NeuroCharter: A Neural Networks Software to Visually Discover the Effects and Contributions between Interrelated Features

Figures & Tables

Different activation functions available in the NeuroCharter program.

Name	Formula	Derivative
Sigmoid	$f (x) = 1 / 1 + e^{- x}$	$f^{'} (x) = f (x) \times (1 - f (x))$
Softmax	$\begin{array}{l} s = e^{x - \max {(x_{i})}_{i = 1}^{n}} \\ f (x) = s / \sum_{i = 1}^{n} s_{i} \end{array}$	$f^{'} (x) = f (x) \times (1 - f (x))$
Binary	$f (x) = {\begin{matrix} 0 & x < 0 \\ 1 & x \geq 0 \end{matrix}$	$f^{'} (x) = {\begin{matrix} 0 & x \neq 0 \\ \infty & x = 0 \end{matrix}$
Soft sign	$f (x) = x / (1 + \| x \|)$	$f^{'} (x) = 1 / {(1 + \| x \|)}^{2}$
Bent identity	$f (x) = x + 0.5 (\sqrt{x^{2} + 1} - 1)$	$f^{'} (x) = 1 + 0.5 x / \sqrt{x^{2} + 1}$
Gaussian	$f (x) = e^{- x^{2}}$	$f (x) = e^{- x^{2}}$
Tanh	$f (x) = 2 / 1 + e^{- 2 x} - 1$	$f^{'} (x) = 1 - f {(x)}^{2}$
Linear	$f (x) = x$	$f^{'} (x) = 1$
Arctan	$f (x) = Atn (x)$	$f^{'} (x) = 1 / (1 + x^{2})$
Sinusoid	$f (x) = \sin (x)$	$f^{'} (x) = \cos (x)$
Soft plus	$f (x) = \ln (1 + e^{x})$	$f^{'} (x) = 1 / (1 + e^{x})$
Sinc	$f (x) = {\begin{matrix} \sin (x) / x & x \neq 0 \\ 1 & x = 0 \end{matrix}$	$f^{'} (x) = {\begin{matrix} (\cos (x) - \sin (x) / x) / x & x \neq 0 \\ 0 & x = 0 \end{matrix}$