{\displaystyle \mathrm {LSE} (x_{1},\dots ,x_{n})=\log \left(\exp(x_{1})+\cdots +\exp(x_{n})\right).} The LogSumExp function domain is R n {\displaystyle \mathbb...

Boltzmann distribution. Another smooth maximum is LogSumExp: L S E α ( x 1 , … , x n ) = 1 α log ⁡ ∑ i = 1 n exp ⁡ α x i {\displaystyle \mathrm {LSE} _{\alpha...

The multivariable generalization of single-variable softplus is the LogSumExp with the first argument set to zero: L S E 0 + ⁡ ( x 1 , … , x n ) :=...

\mathbb {R} ^{K},} where the LogSumExp function is defined as LSE ⁡ ( z 1 , … , z n ) = log ⁡ ( exp ⁡ ( z 1 ) + ⋯ + exp ⁡ ( z n ) ) {\displaystyle \operatorname...

then the exponential function of Y, X = exp(Y) , has a log-normal distribution. A random variable that is log-normally distributed takes only positive...

(log multiplication), and takes addition to log addition (LogSumExp), giving an isomorphism of semirings between the probability semiring and the log semiring...

The multivariable generalization of single-variable softplus is the LogSumExp with the first argument set to zero: L S E 0 + ⁡ ( x 1 , … , x n ) :=...

operation, logadd (for multiple terms, LogSumExp) can be viewed as a deformation of maximum or minimum. The log semiring has applications in mathematical...

function is a mathematical function denoted by f ( x ) = exp ⁡ ( x ) {\displaystyle f(x)=\exp(x)} or e x {\displaystyle e^{x}} (where the argument x is...

entropy (negentropy) function is convex, and its convex conjugate is LogSumExp. The inspiration for adopting the word entropy in information theory came...