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The softmax function, also known as softargmax or normalized exponential function, is a generalization of the logistic function to multiple dimensions. It is used in multinomial logistic regression and is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes, based on Luce's choice axiom. The standard (unit) softmax function is defined when is greater than one by the formula In some fields, the base is fixed, corresponding to a fixed scale, while in others the parameter β is varied.

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rdf:type	Thing
rdfs:label	Softmax function (en)
rdfs:comment	The softmax function, also known as softargmax or normalized exponential function, is a generalization of the logistic function to multiple dimensions. It is used in multinomial logistic regression and is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes, based on Luce's choice axiom. The standard (unit) softmax function is defined when is greater than one by the formula In some fields, the base is fixed, corresponding to a fixed scale, while in others the parameter β is varied. (en)
rdfs:seeAlso	Arg max
sameAs	Softmax function Softmax function
dbp:wikiPageUsesTemplate	dbt:About dbt:Efn dbt:Harvtxt dbt:Math dbt:Mvar dbt:Notelist dbt:Quote dbt:Reflist dbt:Rp dbt:See_also dbt:Sfn dbt:Tmath dbt:Differentiable_computing
Subject	Articles with example Julia code Articles with example Python (programming language) code Articles with example R code Artificial neural networks Computational neuroscience Exponentials Functions and mappings Logistic regression
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Softmax_function?oldid=1065998663&ns=0
Wikipage page ID	6152185 (xsd:integer)
page length (characters) of wiki page	26264 (xsd:nonNegativeInteger)
Wikipage revision ID	1065998663 (xsd:integer)
has abstract	The softmax function, also known as softargmax or normalized exponential function, is a generalization of the logistic function to multiple dimensions. It is used in multinomial logistic regression and is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes, based on Luce's choice axiom. The softmax function takes as input a vector z of K real numbers, and normalizes it into a probability distribution consisting of K probabilities proportional to the exponentials of the input numbers. That is, prior to applying softmax, some vector components could be negative, or greater than one; and might not sum to 1; but after applying softmax, each component will be in the interval , and the components will add up to 1, so that they can be interpreted as probabilities. Furthermore, the larger input components will correspond to larger probabilities. The standard (unit) softmax function is defined when is greater than one by the formula In simple words, it applies the standard exponential function to each element of the input vector and normalizes these values by dividing by the sum of all these exponentials; this normalization ensures that the sum of the components of the output vector is 1. Instead of e, a different base b > 0 can be used. If 0 < b < 1, smaller input components will result in larger output probabilities, and decreasing the value of b will create probability distributions that are more concentrated around the positions of the smallest input values. Conversely, if b > 1, larger input components will result in larger output probabilities, and increasing the value of b will create probability distributions that are more concentrated around the positions of the largest input values. Writing or (for real β) yields the expressions: In some fields, the base is fixed, corresponding to a fixed scale, while in others the parameter β is varied. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Softmax_function
is Wikipage redirect of	Normalized exponential Softargmax Softmax activation function Softmax function in statistical mechanics
is Link from a Wikipage to another Wikipage of	LogSumExp Log semiring Logistic function Logistic regression Activation function Artificial neural network Attention (machine learning) Backpropagation Boltzmann distribution Normalized exponential Bregman divergence Capsule neural network Categorical distribution Boltzmann distribution Differentiable neural computer Naive Bayes classifier Compositional data Conformal prediction Connectionist temporal classification Convolutional neural network Darkforest Exponential family Fairness (machine learning) Luce's choice axiom Ludwig Boltzmann Knowledge distillation Mathematics of artificial neural networks Multi-armed bandit Multiclass classification Multinomial logistic regression Neighbourhood components analysis
is known for of	Ludwig Boltzmann

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