Adversarial Training for Gradient Descent: Analysis Through its Continuous-time Approximation

• URL: http://arxiv.org/abs/2105.08037v2
• Date: Wed, 24 May 2023 05:37:58 GMT
• Title: Adversarial Training for Gradient Descent: Analysis Through its Continuous-time Approximation
• Abstract summary: Adversarial training has gained great popularity as one of the most effective defenses for deep neural network. This paper establishes a continuous-time approximation for the mini-max game of adversarial training.
• Score: 11.389868267342491
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Adversarial training has gained great popularity as one of the most effective defenses for deep neural network and more generally for gradient-based machine learning models against adversarial perturbations on data points. This paper establishes a continuous-time approximation for the mini-max game of adversarial training. This approximation approach allows for precise and analytical comparisons between stochastic gradient descent and its adversarial training counterpart; and confirms theoretically the robustness of adversarial training from a new gradient-flow viewpoint. The analysis is then corroborated through various analytical and numerical examples.

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