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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
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
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
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
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
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)
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 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
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
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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Girl/Female
Arabic, Muslim
Ardent; Longing
Boy/Male
Indian, Sanskrit
Sport
Girl/Female
Muslim
Guest, Helper, Assistant, Shining, Luminous
Boy/Male
Arabic, Muslim
Founder King of Rome
Surname or Lastname
English
English : habitational name from places so named in Devon, Hertfordshire, and Wiltshire. The first two were named with Old English sand ‘sand’ + hrycg ‘ridge’.
Boy/Male
Hindu, Indian, Malayalam, Telugu
A Name of Four Vedas; Holistic in Speech and Deed
Girl/Female
Biblical
An answer, their affliction.
Girl/Female
Indian
Lord Vishnu
Boy/Male
Muslim
Crown of religion
Boy/Male
Hindu
Matchless
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