LogSumExp

The LogSumExp (LSE) (also called RealSoftMax or multivariable softplus) function is a smooth maximum – a smoothapproximation to the maximum function, mainly used by machine learning algorithms. It is defined as the logarithm of the sum of the exponentials of the arguments:

$${\displaystyle \mathrm {LSE} (x_{1},\dots ,x_{n})=\log \left(\exp(x_{1})+\cdots +\exp(x_{n}) ight).}$$