{\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...
7 KB (1,152 words) - 17:21, 23 June 2024
Smooth maximum (section LogSumExp)
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...
6 KB (1,073 words) - 08:38, 6 July 2023
\mathbb {R} ^{K},} where the LogSumExp function is defined as LSE ( z 1 , … , z n ) = log ( exp ( z 1 ) + ⋯ + exp ( z n ) ) {\displaystyle \operatorname...
30 KB (4,737 words) - 14:25, 25 September 2024
then the exponential function of Y, X = exp(Y) , has a log-normal distribution. A random variable which is log-normally distributed takes only positive...
80 KB (11,823 words) - 06:13, 28 September 2024
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 ) :=...
17 KB (2,281 words) - 21:10, 5 August 2024
Logarithm (redirect from Log (mathematics))
(log multiplication), and takes addition to log addition (LogSumExp), giving an isomorphism of semirings between the probability semiring and the log semiring...
98 KB (11,600 words) - 17:00, 28 September 2024
operation, logadd (for multiple terms, LogSumExp) can be viewed as a deformation of maximum or minimum. The log semiring has applications in mathematical...
6 KB (1,025 words) - 22:15, 28 March 2023
Exponential function (redirect from Exp(x))
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...
44 KB (5,755 words) - 20:15, 23 September 2024
entropy (negentropy) function is convex, and its convex conjugate is LogSumExp. The inspiration for adopting the word entropy in information theory came...
70 KB (10,018 words) - 14:58, 13 September 2024