Statistical Understanding of Adversarial Training in Neural Networks

The increasing use of AI raises concerns about its reliability in real-world environments. Modern AI models, especially deep learning, can produce incorrect predictions when inputs are slightly and deliberately altered, a phenomenon known as adversarial attacks. These vulnerabilities can lead to critical errors in healthcare, scientific research, and security, where AI models guide important decisions. The project improves the robustness of AI by founding a new statistical framework. By improving the trustworthiness of data-driven tools, the project supports advances in multiple scientific fields. This project will prepare undergraduate and graduate students to be competitive in robust data analysis, and will increase interests in Science and Mathematics at the pre-college level through K-12 outreach. The research objective of this project is to establish statistical frameworks for robust adversarial training in neural networks and extend them to modern pre-training and fine-tuning paradigms. Specifically, the research goals include: (1) developing a theoretical foundation for adversarial training in two-layer neural networks; (2) designing scalable adversarial training algorithms that leverage dynamic attack strategies and selective sampling for computational efficiency; and (3) creating robust fine-tuning methods for pre-trained foundation models used in downstream tasks. These theoretical and algorithmic advances contribute to a deeper understanding of robustness in statistical learning and yield practical tools applicable across a broad range of disciplines. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.