LogSumExp

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The LogSumExp (LSE) (also called RealSoftMax^[1] or multivariable softplus) function is a smooth maximum – a smooth approximation to the maximum function, mainly used by machine learning algorithms.^[2] It is defined as the logarithm of the sum of the exponentials of the arguments:

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