Translations:Neural Networks/20/en: Difference between revisions

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Message definition (Neural Networks)

The '''universal approximation theorem''' (Cybenko 1989, Hornik 1991) states that a feedforward network with a single hidden layer containing a finite number of neurons can approximate any continuous function on a compact subset of <math>\mathbb{R}^n</math> to arbitrary accuracy, provided the {{Term|activation function}} satisfies mild conditions (e.g. is non-constant, bounded, and continuous).

The universal approximation theorem (Cybenko 1989, Hornik 1991) states that a feedforward network with a single hidden layer containing a finite number of neurons can approximate any continuous function on a compact subset of $\mathbb{R}^n$ to arbitrary accuracy, provided the activation function satisfies mild conditions (e.g. is non-constant, bounded, and continuous).

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	The '''universal approximation theorem''' (Cybenko 1989, Hornik 1991) states that a feedforward network with a single hidden layer containing a finite number of neurons can approximate any continuous function on a compact subset of <math>\mathbb{R}^n</math> to arbitrary accuracy, provided the ~~{{Term\|~~activation function}} satisfies mild conditions (e.g. is non-constant, bounded, and continuous).		The '''universal approximation theorem''' (Cybenko 1989, Hornik 1991) states that a feedforward network with a single hidden layer containing a finite number of neurons can approximate any continuous function on a compact subset of <math>\mathbb{R}^n</math> to arbitrary accuracy, provided the activation function satisfies mild conditions (e.g. is non-constant, bounded, and continuous).