Read About sigmoid function

Why Do We Use a Sigmoid Activation Function?

In binary classification tasks, the sigmoid activation function is commonly used because it transforms any input value into a probability between 0 and 1. This makes it ideal for problems where the output needs to represent a probability or a likelihood, such as determining whether an input belongs to class 0 or class 1.

In the example of logistic regression (which can be seen as a very simple neural network with just one layer), the sigmoid function ensures that the output of the model is interpretable as a probability. After applying the sigmoid, the model’s output can be interpreted as the likelihood that the input belongs to the positive class (e.g., class 1).

Key Properties of the Sigmoid Function:

Output Range: The sigmoid function always outputs a value between 0 and 1, regardless of the input value. This is why it is commonly used in cases where the output needs to represent probabilities.
Smooth and Differentiable: The sigmoid function is smooth, meaning its output changes gradually as the input changes. It’s also differentiable, which is important for backpropagation, the algorithm used to train neural networks by adjusting weights and biases.
Squashes Input to [0, 1]: The function takes an input z and squashes it into a value between 0 and 1:

If z is a large positive number, the output will be close to 1.
If z is a large negative number, the output will be close to 0.
If z=0, the output will be 0.5.

This behavior makes it ideal for binary classification, where we want the model to output a probability (a value between 0 and 1) indicating the likelihood that a particular input belongs to the positive class.

Why It's Useful in Binary Classification:

In binary classification tasks (where the output is either 0 or 1):

The sigmoid function ensures that the model outputs a probability for each class. For example, if the output of the sigmoid is 0.9, it means there’s a 90% chance the input belongs to class 1.
This probability can then be compared to a threshold (usually 0.5) to make the final prediction. If the output is greater than 0.5, the model predicts class 1; otherwise, it predicts class 0.

Example:

Summary:

The sigmoid activation function is used in binary classification tasks to convert the model’s output into a probability between 0 and 1.
It squashes the input into a range of [0, 1], allowing the model to output values that represent probabilities.
The smooth and differentiable nature of the sigmoid function makes it suitable for training models through backpropagation.
It is ideal for problems where the output needs to be interpreted as a probability, especially in simple models like logistic regression or binary classifiers in neural networks.