A Numerical Investigation of the Minimum Width of a Neural Network

no code implementations • 25 Oct 2019 • Ibrohim Nosirov, Jeffrey M. Hokanson

Neural network width and depth are fundamental aspects of network topology.

The Lipschitz Matrix: A Tool for Parameter Space Dimension Reduction

1 code implementation • 31 May 2019 • Jeffrey M. Hokanson, Paul G. Constantine

Assuming a multivariate function is Lipschitz continuous is one way to arrive at the curse of dimensionality---the situation where the cost of tasks such as approximation, integration, and optimization grow exponentially in the input dimension of the function.

Numerical Analysis 26B35, 62K05, 68Q25

Data-driven polynomial ridge approximation using variable projection

1 code implementation • 20 Feb 2017 • Jeffrey M. Hokanson, Paul G. Constantine

A ridge approximation is one class of surrogate that models a quantity of interest as a nonlinear function of a few linear combinations of the input parameters.

Numerical Analysis 49M15, 62J02, 90C53