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LogSumExp

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

Measurement, Properties & Log-sum-exp trick for log-domain calculations

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Properties

DomainReal coordinate spaceReal lineInequalityConvex
14 related topics

Log-sum-exp trick for log-domain calculations

Logarithmic scaleLog probabilityIT++
3 related topics

A strictly convex log-sum-exp type function

DifferentiableTropical analysisLog semiring
3 related topics

Overview

SoftplusFunctionSmooth maximumSmoothApproximation
9 related topics

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Properties

Log-sum-exp trick for log-domain calculations

A strictly convex log-sum-exp type function

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LogSumExp

Nodes34
Edges33
Triples13
Avg. degree1.94
Density0.058824
Components1

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LogSumExp

Top relations

related to Properties · 11
LogSumExp → Applying, Consider, In, It, Let, LSE, Proof, Replace, The, The LogSumExp, Then
is a · 1
LogSumExp → softmax function.The convex conjugate of LogSumExp is the negative entropy. log-sum-exp trick for log-domain calculationsThe LSE function is often encountered when the usual ari…

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Important terminology

lse displaystyle log function mathrm dots convex max exp strictly leq sum also maximum approximation frac tx domain inequality smooth

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SubjectPredicateObjectConfidenceSrc
LogSumExpis asoftmax function.The convex conjugate of LogSumExp is the negative entropy. log-sum-exp trick for log-domain calculationsThe LSE function is often encountered when the usual ari…0.90text
ITinstance ofMany math libraries0.80text
LogSumExprelated to PropertiesThe LogSumExp0.60section
LogSumExprelated to PropertiesIt0.60section
LogSumExprelated to PropertiesLSE0.60section
LogSumExprelated to PropertiesThe0.60section
LogSumExprelated to PropertiesProof0.60section
LogSumExprelated to PropertiesLet0.60section
LogSumExprelated to PropertiesThen0.60section
LogSumExprelated to PropertiesApplying0.60section
LogSumExprelated to PropertiesIn0.60section
LogSumExprelated to PropertiesConsider0.60section

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    Min side: 3
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