ActivationFun

object ActivationFun

The ActivationFun object contains common Activation functions and provides both scalar and vector versions.

See also: en.wikipedia.org/wiki/Activation_function Convention: fun activation function (e.g., sigmoid) funV vector version of activation function (e.g., sigmoidV) funM matrix version of activation function (e.g., sigmoidM) funDV vector version of dervivative (e.g., sigmoidDV) funDM matrix version of dervivative (e.g., sigmoidDM) ------------------------------------------------------------------------------ Supports: id, reLU, tanh, sigmoid, gaussain, softmax Related functions: logistic, logit

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def gaussian(t: Double): Double
Compute the value of the 'gaussian' function at scalar 't'.
Compute the value of the 'gaussian' function at scalar 't'.
t
the gaussian function argument
def gaussianDM(yp: MatriD, tt: MatriD): MatriD
Compute the derivative matrix for 'sigmoid' function at matrix 'yp' where 'yp' is pre-computed by 'yp = gaussianM (tt)'.
Compute the derivative matrix for 'sigmoid' function at matrix 'yp' where 'yp' is pre-computed by 'yp = gaussianM (tt)'.
yp
the derivative function vector argument
tt
the domain value for the function
def gaussianDV(yp: VectoD, tt: VectoD): VectoD
Compute the derivative vector for 'gaussian' function at vector 'yp' where 'yp' is pre-computed by 'yp = gaussianV (tt)'.
Compute the derivative vector for 'gaussian' function at vector 'yp' where 'yp' is pre-computed by 'yp = gaussianV (tt)'.
yp
the derivative function vector argument
tt
the domain value for the function
val gaussianM: FunctionM_2M
val gaussianV: FunctionV_2V
final def getClass(): Class[_]

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def id(t: Double): Double
Compute the value of the identity 'id' function at scalar 't'.
Compute the value of the identity 'id' function at scalar 't'.
t
the id function argument
val idDM: FunctionM_2M
def idDV(yp: VectoD): VectoD
Compute the derivative vector for 'id' function at vector 'yp' where 'yp' is pre-computed by 'yp = idV (tt)'.
Compute the derivative vector for 'id' function at vector 'yp' where 'yp' is pre-computed by 'yp = idV (tt)'.
yp
the derivative function vector argument
def idM(tt: MatriD): MatriD
def idV(tt: VectoD): VectoD
final def isInstanceOf[T0]: Boolean

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def logistic(t: Double, a: Double = 1.0, b: Double = 1.0, c: Double = 1.0): Double
Compute the value of the 'logistic' function at scalar 't'.
Compute the value of the 'logistic' function at scalar 't'. With the default settings, it is identical to 'sigmoid'. Note, it is not typically used as an activation function
t
the logistic function argument
a
the shift parameter (1 => mid at 0, <1 => mid shift left, >= mid shift right
b
the spread parameter (1 => sigmoid rate, <1 => slower than, >1 => faster than) althtough typically positive, a negative b will cause the function to decrease
c
the scale parameter (range is 0 to c)

