Softplus
Smooth positive-space transform used as an alternative to log.
Parameters
This transform has no parameters.
Transformation
\[
x \in (0,\infty) \mapsto y = \log(e^x - 1) \in \mathbb{R}
\]
\[
y \in \mathbb{R} \mapsto x = \log(1 + e^y) \in (0,\infty)
\]