# Sparta: Spatially Attentive and Adversarially Robust Activation

arXiv: https://arxiv.org/abs/2105.08269 · HTML: https://mlsanity.com/paper/2105.08269/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 54 references that are in the map.
- First posted on arXiv 18 May 2021.

## Builds on (most cited first, 30 of 44)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (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)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Mitigating Adversarial Effects Through Randomization](https://mlsanity.com/paper/1711.01991/) (2017)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Dynamic Convolution: Attention over Convolution Kernels](https://mlsanity.com/paper/1912.03458/) (2019)
- [Defense against Adversarial Attacks Using High-Level Representation Guided Denoiser](https://mlsanity.com/paper/1712.02976/) (2017)
- [Feature Denoising for Improving Adversarial Robustness](https://mlsanity.com/paper/1812.03411/) (2018)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examples](https://mlsanity.com/paper/1710.10766/) (2017)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [SCA-CNN: Spatial and Channel-wise Attention in Convolutional Networks for Image Captioning](https://mlsanity.com/paper/1611.05594/) (2016)
- [Bag of Tricks for Adversarial Training](https://mlsanity.com/paper/2010.00467/) (2020)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)

## Built on by (most cited first, 2 of 2)

- [MISF: Multi-level Interactive Siamese Filtering for High-Fidelity Image Inpainting](https://mlsanity.com/paper/2203.06304/) (2022)
- [On the Robustness of Segment Anything](https://mlsanity.com/paper/2305.16220/) (2023)

## Abstract (arXiv)

Adversarial training (AT) is one of the most effective ways for improving the robustness of deep convolution neural networks (CNNs). Just like common network training, the effectiveness of AT relies on the design of basic network components. In this paper, we conduct an in-depth study on the role of the basic ReLU activation component in AT for robust CNNs. We find that the spatially-shared and input-independent properties of ReLU activation make CNNs less robust to white-box adversarial attacks with either standard or adversarial training. To address this problem, we extend ReLU to a novel Sparta activation function (Spatially attentive and Adversarially Robust Activation), which enables CNNs to achieve both higher robustness, i.e., lower error rate on adversarial examples, and higher accuracy, i.e., lower error rate on clean examples, than the existing state-of-the-art (SOTA) activation functions. We further study the relationship between Sparta and the SOTA activation functions, providing more insights about the advantages of our method. With comprehensive experiments, we also find that the proposed method exhibits superior cross-CNN and cross-dataset transferability. For the former, the adversarially trained Sparta function for one CNN (e.g., ResNet-18) can be fixed and directly used to train another adversarially robust CNN (e.g., ResNet-34). For the latter, the Sparta function trained on one dataset (e.g., CIFAR-10) can be employed to train adversarially robust CNNs on another dataset (e.g., SVHN). In both cases, Sparta leads to CNNs with higher robustness than the vanilla ReLU, verifying the flexibility and versatility of the proposed method.