See also
www.cs.xu.edu/math/math120/01f/logistic.pdf
def logisticV(tt: VectoD, a: Double = 1.0, b: Double = 1.0, c: Double = 1.0): VectoD
def logit(p: Double): Double
Compute the log of the odds of an event occurring (e.g., success, 1).
Compute the log of the odds of an event occurring (e.g., success, 1). The inverse of the 'logit' function is the standard logistic function (sigmoid function). Note, it is not typically used as an activation function
p
the probability, a number between 0 and 1.
val logitV: FunctionV_2V
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def reLU(t: Double): Double
Compute the value of the identity 'reLU' function at scalar 't'.
Compute the value of the identity 'reLU' function at scalar 't'.
t
the id function argument
val reLUDM: FunctionM_2M
def reLUDV(yp: VectoD): VectoD
Compute the derivative vector for 'id' function at vector 'yp' where 'yp' is pre-computed by 'yp = idV (tt)'.
Compute the derivative vector for 'id' function at vector 'yp' where 'yp' is pre-computed by 'yp = idV (tt)'.
yp
the derivative function vector argument
val reLUM: FunctionM_2M
val reLUV: FunctionV_2V
def sigmoid(t: Double): Double
Compute the value of the 'sigmoid' function at 't'.
Compute the value of the 'sigmoid' function at 't'. This is a special case of the logistic function, where 'a = 0' and 'b = 1'. It is also referred to as the standard logistic function. It is also the inverse of the logit function.
t
the sigmoid function argument
val sigmoidDM: FunctionM_2M
def sigmoidDV(yp: VectoD): VectoD
Compute the derivative vector for 'sigmoid' function at vector 'yp' where 'yp' is pre-computed by 'yp = sigmoidV (tt)'.
Compute the derivative vector for 'sigmoid' function at vector 'yp' where 'yp' is pre-computed by 'yp = sigmoidV (tt)'.
yp
the derivative function vector argument
val sigmoidM: FunctionM_2M
val sigmoidV: FunctionV_2V
def softmaxDM(yp: VectoD): MatriD
Compute the derivative vector for 'softmax' function at vector 'yp' where 'yp' is pre-computed by 'yp = softmaxV (tt)'.
Compute the derivative vector for 'softmax' function at vector 'yp' where 'yp' is pre-computed by 'yp = softmaxV (tt)'.
yp
the derivative function vector argument
val softmaxM: FunctionM_2M
def softmaxV(tt: VectoD): VectoD
Compute the vector of values of the 'softmax' function applied to vector 'tt'.
Compute the vector of values of the 'softmax' function applied to vector 'tt'.
tt
the softmax function vector argument

See also
https://en.wikipedia.org/wiki/Softmax_function Note, scalar function version is not needed.
final def synchronized[T0](arg0: ⇒ T0): T0

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val tanhDM: FunctionM_2M
def tanhDV(yp: VectoD): VectoD
Compute the derivative vector for 'tanh' function at vector 'yp' where 'yp' is pre-computed by 'yp = tanhV (tt)'.
Compute the derivative vector for 'tanh' function at vector 'yp' where 'yp' is pre-computed by 'yp = tanhV (tt)'.
yp
the derivative function vector argument
val tanhM: FunctionM_2M
def tanhV(tt: VectoD): VectoD
Compute the vector of values of the 'tanh' function applied to vector 'tt'.
Compute the vector of values of the 'tanh' function applied to vector 'tt'.
tt
the tanh function vector argument
def toString(): String

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def gaussian(t: Double): Double
Compute the value of the 'gaussian' function at scalar 't'.
Compute the value of the 'gaussian' function at scalar 't'.
t
the gaussian function argument
def gaussianDM(yp: MatriD, tt: MatriD): MatriD
Compute the derivative matrix for 'sigmoid' function at matrix 'yp' where 'yp' is pre-computed by 'yp = gaussianM (tt)'.
Compute the derivative matrix for 'sigmoid' function at matrix 'yp' where 'yp' is pre-computed by 'yp = gaussianM (tt)'.
yp
the derivative function vector argument
tt
the domain value for the function
def gaussianDV(yp: VectoD, tt: VectoD): VectoD
Compute the derivative vector for 'gaussian' function at vector 'yp' where 'yp' is pre-computed by 'yp = gaussianV (tt)'.
Compute the derivative vector for 'gaussian' function at vector 'yp' where 'yp' is pre-computed by 'yp = gaussianV (tt)'.
yp
the derivative function vector argument
tt
the domain value for the function
val gaussianM: FunctionM_2M
val gaussianV: FunctionV_2V
final def getClass(): Class[_]

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def id(t: Double): Double
Compute the value of the identity 'id' function at scalar 't'.
Compute the value of the identity 'id' function at scalar 't'.
t
the id function argument
val idDM: FunctionM_2M
def idDV(yp: VectoD): VectoD
Compute the derivative vector for 'id' function at vector 'yp' where 'yp' is pre-computed by 'yp = idV (tt)'.
Compute the derivative vector for 'id' function at vector 'yp' where 'yp' is pre-computed by 'yp = idV (tt)'.
yp
the derivative function vector argument
def idM(tt: MatriD): MatriD
def idV(tt: VectoD): VectoD
final def isInstanceOf[T0]: Boolean

