5 papers
Rational Neural Networks have Expressivity Advantages
Maosen Tang, Alex Townsend
We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smo…
Convergence of Pivoted Cholesky Algorithm for Lipschitz Kernels
Sungwoo Jeong, Alex Townsend
We investigate the continuous analogue of the Cholesky factorization, namely the pivoted Cholesky algorithm. Our analysis establishes quantitative convergence guarantees for kernel…
Operator learning for hyperbolic partial differential equations
Christopher Wang, Alex Townsend
We construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from i…
Extending Mercer's expansion to indefinite and asymmetric kernels
Sungwoo Jeong, Alex Townsend
Mercer's expansion and Mercer's theorem are cornerstone results in kernel theory. While the classical Mercer's theorem only considers continuous symmetric positive definite kernels…
The Distributional Koopman Operator for Random Dynamical Systems
Maria Oprea, Alex Townsend, Yunan Yang
The Distributional Koopman Operator (DKO) is introduced as a way to perform Koopman analysis on random dynamical systems where only aggregate distribution data is available, thereb…