Universal Approximation Theorem - An intuitive proof using graphs | Machine Learning| Neural network

Описание: The Universal Approximation Theorem is a fundamental result in the field of neural networks and machine learning. It states that a feedforward neural network with a single hidden layer containing a finite number of neurons can approximate any continuous function on a compact subset of inputs to any desired degree of accuracy, provided the activation function is non-constant, bounded, and continuous.

Here are the key points to understand about the Universal Approximation Theorem:

1) Single Hidden Layer: The theorem applies to neural networks with just one hidden layer. This means even a relatively simple network architecture has powerful approximation capabilities.

2) Finite Number of Neurons: The hidden layer must have a finite number of neurons, but there is no specific limit on how many neurons are needed. The number of neurons required depends on the complexity of the function being approximated.

3) Activation Function: The activation function in the hidden layer must be non-constant, bounded, and continuous. Common activation functions that satisfy these conditions include the sigmoid function, ReLU etc.

This video is a simple, illustrative proof of this theorem. More than a technically rigorous proof, this lecture serves as a simple demonstration.