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def logistic(t: Double, a: Double = 1.0, b: Double = 1.0, c: Double = 1.0): Double
Compute the value of the 'logistic' function at scalar 't'.
Compute the value of the 'logistic' function at scalar 't'. With the default settings, it is identical to 'sigmoid'. Note, it is not typically used as an activation function
t
the logistic function argument
a
the shift parameter (1 => mid at 0, <1 => mid shift left, >= mid shift right
b
the spread parameter (1 => sigmoid rate, <1 => slower than, >1 => faster than) althtough typically positive, a negative b will cause the function to decrease
c
the scale parameter (range is 0 to c)

See also
www.cs.xu.edu/math/math120/01f/logistic.pdf
def logisticV(tt: VectoD, a: Double = 1.0, b: Double = 1.0, c: Double = 1.0): VectoD
def logit(p: Double): Double
Compute the log of the odds of an event occurring (e.g., success, 1).
Compute the log of the odds of an event occurring (e.g., success, 1). The inverse of the 'logit' function is the standard logistic function (sigmoid function). Note, it is not typically used as an activation function
p
the probability, a number between 0 and 1.
val logitV: FunctionV_2V
final def ne(arg0: AnyRef): Boolean

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final def notify(): Unit

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def reLU(t: Double): Double
Compute the value of the identity 'reLU' function at scalar 't'.
Compute the value of the identity 'reLU' function at scalar 't'.
t
the id function argument
val reLUDM: FunctionM_2M
def reLUDV(yp: VectoD): VectoD
Compute the derivative vector for 'id' function at vector 'yp' where 'yp' is pre-computed by 'yp = idV (tt)'.
Compute the derivative vector for 'id' function at vector 'yp' where 'yp' is pre-computed by 'yp = idV (tt)'.
yp
the derivative function vector argument
val reLUM: FunctionM_2M
val reLUV: FunctionV_2V
def sigmoid(t: Double): Double
Compute the value of the 'sigmoid' function at 't'.
Compute the value of the 'sigmoid' function at 't'. This is a special case of the logistic function, where 'a = 0' and 'b = 1'. It is also referred to as the standard logistic function. It is also the inverse of the logit function.
t
the sigmoid function argument
val sigmoidDM: FunctionM_2M
def sigmoidDV(yp: VectoD): VectoD
Compute the derivative vector for 'sigmoid' function at vector 'yp' where 'yp' is pre-computed by 'yp = sigmoidV (tt)'.
Compute the derivative vector for 'sigmoid' function at vector 'yp' where 'yp' is pre-computed by 'yp = sigmoidV (tt)'.
yp
the derivative function vector argument
val sigmoidM: FunctionM_2M
val sigmoidV: FunctionV_2V
def softmaxDM(yp: VectoD): MatriD
Compute the derivative vector for 'softmax' function at vector 'yp' where 'yp' is pre-computed by 'yp = softmaxV (tt)'.
Compute the derivative vector for 'softmax' function at vector 'yp' where 'yp' is pre-computed by 'yp = softmaxV (tt)'.
yp
the derivative function vector argument
val softmaxM: FunctionM_2M
def softmaxV(tt: VectoD): VectoD
Compute the vector of values of the 'softmax' function applied to vector 'tt'.
Compute the vector of values of the 'softmax' function applied to vector 'tt'.
tt
the softmax function vector argument

See also
https://en.wikipedia.org/wiki/Softmax_function Note, scalar function version is not needed.
final def synchronized[T0](arg0: ⇒ T0): T0

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val tanhDM: FunctionM_2M
def tanhDV(yp: VectoD): VectoD
Compute the derivative vector for 'tanh' function at vector 'yp' where 'yp' is pre-computed by 'yp = tanhV (tt)'.
Compute the derivative vector for 'tanh' function at vector 'yp' where 'yp' is pre-computed by 'yp = tanhV (tt)'.
yp
the derivative function vector argument
val tanhM: FunctionM_2M
def tanhV(tt: VectoD): VectoD
Compute the vector of values of the 'tanh' function applied to vector 'tt'.
Compute the vector of values of the 'tanh' function applied to vector 'tt'.
tt
the tanh function vector argument
def toString(): String

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ActivationFun 

object ActivationFun

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ActivationFun