Abstract
We propose a general method for estimating the distance between a compact subspace K of the space L 1([0,1]s) of Lebesgue measurable functions defined on the hypercube [0,1]s, and the class of functions computed by artificial neural networks using a single hidden layer, each unit evaluating a sigmoidal activation function. Our lower bounds are stated in terms of an invariant that measures the oscillations of functions of the space K around the origin. As an application we estimate the minimal number of neurons required to approximate bounded functions satisfying uniform Lipschitz conditions of order α with accuracy ε.
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Montaña, J.L., Borges, C.E. (2009). Lower Bounds for Approximation of Some Classes of Lebesgue Measurable Functions by Sigmoidal Neural Networks. In: Cabestany, J., Sandoval, F., Prieto, A., Corchado, J.M. (eds) Bio-Inspired Systems: Computational and Ambient Intelligence. IWANN 2009. Lecture Notes in Computer Science, vol 5517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02478-8_1
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DOI: https://doi.org/10.1007/978-3-642-02478-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02477-1
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