UCLA PI Name: Guido Montufar
E-Mail: montufar@math.ucla.edu
Division/Department: Mathematics and Statistics & Data Science
Lab website: https://www.math.ucla.edu/~montufar/
Expected Weekly Time Commitment: 10 hr

This project offers motivated undergraduate students the opportunity to contribute to cutting-edge research on the theoretical foundations of deep learning, with a focus on the quantification and certification of AI systems. As AI models are increasingly deployed in high-stakes environments, a central challenge is to understand how to measure their capabilities, predict their behavior, and certify their reliability. This project will explore mathematical and computational methods for tackling these challenges, bridging theory and practice.

The student will join an active research lab and participate in ongoing work at the interface of applied mathematics and machine learning. Possible directions include: developing quantitative measures of generalization and robustness, analyzing the role of overparameterization, or studying algorithmic behavior (e.g., gradient descent, bias, double descent). The student will be encouraged to explore open research questions and contribute to building methods that could form the basis of trustworthy AI pipelines.

Expectations: The student should bring a strong interest in machine learning and a readiness to engage deeply with research questions. Solid programming skills (e.g., Python, PyTorch, or similar) are essential, along with enthusiasm, persistence, and a willingness to ask questions and participate actively in group discussions (weekly group meeting and weekly group seminar). Good communication skills and an eagerness to contribute to a collaborative research environment are highly valued.

This project is ideal for an undergraduate looking to gain first-hand experience in high-level AI research, develop problem-solving skills, and contribute to foundational work at the frontier of mathematics and machine learning.

Application Instructions

To apply, please send a resume/CV to montufar@math.ucla.edu.