Sigmoid Activation

What is a Sigmoid Activation Function? Sigmoid Activation Function Explained

The sigmoid activation function, also known as the logistic function, is a widely used activation function in neural networks. It is a smooth, S-shaped function that maps the input values to a range between 0 and 1.

The mathematical form of the sigmoid activation function is:

σ(x) = 1 / (1 + e^(-x))

where σ(x) is the output of the sigmoid function for input x, and e is the base of the natural logarithm.

Key characteristics of the sigmoid activation function:

Range: The sigmoid function outputs values between 0 and 1, which makes it suitable for binary classification problems where the output represents the probability of belonging to a particular class.

Smoothness: The sigmoid function is a smooth and continuous function, which means that small changes in the input result in small changes in the output. This property facilitates gradient-based optimization during neural network training.

Non-linearity: The sigmoid function introduces non-linearity into the neural network, enabling it to learn complex relationships between inputs and outputs. This non-linearity is essential for the network to model and represent non-linear patterns in the data.

Vanishing Gradient: One limitation of the sigmoid function is the vanishing gradient problem, especially in deep neural networks. The gradients of the sigmoid function become very small as the input moves away from the origin, which can hinder the learning process and lead to slow convergence or gradient saturation.

While the sigmoid activation function was popular in the early days of neural networks, it is less commonly used in hidden layers of deep neural networks today. Instead, activation functions like ReLU (Rectified Linear Unit) and its variants are often preferred because they address the vanishing gradient problem and offer better learning properties.

However, the sigmoid activation function is still commonly used in the output layer of binary classification problems, where the goal is to predict probabilities or make binary decisions based on a threshold.

It’s worth noting that when using the sigmoid activation function, careful initialization of network weights and proper tuning of learning rates are important to avoid gradient-related issues and ensure effective learning.