Nonlocal Perimeter

Nonlocal perimeter is a mathematical concept gaining traction in machine learning, particularly within the context of adversarial training for robust classification. Current research focuses on understanding the geometric properties of nonlocal perimeters and their connection to regularization techniques, often employing minimizing movements schemes and Gamma-convergence analysis to study their behavior and asymptotic limits. This work reveals a link between adversarial robustness and the minimization of a decision boundary's "length," offering a novel geometric perspective on improving the generalization and stability of machine learning models, especially in low-data regimes. The insights gained are contributing to a deeper understanding of adversarial training and informing the development of more robust and efficient algorithms.