Mathematics Colloquium
April 28, 2026 11:00AM—12:00PM
Location:
In Person
-
Wean Hall 8220
Speaker:
JIANGENG LIU,
J.B. Duke Distinguished Professor, Department of Mathematics, Duke University
https://sites.math.duke.edu/~jianfeng/
The interactions between the fields of optimal control and deep learning have been quite fruitful in recent years. In this talk, we consider the state-space models (SSM), recently emerged effective architectures for sequential modeling, through the lens of ensemble control, where a shared control law governs a population of input-dependent dynamical systems.
We derive Pontryagin's maximum principle (PMP) for this ensemble control formulation, providing necessary conditions for optimality. Motivated by these conditions, we introduce an algorithm based on the method of successive approximations. We prove convergence of this iterative scheme and establish sufficient conditions for global optimality. The resulting framework provides a control-theoretic perspective on SSM training. Joint work with Ye Feng.
For More Information:
nboffi@andrew.cmu.edu