Activation functions are a crucial part of neural networks, as they determine the output of a node or neuron in a neural network. Activation functions determine whether a neuron should be activated or not, based on the input received. Activation functions are essential in neural networks because they allow the network to learn and make predictions on unseen data.

There are several types of activation functions, including sigmoid, tanh, ReLU, and softmax. Each activation function has its own unique characteristics and is suitable for different types of tasks.

One common activation function is the sigmoid function, which is a type of logistic function. The sigmoid function is used in binary classification tasks and outputs a value between 0 and 1. For example, if the input to the sigmoid function is -10, the output will be 0, and if the input is 10, the output will be 1. The sigmoid function is defined by the following equation:

f(x) = 1 / (1 + e^-x)

Another common activation function is the tanh function, which is a hyperbolic tangent function. The tanh function is used in classification and regression tasks and outputs a value between -1 and 1. For example, if the input to the tanh function is -10, the output will be -1, and if the input is 10, the output will be 1. The tanh function is defined by the following equation:

f(x) = (e^x – e^-x) / (e^x + e^-x)

One of the most popular activation functions is the ReLU (Rectified Linear Unit) function. The ReLU function is used in regression and classification tasks and outputs the maximum of 0 and the input. For example, if the input to the ReLU function is -10, the output will be 0, and if the input is 10, the output will be 10. The ReLU function is defined by the following equation:

f(x) = max(0, x)

The softmax function is another popular activation function used in classification tasks. The softmax function outputs the probability of each class in the classification task. For example, if there are three classes in a classification task, the softmax function will output the probabilities of each class. The softmax function is defined by the following equation:

f(x) = e^xi / sum(e^xj)

Each activation function has its own strengths and weaknesses, and choosing the appropriate activation function is crucial to the success of a neural network. The sigmoid function is useful in binary classification tasks but is not suitable for tasks with multiple classes. The tanh function is useful in classification and regression tasks but can suffer from vanishing gradients, which can hinder the training of the neural network. The ReLU function is useful in regression and classification tasks and is computationally efficient, but it can suffer from the dying ReLU problem, where the output is always 0. The softmax function is useful in classification tasks but is not suitable for regression tasks.

In conclusion, activation functions are an essential part of neural networks, as they determine the output of a node or neuron. Activation functions allow the network to learn and make predictions on unseen data. There are several types of activation functions, each with its own unique characteristics, and choosing the appropriate activation function is crucial to the success of a neural network.