Approximation by ridge functions and neural networks with a bounded number of neurons |
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Authors: | Vugar E Ismailov |
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Institution: | 1. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Az-1141 Baku, Azerbaijan.vugaris@mail.ru |
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Abstract: | In this paper, we consider the problem of approximation of continuous multivariate functions by neural networks with a bounded number of neurons in hidden layers. We prove the existence of single-hidden-layer networks with bounded number of neurons, which have approximation capabilities not worse than those of networks with arbitrarily many neurons. Our analysis is based on the properties of ridge functions. |
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Keywords: | neural network MLP model activation function weight ridge function extremal element path orbit |
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