A stable mapping of nmODE

Adversarial attacks pose significant challenges to the reliability and performance of neural networks. Despite the development of several defense mechanisms targeting various types of adversarial perturbations, only a few manage to strike a balance between theoretical soundness and practical efficacy. nmODE (neural memory ordinary differential equation) is a recently proposed model with several intriguing properties. By delving into the rare attribute of global attractors inherent in nmODE, this paper unveils its stable mapping, thereby conferring certified defense capabilities upon it. Moreover, a novel quantitative approach is proposed, establishing a mathematical link between perturbations and nmODE’s defense proficiency. Additionally, a training technique termed as nmODE⁺ is put forward, enhancing the defense capability of nmODE without imposing additional training burdens. Extensive experiments demonstrate nmODE’s resilience to various perturbations, showcasing its seamless integration with neural networks and existing defense mechanisms. These findings offer valuable insights into leveraging differential equations for robust neural network security.