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

Показать 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.

Vizuara

Рекомендации по теме

Комментарии

Simply amazing.. before that I used to think neurons as some ambiguous units which was responsible for calculating some values with different weights and biases. But now, its just so clear to me why we needed these small computation units it the first place... they simply represents the little segments of our continuous function and by training the model, we are simply trying to find the approximated values of those factors associated with a particular ReLU. Thank you very much.

sonugupta

Fantastic explanation of the Universal Approximation Theorem! The breakdown of key points, like the significance of a single hidden layer, finite neurons, and suitable activation functions, made the concept very accessible. The illustrative proof was particularly helpful. Thank you for such a clear and insightful lecture!!!!

Anon-omwc

Here from r/learnmachinelearning
Great explanation, Dr. Thank you!

thenoblerot

This is great stuff. Can we use y = mx plus c type of equation.?

KumR

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

The Universal Approximation Theorem for neural networks

Universal Approximation Theorem

Visualization of the universal approximation theorem

The Universal Approximation Theorem of Neural Networks

Why Neural Networks Can Learn Any Function | The Universal Approximation Theorem

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

Deep Learning : Universal Approximation Theorem

8.2 Neural Networks: Universal Approximation Theorem (UvA - Machine Learning 1 - 2020)

Approximate independence of permutation mixtures

Lecture 2 | The Universal Approximation Theorem

Universal Approximation

A shallow grip on neural networks (What is the 'universal approximation theorem'?)

Kolmogorov-Arnold Networks: MLP vs KAN, Math, B-Splines, Universal Approximation Theorem

16 Intro to Deep Learning Part3: Universal Approximation Theorem

Neural Networks 7: universal approximation

Neural Network : The Universal Approximation Theorem

[50 seconds] Universal Approximation with Deep Narrow Networks

Proof why Deep Learning is a universal approximation function

Why Neural Networks can learn (almost) anything

Introduction to Deep Learning - Module 1 - Video 15: Universal Approximation Theorem

ee53 lec21 Universal approximation function

Image understanding: supervised learning: classification: ANN: universal approximation theorem

The Universal Approximation Theorem #shorts

Why greatest Mathematicians are not trying to prove Riemann Hypothesis? || #short #terencetao #maths