3 papers
cs.LG2026
A Nonlinear Singular Value Theory for Neural Networks
Brian Charles Brown, Mauricio Munoz, Robert Bridges +2
Recently Brown et al. [2025] established a singular value decomposition (SVD) for maps (especially nonlinear) satisfying certain norm conditions. We prove that most modern neural a…
math.OC2025
Gramians for a New Class of Nonlinear Control Systems Using Koopman and a Novel Generalized SVD
Brian Brown, Michael King
Certified model reduction for high-dimensional nonlinear control systems remains challenging: unlike balanced truncation for LTI systems, most nonlinear reduction methods either la…
math.OC2024
An SVD-like Decomposition of Bounded-Input Bounded-Output Functions
Brian Charles Brown, Michael King, Sean Warnick +2
The Singular Value Decomposition (SVD) of linear functions facilitates the calculation of their 2-induced norm and row and null spaces, hallmarks of linear control theory. In this…