For the high-order Taylor expansion of neural networks, we provide two implementations, HOPE and Autograd. Users can conveniently compute high-order derivatives of neural networks and obtain Taylor ...

1 Warwick Mathematics Institute, The University of Warwick, Coventry, United Kingdom 2 School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China To ...

A method of near-minimax polynomial approximation is described. As a by-product, this method provides a formula for an estimate of the maximum error associated with a ...

Dominique Guillot, an associate professor in the University of Delaware's Department of Mathematical Sciences, was recently awarded the grant "Polynomial approximation in spaces of analytic functions" ...

Research supported (in part) by the Office of Naval Research, U.S. Navy, and by the Office of Scientific Research, Air Research and Development Command. Reproduction in whole or in part is permitted ...

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Abstract: In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing ...

This research was sponsored in part by the Office of Naval Research, United States Navy, and by the Office of Scientific Research, Air Research and Development Command. Note: The article usage is ...

1 Intel Corporation, Santa Clara, CA, United States 2 Faculty of Mathematics and Computer Science, Friedrich-Schiller-Universität Jena, Jena, Germany We identify that the common source of the problems ...