Nonlinearity creates linear independence

DOI10.1007/BF02124743zbMath0855.92007MaRDI QIDQ1923888

Yoshifusa Ito

Publication date: 9 February 1997

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

zbMATH Keywords

Fourier transformplane wavesscalinglinear independencenonlinear mappingactivation functionshiftingcomplete linear independencefinite mappingstrict linear independencestructural uniqueness of neural networks

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Neural networks for/in biological studies, artificial life and related topics (92B20)

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Cites Work

• Multilayer feedforward networks are universal approximators
• Differentiable approximation by means of the Radon transformation and its applications to neural networks
• Approximation Capability of Layered Neural Networks with Sigmoid Units on Two Layers
• Learning representations by back-propagating errors
• A logical calculus of the ideas immanent in nervous activity
• Approximation by superpositions of a sigmoidal function
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