Soft thresholding

$$\mathrm{soft}(x,T) := \begin{cases} x + T & x \leq -T \\ 0 & |x| \leq T \\ x - T & x \geq T \end{cases}$$

See also:

• https://en.wikipedia.org/wiki/LogSumExp
• https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#Softplus