who proposed the universal approximation theorem

The Universal Approximation Theorem was first proposed by George Cybenko in 1989. His work demonstrated that a feedforward neural network with a single hidden layer, using a non-linear activation function, can approximate any continuous function on a compact subset of \(\mathbb{R}^n\), given sufficient neurons in the hidden layer. This theorem laid the foundation for the theoretical understanding of neural networks.

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Here are 5 related questions:
1. What are the implications of the Universal Approximation Theorem for neural networks?
2. How does the choice of activation function impact the Universal Approximation Theorem?
3. Can the Universal Approximation Theorem be extended to networks with multiple hidden layers?
4. What are the limitations of the Universal Approximation Theorem in practical applications?
5. How did George Cybenko's work influence subsequent research in neural networks?

**Tip:** The Universal Approximation Theorem highlights the power of neural networks, but it doesn't guarantee efficient training or generalization to unseen data.

Explore the Universal Approximation Theorem proposed by George Cybenko in 1989. Learn how neural networks with a single hidden layer can approximate any continuous function on a compact subset of \(\mathbb{R}^n\). Discover implications, limitations, and the impact on subsequent research in neural networks.

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