# Fast-M Adversarial Training Algorithm for Deep Neural Networks
## 1 Introduction  
The rise of deep learning has led to rapid developments in the field of artificial intelligence, attracting an increasing number of researchers to the field. At the same time, the number of fields in which deep learning is being applied is constantly increasing; such fields include image classification, object detection, autonomous driving, and natural language processing. However, while deep learning technology is seemingly successful, like most traditional internet technologies, it also has its own shortcomings and security issues [1].  
[PERSON] et al. [2] made a discovery in image classification using deep neural networks; by adding specific, imperceptible perturbations to an original image that can be successfully classified by a neural network model and then classifying the perturbed im-age with the same model, the result obtained is completely different from that before. This indicates that seemingly small perturbations easily interfere with neural network models, leading to a significant drop in classification accuracy. [PERSON] et al. [3] called these data perturbations that produce classification errors \"adversarial examples\", officially introducing the concept of adversarial attacks. Since then, many researchers have started working in this field.  
Determining the extent to which deep neural network models resist adversarial attacks is called the robustness problem of deep neural networks, which is still a very active research area, especially in some application fields that prioritize security and safety, such as facial recognition, autonomous driving, and object detection [4]. The goal of improving neural network robustness is to train a robust neural network model or to add a detection mechanism when processing data inputs, so that the neural network model is accurate not only for the original data but also for data with adversarial perturbations.  
To this end, researchers have proposed many methods, such as defensive distillation [5], adversarial detection [6; 7], sample randomization [8], and adversarial training, to improve the robustness of deep neural network models. Currently, adversarial training is considered the most effective among these methods of defense and is the main focus of this article.  
To improve the training effect without significantly increasing the training time, this paper proposed an improved Fast-M adversarial training algorithm based on the fast adversarial training paradigm. The main contributions are summarized as follows:  
* This paper analyzes the differences between PGD adversarial training and free and fast adversarial training in training overhead and discusses the influence of the step size and the number of iterations on the training performance.
* This paper proposes an improved Fast-M adversarial training algorithm based on the fast adversarial training method to reduce the computational overload while maintaining the training performance.
* Extensive experiments are conducted with the MNIST, CIFAR10, and CIFAR100 datasets. Results show that the Fast-M algorithm achieves the same training effect as the commonly used adversarial training method, with a training time that is only one-third that of PGD adversarial training.