The sigmoid function is a mathematical function that has an "S"-shaped curve (hence the name "sigmoid," derived from the Greek letter sigma). It is often used in statistics, machine learning, and artificial neural networks due to its property of mapping any real-valued input to an output in the range of 0 to 1.
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A sigmoid function has an S-shaped graph, typically increasing between finite lower and upper limits. The standard logistic function, often called the sigmoid in neural networks, isThe hyperbolic tangent is another sigmoid: . Thus sigmoid names a broader family than the logistic formula alone. Logistic outputs lie in and can represent a binary classification probability, but using this activation function alone does not ensure that the fitted probabilities are calibrated. Its derivative tends to zero in both tails, one mechanism behind the vanishing gradient problem.