# Smooth Adversarial Training

Source: [Smooth Adversarial Training](<https://www.sota2.com/research/paper/68fa6a531e209131cea275d2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-01-04T03:18:21.670Z

Authors: Cihang Xie, Mingxing Tan, Boqing Gong, Alan Yuille, Quoc V. Le

Published: 2020-06-25T16:34:39.000Z

## Abstract

It is commonly believed that networks cannot be both accurate and robust, that gaining robustness means losing accuracy. It is also generally believed that, unless making networks larger, network architectural elements would otherwise matter little in improving adversarial robustness. Here we present evidence to challenge these common beliefs by a careful study about adversarial training. Our key observation is that the widely-used ReLU activation function significantly weakens adversarial training due to its non-smooth nature. Hence we propose smooth adversarial training (SAT), in which we replace ReLU with its smooth approximations to strengthen adversarial training. The purpose of smooth activation functions in SAT is to allow it to find harder adversarial examples and compute better gradient updates during adversarial training.   Compared to standard adversarial training, SAT improves adversarial robustness for "free", i.e., no drop in accuracy and no increase in computational cost. For example, without introducing additional computations, SAT significantly enhances ResNet-50's robustness from 33.0% to 42.3%, while also improving accuracy by 0.9% on ImageNet. SAT also works well with larger networks: it helps EfficientNet-L1 to achieve 82.2% accuracy and 58.6% robustness on ImageNet, outperforming the previous state-of-the-art defense by 9.5% for accuracy and 11.6% for robustness. Models are available at https://github.com/cihangxie/SmoothAdversarialTraining.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on ImageNet (val) (Accuracy and Robustness)](<https://www.sota2.com/research/sota/image-classification-on-imagenet-val-accuracy-and-robustness.md>): Image Classification; ImageNet (val); Accuracy: 82.2.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2006.14536>)

[PDF](<https://arxiv.org/pdf/2006.14536.pdf>)

[Implementation](<https://github.com/cihangxie/SmoothAdversarialTraining>)