Neural Foundations · 1989
Universal Approximation Theorem
The Universal Approximation Theorem proved that a feedforward network with a single hidden layer and a suitable nonlinear activation can approximate any continuous function on a bounded domain to arbitrary accuracy, establishing that neural networks are in principle expressive enough to represent essentially any target mapping.
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Plain-language summary
Cybenko (1989) showed this for sigmoid-type activations and Hornik (1991) generalized it to broad classes of activation functions, proving that finite sums of scaled, shifted activations are dense in the space of continuous functions. The result is an existence guarantee: for any target accuracy some network with enough hidden units achieves it. It does not say how many units are needed or how to find the weights by training, but it removed the theoretical objection that networks might be fundamentally incapable of representing complex functions.
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Provenance
- Record ID
- A-014
- Record created
- 2026-07-13
- Last reviewed
- 2026-07-14
- Record version
- 2
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