CIFAR100 dataset with the ShuffleNet V2 model.