\section{Flexible\+Re\+LU$<$ Input\+Data\+Type, Output\+Data\+Type $>$ Class Template Reference} \label{classmlpack_1_1ann_1_1FlexibleReLU}\index{Flexible\+Re\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$@{Flexible\+Re\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$}} The \doxyref{Flexible\+Re\+LU}{p.}{classmlpack_1_1ann_1_1FlexibleReLU} activation function, defined by. \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ Flexible\+Re\+LU} (const double alpha=0) \begin{DoxyCompactList}\small\item\em Create the \doxyref{Flexible\+Re\+LU}{p.}{classmlpack_1_1ann_1_1FlexibleReLU} object using the specified parameters. \end{DoxyCompactList}\item double const \& \textbf{ Alpha} () const \begin{DoxyCompactList}\small\item\em Get the parameter controlling the range of the relu function. \end{DoxyCompactList}\item double \& \textbf{ Alpha} () \begin{DoxyCompactList}\small\item\em Modify the parameter controlling the range of the relu function. \end{DoxyCompactList}\item {\footnotesize template$<$typename Data\+Type $>$ }\\void \textbf{ Backward} (const Data\+Type \&input, const Data\+Type \&gy, Data\+Type \&g) \begin{DoxyCompactList}\small\item\em Ordinary feed backward pass of a neural network, calculating the function f(x) by propagating x backwards through f. \end{DoxyCompactList}\item Output\+Data\+Type const \& \textbf{ Delta} () const \begin{DoxyCompactList}\small\item\em Get the delta. \end{DoxyCompactList}\item Output\+Data\+Type \& \textbf{ Delta} () \begin{DoxyCompactList}\small\item\em Modify the delta. \end{DoxyCompactList}\item {\footnotesize template$<$typename Input\+Type , typename Output\+Type $>$ }\\void \textbf{ Forward} (const Input\+Type \&input, Output\+Type \&output) \begin{DoxyCompactList}\small\item\em Ordinary feed forward pass of a neural network, evaluating the function f(x) by propagating the activity forward through f. \end{DoxyCompactList}\item {\footnotesize template$<$typename eT $>$ }\\void \textbf{ Gradient} (const arma\+::\+Mat$<$ eT $>$ \&input, const arma\+::\+Mat$<$ eT $>$ \&error, arma\+::\+Mat$<$ eT $>$ \&gradient) \begin{DoxyCompactList}\small\item\em Calculate the gradient using the output delta and the input activation. \end{DoxyCompactList}\item Output\+Data\+Type const \& \textbf{ Gradient} () const \begin{DoxyCompactList}\small\item\em Get the gradient. \end{DoxyCompactList}\item Output\+Data\+Type \& \textbf{ Gradient} () \begin{DoxyCompactList}\small\item\em Modify the gradient. \end{DoxyCompactList}\item Output\+Data\+Type const \& \textbf{ Output\+Parameter} () const \begin{DoxyCompactList}\small\item\em Get the output parameter. \end{DoxyCompactList}\item Output\+Data\+Type \& \textbf{ Output\+Parameter} () \begin{DoxyCompactList}\small\item\em Modify the output parameter. \end{DoxyCompactList}\item Output\+Data\+Type const \& \textbf{ Parameters} () const \begin{DoxyCompactList}\small\item\em Get the parameters. \end{DoxyCompactList}\item Output\+Data\+Type \& \textbf{ Parameters} () \begin{DoxyCompactList}\small\item\em Modify the parameters. \end{DoxyCompactList}\item void \textbf{ Reset} () \begin{DoxyCompactList}\small\item\em Reset the layer parameter. \end{DoxyCompactList}\item {\footnotesize template$<$typename Archive $>$ }\\void \textbf{ serialize} (Archive \&ar, const unsigned int) \begin{DoxyCompactList}\small\item\em Serialize the layer. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} \subsubsection*{template$<$typename Input\+Data\+Type = arma\+::mat, typename Output\+Data\+Type = arma\+::mat$>$\newline class mlpack\+::ann\+::\+Flexible\+Re\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$} The \doxyref{Flexible\+Re\+LU}{p.}{classmlpack_1_1ann_1_1FlexibleReLU} activation function, defined by. \begin{eqnarray*} f(x) &=& \max(0,x)+alpha \\ f'(x) &=& \left\{ \begin{array}{lr} 1 & : x > 0 \\ 0 & : x \le 0 \end{array} \right. \end{eqnarray*} For more information, read the following paper\+: \begin{DoxyCode} @article\{Qiu2018, author = \{Suo Qiu, Xiangmin Xu and Bolun Cai\}, title = \{FReLU: Flexible Rectified Linear Units \textcolor{keywordflow}{for} Improving Convolutional Neural Networks\} journal = \{arxiv preprint\}, URL = \{https:\textcolor{comment}{//arxiv.org/abs/1706.08098\},} year = \{2018\} \} \end{DoxyCode} \begin{DoxyTemplParams}{Template Parameters} {\em Input\+Data\+Type} & Type of the input data (arma\+::colvec, arma\+::mar, arma\+::sp\+\_\+mat or arma\+::cube) \\ \hline {\em Output\+Data\+Type} & Type of the output data (arma\+::colvec, arma\+::mat, arma\+::sp\+\_\+mat or arma\+::cube) \\ \hline \end{DoxyTemplParams} Definition at line 59 of file flexible\+\_\+relu.