# Studying Various Activation Functions and Non-IID Data for Machine Learning Model Robustness

arXiv: https://arxiv.org/abs/2512.04264 · HTML: https://mlsanity.com/paper/2512.04264/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 67 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Mitigating Adversarial Effects Through Randomization](https://mlsanity.com/paper/1711.01991/) (2017)
- [MagNet: a Two-Pronged Defense against Adversarial Examples](https://mlsanity.com/paper/1705.09064/) (2017)
- [Detecting Adversarial Samples from Artifacts](https://mlsanity.com/paper/1703.00410/) (2017)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Stochastic Activation Pruning for Robust Adversarial Defense](https://mlsanity.com/paper/1803.01442/) (2018)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)

## Abstract (arXiv)

Adversarial training is an effective method to improve the machine learning (ML) model robustness. Most existing studies typically consider the Rectified linear unit (ReLU) activation function and centralized training environments. In this paper, we study the ML model robustness using ten different activation functions through adversarial training in centralized environments and explore the ML model robustness in federal learning environments. In the centralized environment, we first propose an advanced adversarial training approach to improving the ML model robustness by incorporating model architecture change, soft labeling, simplified data augmentation, and varying learning rates. Then, we conduct extensive experiments on ten well-known activation functions in addition to ReLU to better understand how they impact the ML model robustness. Furthermore, we extend the proposed adversarial training approach to the federal learning environment, where both independent and identically distributed (IID) and non-IID data settings are considered. Our proposed centralized adversarial training approach achieves a natural and robust accuracy of 77.08% and 67.96%, respectively on CIFAR-10 against the fast gradient sign attacks. Experiments on ten activation functions reveal ReLU usually performs best. In the federated learning environment, however, the robust accuracy decreases significantly, especially on non-IID data. To address the significant performance drop in the non-IID data case, we introduce data sharing and achieve the natural and robust accuracy of 70.09% and 54.79%, respectively, surpassing the CalFAT algorithm, when 40% data sharing is used. That is, a proper percentage of data sharing can significantly improve the ML model robustness, which is useful to some real-world applications.