How Non-Linear Activation Functions Make Neural Networks Learnable

Sunday, July 16, 2023

Introduction

Neural networks are a type of machine learning algorithm that are inspired by the human brain. They are made up of layers of neurons, and each neuron performs a linear transformation on its inputs. This means that a neural network with only linear activation functions can only learn linear functions. However, most real-world problems are not linear, so neural networks need to be able to learn non-linear functions.

This is where non-linear activation functions come in. Non-linear activation functions introduce non-linearity into the neural network, which allows it to learn non-linear functions. For example, the sigmoid activation function squashes its inputs to a range between 0 and 1, while the ReLU activation function simply sets all negative inputs to 0. These non-linearities allow the neural network to learn complex functions that would not be possible with only linear activation functions.

In addition to making neural networks learnable, non-linear activation functions also have other benefits. For example, they can help to prevent the neural network from overfitting the training data. Overfitting occurs when the neural network learns the training data too well, and as a result, it is not able to generalize to new data. Non-linear activation functions can help to prevent overfitting by introducing noise into the neural network, which makes it more difficult for the network to learn the training data perfectly.

Overall, non-linear activation functions are essential for making neural networks learnable and preventing overfitting. They are a key component of neural networks, and they play a vital role in the ability of neural networks to solve complex problems.

What are Non-Linear Activation Functions?

An activation function is a function that is applied to the output of a neuron before it is passed on to the next layer of neurons. The activation function determines how the output of the neuron is transformed, and it can have a significant impact on the learning ability of the neural network.

Linear activation functions simply multiply the input by a constant value. This means that the output of the neuron is simply a linear transformation of the input. For example, the identity activation function simply returns the input unchanged.

Non-linear activation functions, on the other hand, introduce non-linearity into the neural network. This means that the output of the neuron is not simply a linear transformation of the input. Non-linear activation functions allow the neural network to learn complex functions that would not be possible with only linear activation functions.

Some Common Non-Linear Activation Functions

There are many different non-linear activation functions that can be used in neural networks. Some of the most common ones include:

Sigmoid: The sigmoid activation function is a S-shaped function that squashes its inputs to a range between 0 and 1. It is often used in binary classification problems, where the output of the neural network is a probability.
Tanh: The tanh activation function is similar to the sigmoid activation function, but it has a range of -1 to 1. It is often used in regression problems, where the output of the neural network is a continuous value.
ReLU: The ReLU activation function is a piecewise linear function that is zero for negative inputs and equal to the input for positive inputs. It is a very popular activation function because it is computationally efficient and it helps to prevent overfitting.
Leaky ReLU: The Leaky ReLU activation function is a variant of the ReLU activation function that allows for a small positive slope for negative inputs. This helps to prevent the neural network from becoming too saturated, which can lead to decreased accuracy.

How Non-Linear Activation Functions Make Neural Networks Learnable

Non-linear activation functions make neural networks learnable by introducing non-linearity into the network. This means that the neural network can learn complex functions that would not be possible with only linear activation functions.

For example, consider the problem of classifying images of cats and dogs. A linear neural network with only linear activation functions would only be able to learn a linear decision boundary between the two classes. This would not be very effective, as most real-world data does not have linear decision boundaries.

However, a neural network with non-linear activation functions can learn a non-linear decision boundary. This allows the neural network to learn more complex functions, and it can therefore achieve better accuracy on the classification task.

How Non-Linear Activation Functions Prevent Overfitting

Non-linear activation functions can also help to prevent overfitting in neural networks. Overfitting occurs when the neural network learns the training data too well, and as a result, it is not able to generalize to new data.

Non-linear activation functions introduce noise into the neural network, which makes it more difficult for