Abstract
AbstractThe paper reconsiders multilayer perceptron networks for the case where the Euclidean inner product is replaced by a semi-inner product. This would be of interest, if the dissimilarity measure between data is given by a general norm such that the Euclidean inner product is not longer consistent to that situation. We prove mathematically that the universal approximation completeness is guaranteed also for those networks where the used semi-inner products are related either to uniformly convex or to reflexive Banach-spaces. Most famous examples of uniformly convex Banach spaces are the spaces \(L_{p}\) and \(l_{p}\) for \(1<p<\infty \). The result is valid for all discriminatory activation functions including the sigmoid and the ReLU activation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.