Guido Montufar

Guido Montufar is a Full Professor in the Departments of Mathematics and Statistics & Data Science at UCLA since 2024, and Research Group Leader at the Max Planck Institute for Mathematics in the Sciences since 2018. Previously, he served as Associate Professor at UCLA (2022-2024) and Assistant Professor (2017-2022). His academic journey includes postdoctoral positions at MPI MIS and Pennsylvania State University, following his PhD at MPI MIS/Leipzig University.

Montufar's research spans deep learning theory, mathematical machine learning, graphical models, information geometry, and algebraic statistics. His work investigates the geometric and combinatorial properties of neural networks, optimization landscapes, and theoretical foundations of deep learning. He has made significant contributions to understanding the expressive power of neural architectures, implicit regularization, and the geometry of loss surfaces.

His recent publications (2023-2025) demonstrate a strong focus on theoretical aspects of deep learning, with particular attention to neural network geometry, optimization properties, and mathematical frameworks for understanding learning phenomena. His work often bridges abstract mathematical concepts with practical deep learning challenges, examining topics like low-rank gradient structures, linear regions in ReLU networks, and topological aspects of message-passing architectures.

• ERC Starting Grant: Deep Learning Theory 2018-2023
• DFG SPP 2298 Theoretical Foundations of Deep Learning
• NSF CAREER: Neural Networks in the Practical Regime 2022
• Sloan Research Fellowship
• NSF Collaborative Research: RI: Medium: MoDL
• DARPA AIQ: Constraints for Provable Extrapolation

Montufar actively advises PhD students, with a current cohort including Hao Duan, Kedar Karhadkar, and Shuang Liang. His Mathematical Machine Learning Group fosters collaboration between UCLA and MPI MIS, providing students with access to both American and European research networks. The group focuses on rigorous mathematical approaches to understanding modern machine learning systems, with emphasis on geometric and information-theoretic perspectives.

Leading the Mathematical Machine Learning Group at MPI MIS and maintaining an active research program at UCLA, Montufar has established himself as a leading figure in theoretical machine learning. His dual appointments facilitate international collaboration and provide unique opportunities for students to engage with both West Coast academic networks and European research institutions.