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A sigmoid function is a function whose graph is shaped like the letter S. It could be defined as a differentiable bijection $ f $ from the real numbers to an open interval $ (a,b) $ , with $ \lim_{x\to\infty}f(x)=b\ ,\ \lim_{x\to-\infty} f(x)=a $ .

"The" sigmoid function $ S(x)=\frac{1}{1+e^{-x}} $ , a special case of the logistic function. Other sigmoid functions include arctan and erf.

One application of sigmoid functions is neural networks in AI programming.

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