Sigmoidfunktio

The sigmoid function, also known as the logistic function, is a mathematical function that produces an "S"-shaped curve. It is defined by the formula f(x) = 1 / (1 + e^(-x)), where 'e' is the base of the natural logarithm. The output of the sigmoid function is always between 0 and 1, regardless of the input value. As the input approaches positive infinity, the output approaches 1, and as the input approaches negative infinity, the output approaches 0.

This function has found widespread applications in various fields due to its smooth, continuous nature and its ability to map any real-valued number to a value between 0 and 1. In machine learning, the sigmoid function is commonly used as an activation function in artificial neural networks, particularly in binary classification problems. It helps to introduce non-linearity into the network, allowing it to learn complex patterns. The output of a sigmoid neuron can be interpreted as a probability.

Historically, the sigmoid function was also used in statistical modeling, such as logistic regression, to model the probability of a binary outcome. Its characteristic S-shape makes it suitable for representing cumulative distribution functions. Despite its utility, the sigmoid function has some limitations, such as the vanishing gradient problem, where gradients become very small for very large or very small inputs, hindering the learning process in deep neural networks. Other activation functions like ReLU (Rectified Linear Unit) have been developed to address some of these issues.

---