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Smooth approximation to the maximum function
The LogSumExp (LSE) (also called RealSoftMax or multivariable softplus) function is a smooth maximum – a smooth approximation to the maximum function
LogSumExp
Smoothed ramp function
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 ) :=
Softplus
Mathematical approximation
engineering. LogSumExp and Mellowmax are the same function differing by a constant log n α {\displaystyle {\frac {\log {n}}{\alpha }}} . LogSumExp is always
Smooth_maximum
Smooth approximation of one-hot arg max
maximum function). The term "softmax" is also used for the closely related LogSumExp function, which is a smooth maximum. For this reason, some prefer the
Softmax_function
Mathematical function, inverse of an exponential function
to addition (log multiplication), and takes addition to log addition (LogSumExp), giving an isomorphism of semirings between the probability semiring
Logarithm
Type of activation function
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 ) :=
Rectified_linear_unit
Measure of distance to normality
function, in physics interpreted as free entropy) is the convex conjugate of LogSumExp (in physics interpreted as the free energy). In 1953, Léon Brillouin derived
Negentropy
Average uncertainty in variable's states
entropy (negentropy) function is convex, and its convex conjugate is LogSumExp. The inspiration for adopting the word entropy in information theory came
Entropy_(information_theory)
Semiring arising in tropical analysis
semiring. Notably, the addition operation, logadd (for multiple terms, LogSumExp) can be viewed as a deformation of maximum or minimum. The log-semiring
Log_semiring
Logarithmic number system Logarithmic scale Logarithmic spiral Logit LogSumExp Mantissa is a disambiguation page; see common logarithm for the traditional
Index_of_logarithm_articles
S-shaped curve
of max ( x 0 , x 1 ) {\displaystyle \max(x_{0},x_{1})} , specifically LogSumExp. Softplus thus generalizes as (note the 0 and the corresponding 1 for
Logistic_function
Generalization of addition, multiplication, exponentiation, tetration, etc.
{\displaystyle F_{0}(a,b)=\ln \left(e^{a}+e^{b}\right)} Smooth maximum (LogSumExp) 1 F 1 ( a , b ) = a + b {\displaystyle F_{1}(a,b)=a+b} 2 F 2 ( a , b
Hyperoperation
Generalization of means
mean in the log semiring, which is a constant-shifted version of the LogSumExp (LSE) function (which is the logarithmic sum), M f ( x 1 , … ,
Quasi-arithmetic_mean
Real function with secant line between points above the graph itself
\infty )} , because of the singularity at x = 0. {\displaystyle x=0.} LogSumExp function, also called softmax function, is a convex function. The function
Convex_function
Iterative simulation method
D(x^{i}-c_{\alpha }(x))\,B^{i}.} If one can employ an efficient implementation of the LogSumExp functions, this can be beneficial for numerical stability of the consensus
Consensus_based_optimization
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Boy/Male
British, English, German, Norwegian, Swedish
Wolf; Messenger Wolf
Girl/Female
Indian
Pure
Girl/Female
Hindu, Indian
Bird Sound
Boy/Male
British, English
Mortal
Surname or Lastname
English
English : habitational name from places in Oxfordshire and Shropshire, so named with Old English burh ‘stronghold’, ‘fortified manor’ + ford ‘ford’.
Male
English
English unisex name derived from the vocabulary word, "spirit," from Latin spiritus, SPIRIT means "breath."
Girl/Female
Hindu, Indian
Pretty
Girl/Female
Muslim/Islamic
Beautiful
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Tamil, Telugu, Traditional
Bravery; The Sun of Valour; Lord Hanuman; Praiseworthy; Record; Strong Strong; One who Continue Progress
Boy/Male
Tamil
Being near name of the river
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