## What are Activation Functions?

Mathematical activation functions are used to the outputs of artificial neurons in a neural network to make the model nonlinear. They decide whether or not to activate a neuron based on the weighted total of inputs and a bias term. They are an important part of neural networks because they assist the network in learning complicated and nonlinear correlations between inputs and outputs.

In neural networks, different activation functions are routinely utilized, including:

**Sigmoid**– This activation function assigns the input a value between 0 and 1. It is effective in binary classification situations but suffers from the vanishing gradient issue and is seldom employed in deep networks.**Softmax**– In multi-class classification issues, this activation function transfers the input to a probability distribution across many classes.**Tanh**– This activation function maps the input to a value between -1 and 1. It is similar to the sigmoid function in that it generates results that are centered on zero.**ReLU**– (Rectified Linear Unit): Transfers a negative input to zero and a positive input to itself. Because of its simplicity and efficacy, it is often employed in deep neural networks.**Leaky ReLU**– This one is similar to ReLU but adds a slight slope for negative inputs to avoid the dead neuron issue that ReLU may cause.

Each activation function in a neural network has advantages and disadvantages, and the choice of activation function is determined by the particular job at hand as well as the features of the data being employed.

## Activation Functions and Neural Networks

There are several applications for activation functions in conjunction with neural networks:

**Gradient-Based Optimization**– Functions allow gradient-based optimization techniques like backpropagation to adjust the neural network’s weights and biases as needed during training. This is possible because of the differentiability of functions, which permits the determination of the loss function’s gradient with regard to the weights and biases.**Generate nonlinearity**– One of the primary goals of utilizing this type of function in a neural network is to generate nonlinearity. Without functions, the neural network’s capacity to learn complicated and nonlinear correlations between inputs and outputs would be severely hindered.**Limiting the Output Range**– In order to keep the network from becoming fragile or generating very high or tiny output values, functions might restrict the range of each neuron’s output.**Normalizing the Output**– Batch normalization and ReLU are two examples of functions that may be used to normalize the output of each layer in a neural network, which in turn facilitates the training of deeper networks.

Activation functions are crucial to neural networks because they provide efficient gradient-based optimization during training and allow the network to learn complicated and nonlinear correlations between inputs and outputs.

## Identity Activation Function

The identity activation function is an example of a basic activation function that maps the input to itself. This activation function may be thought of as a linear function with a slope of 1.

- Activation function identity is defined as:

**f(x) = x**

in which x represents the neuron’s input.

In regression issues, the identical activation function is often used when the aim is to predict a continuous output value. Since it allows the network to learn a linear connection between the inputs and outputs, the identity function is useful when the neural network’s output should be as close to the genuine output value as feasible.

To better capture complicated, non-linear interactions between inputs and outputs, however, non-linear activation functions are sometimes utilized in place of the identity function. When comparing the efficiency of various functions or gauging a neural network’s efficacy on a regression task, the identity function is often used as a benchmark comparison.

## Linear Activation Function

Simply described, the linear activation function transfers the input onto itself with a certain slope or weight. This function is linear, meaning that its output is directly proportionate to its input.

- The linear activation function formula is as follows:

**f(x) = wx + b**

Where x is the neuron’s input, w represents the neuron’s weight factor or slope, and b represents the bias term.

It’s often used in regression applications when seeking a continuous output value prediction. As the neural network may learn a linear connection between its inputs and outputs, the linear function can help it produce results that are closer to the genuine output value.

However, many real-world applications suffer from the inability of the linear function to represent non-linear connections between inputs and outputs. In order to better capture complicated, non-linear interactions between inputs and outputs, non-linear activation functions are often utilized instead of the linear function.