School of Mathematical Sciences, Shenzhen University  

Liyuan Scholar Colloquium No. 146  

Lecture Title: Optimization Perspectives on the Differentiation of Programs  

Speaker: Professor Jérôme Bolte (Université Toulouse Capitole / University of Toulouse Capitole)  

Lecture Time: October 28, 2025, 10:30-11:30 (morning)  

Venue: Conference Room 303, Alumni Plaza, Yuehai Campus, Shenzhen University  

Abstract:  

Differentiable programming is reshaping how we build systems—born in AI, now spreading across science and engineering. Many modern systems use solvers (optimisers, fixed-point, and equilibrium layers) with kinks and constraints that standard calculus doesn’t handle well. I will outline a compact mathematical view—conservative calculus—that avoids fragile qualification assumptions and aligns with practical autodiff (PyTorch, JAX, TensorFlow). In essence: even when models are piecewise or defined implicitly, we can propagate “subgradient-style” information through a chain rule to obtain a reliable conservative Jacobian. This enables robust differentiation for deep and implicit networks, solution maps, and even the algorithms themselves, which is where the talk will focus.

Speaker’s Biography:  

Professor Jérôme Bolte is a Professor at the School of Economics, University of Toulouse 1 Capitole (France), and also holds the position of AI Chair Professor at the Toulouse Institute for Artificial Intelligence. His research focuses on continuous optimization, semi-algebraic geometry, and machine learning—with particular expertise in combining first-order methods with semi-algebraic structures to solve complex optimization problems. Together with his collaborators Shoham Sabach and Marc Teboulle, he was awarded the 2017 SIAM Optimization Society Best Paper Prize for their outstanding achievements at the intersection of semi-algebraic geometry and first-order optimization methods. In 2024, Professor Bolte and Edouard Pauwels received the Lagrange Prize in recognition of their remarkable contributions to the field of continuous optimization. Additionally, Professor Bolte currently serves as an Associate Editor for renowned international academic journals including Mathematical Programming and Foundations of Computational Mathematics.  

Faculty and students are welcome to attend!  

School of Mathematical Sciences  

October 14, 2025