ABSTRACT 

Learning-based models have become central to modern prediction and decision-making tasks, but strong empirical performance alone does not ensure reliable behavior in safety-critical settings. This talk presents recent progress toward scalable robustness certification and robustness-aware learning for neural networks. We begin with Lipschitz constants as a fundamental measure of model sensitivity and introduce ECLipsE, a compositional certification framework that replaces large semidefinite programs with small layer-wise subproblems, yielding tight and scalable robustness bounds for deep networks. We then discuss local certification methods that exploit information about the relevant input region, leading to substantially less conservative guarantees than global worst-case bounds. From this viewpoint, Lipschitz certification can also be seen as one instance of a broader class of quadratic constraints, which provide a flexible language for describing robustness, stability, and input-output behavior of learned models. Building on this connection, we examine how such constraints can serve as structural regularizers for learning models with prescribed properties, including neural dynamical models. Finally, we discuss broader future directions for robustness in learning, including tighter and more scalable certificates, robustness-aware training objectives, geometry-informed representations, and methods that enforce desired model behavior by design. Overall, the talk highlights how scalable certification, local robustness analysis, and structure-aware learning can help move neural networks from high empirical accuracy toward reliable deployment.

BIOGRAPHY

Yuezhu (Ruby) Xu is a 4th year Ph.D. student in the School of Industrial Engineering at Purdue University, advised by Dr. Sivaranjani Seetharaman. Her research lies in trustworthy machine learning, with a focus on scalable robustness certification, robust learning, physics-informed neural networks, and learning-based system modeling and control with provable guarantees. More broadly, her work aims to develop efficient algorithms and principled learning frameworks that make neural networks more reliable for complex decision-making and dynamical systems.