تابع سیگموئید - ویکی‌پدیا، دانشنامهٔ آزاد

${\displaystyle S(x)={\frac {1}{1+e^{-x}}}={\frac {e^{x}}{e^{x}+1}}=1-S(-x).}$

${\displaystyle \lim _{x\to -\infty }{\frac {1}{1+e^{-x}}}=0}$

${\displaystyle \lim _{x\to +\infty }{\frac {1}{1+e^{-x}}}=1}$

${\displaystyle y'={\cfrac {dy}{dx}}={\frac {e^{-x}}{(1+e^{-x})^{2}}}=y(1-y)}$

${\displaystyle \sigma (x)={\frac {1}{1+e^{-x}}}}$

${\displaystyle tanh(x)={\frac {e^{x}-e^{-x}}{e^{x}+e^{-x}}}}$

${\displaystyle Gompertz(x)=e^{e^{-x}}}$

${\displaystyle ISRU(x)={\frac {x}{\sqrt {1+\alpha x^{2}}}}}$

${\displaystyle ISRLU(x)={\frac {x}{\sqrt {1+\alpha x^{2}}}}\quad {\text{for}}\quad x<0}$

${\displaystyle ISRLU(x)=x\quad {\text{for}}\quad x\geq 0}$