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Across my studies I have noticed the following statement in my Subject Guide; namely, that two-layer feed-forward neural networks using the sigmoidal activation function are universal. My question is how are the networks 'universal' and what does 'universal' actually mean in this instance?

Thanks in advance.

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I think they are talking about the universal approximation theorem which states that given a continuous function $f$ over an n-dimensional input vector $\vec{x}$, then a neural network with a single hidden layer can approximate $f(\vec{x})$ arbitrarily closely.

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  • $\begingroup$ Thanks, that point really helped. Are there any other references that discuss the universal approximation theorem? $\endgroup$ – blackpanther Apr 26 '13 at 20:53
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    $\begingroup$ LMGTFY bit.ly/ZB0HBY $\endgroup$ – Sasho Nikolov Apr 26 '13 at 21:45

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