sigmoid function

sigmoid function (plural sigmoid functions)

1. (mathematical analysis, statistics) Any of various real functions whose graph resembles an elongated letter "S"; specifically, the logistic function ${\displaystyle y={\frac {e^{x}}{e^{x}+1}}={\frac {1}{1+e^{-x}}}}$ .
   • 1995, Jun Han, Claudio Moraga, The Influence of the Sigmoid Function Parameters on the Speed of Backpropagation Learning, José Mira, Francisco Sandoval (editors), From Natural to Artificial Neural Computation: International Workshop on Artificial Neural Networks, Proceedings, Springer, LNCS 930, page 195,

     [The] [s]igmoid function is the most commonly known function used in feed forward neural networks because of its nonlinearity and the computational simplicity of its derivative.

   • 2012, Walter Freeman, Neurodynamics: An Exploration in Mesoscopic Brain Dynamics, Springer, page 241,

     The first significant new insight from gamma spatial analysis emerged on re-examination of the sigmoid function representing bilateral saturation.

   • 2016, Roumen Anguelov, Svetoslav Markov, Hausdorff Continuous Interval Functions and Applications, Marco Nehmeier, Jürgen Wolff von Gudenberg, Warwick Tucker (editors), Scientific Computing, Computer Arithmetic, and Validated Numerics: 16th International Symposium, SCAN 2014, Springer, LNCS 9553, page 10,

     Sigmoid functions find multiple applications to neural networks and cell growth population models [14,20]. A sigmoid function on ${\displaystyle \mathbb {R} }$ with a range ${\displaystyle [a,b]}$ is defined as a monotone function ${\displaystyle s(t):\mathbb {R} \to [a,b]}$ such that ${\displaystyle \textstyle \lim _{t\to -\infty }s(t)=a}$ , and ${\displaystyle \textstyle \lim _{t\to \infty }s(t)=b}$ .

• ("S"-shaped function): sigmoid

• logit
• sigma function

• Logistic function on Wikipedia.Wikipedia
• Generalised logistic function on Wikipedia.Wikipedia
• Gompertz function on Wikipedia.Wikipedia
• Cumulative distribution function on Wikipedia.Wikipedia
• Hard sigmoid on Wikipedia.Wikipedia
• S-function on Wikipedia.Wikipedia
• Sigma function on Wikipedia.Wikipedia
• Sigmoid Function on Wolfram MathWorld