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a76fe1c4417c6044ce1275ba7fd9afc76}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Flexible\+Re\+LU@{Flexible\+Re\+LU}} \index{Flexible\+Re\+LU@{Flexible\+Re\+LU}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Flexible\+Re\+L\+U()} {\footnotesize\ttfamily \textbf{ Flexible\+Re\+LU} (\begin{DoxyParamCaption}\item[{const double}]{alpha = {\ttfamily 0} }\end{DoxyParamCaption})} Create the \doxyref{Flexible\+Re\+LU}{p.}{classmlpack_1_1ann_1_1FlexibleReLU} object using the specified parameters. The non zero parameter can be adjusted by specifying the parameter alpha which controls the range of the relu function. (Default alpha = 0) This parameter is trainable. \begin{DoxyParams}{Parameters} {\em alpha} & Parameter for adjusting the range of the relu function. \\ \hline \end{DoxyParams} \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a21679485637bdec3078ec74d71572980}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Alpha@{Alpha}} \index{Alpha@{Alpha}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Alpha()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double const\& Alpha (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the parameter controlling the range of the relu function. Definition at line 134 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_acbb0e4747a3a307bee88bad71e5eeaf1}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Alpha@{Alpha}} \index{Alpha@{Alpha}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Alpha()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double\& Alpha (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the parameter controlling the range of the relu function. Definition at line 136 of file flexible\+\_\+relu.\+hpp. References Flexible\+Re\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$\+::serialize(). \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_aef8c56f1f8624bd006afec8b3bcda9d6}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Backward@{Backward}} \index{Backward@{Backward}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Backward()} {\footnotesize\ttfamily void Backward (\begin{DoxyParamCaption}\item[{const Data\+Type \&}]{input, }\item[{const Data\+Type \&}]{gy, }\item[{Data\+Type \&}]{g }\end{DoxyParamCaption})} Ordinary feed backward pass of a neural network, calculating the function f(x) by propagating x backwards through f. Using the results from the feed forward pass. \begin{DoxyParams}{Parameters} {\em input} & The propagated input activation. \\ \hline {\em gy} & The backpropagated error. \\ \hline {\em g} & The calculated gradient. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a797f7edb44dd081e5e2b3cc316eef6bd}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Delta@{Delta}} \index{Delta@{Delta}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Delta()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily Output\+Data\+Type const\& Delta (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the delta. Definition at line 124 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_ad6601342d560219ce951d554e69e5e87}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Delta@{Delta}} \index{Delta@{Delta}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Delta()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily Output\+Data\+Type\& Delta (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the delta. Definition at line 126 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a09440df0a90bdcc766e56e097d91205b}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Forward@{Forward}} \index{Forward@{Forward}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Forward()} {\footnotesize\ttfamily void Forward (\begin{DoxyParamCaption}\item[{const Input\+Type \&}]{input, }\item[{Output\+Type \&}]{output }\end{DoxyParamCaption})} Ordinary feed forward pass of a neural network, evaluating the function f(x) by propagating the activity forward through f. \begin{DoxyParams}{Parameters} {\em input} & Input data used for evaluating the specified function. \\ \hline {\em output} & Resulting output activation. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_aaf577db350e2130754490d8486fba215}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Gradient@{Gradient}} \index{Gradient@{Gradient}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Gradient()\hspace{0.1cm}{\footnotesize\ttfamily [1/3]}} {\footnotesize\ttfamily void Gradient (\begin{DoxyParamCaption}\item[{const arma\+::\+Mat$<$ eT $>$ \&}]{input, }\item[{const arma\+::\+Mat$<$ eT $>$ \&}]{error, }\item[{arma\+::\+Mat$<$ eT $>$ \&}]{gradient }\end{DoxyParamCaption})} Calculate the gradient using the output delta and the input activation. \begin{DoxyParams}{Parameters} {\em input} & The input parameter used for calculating the gradient. \\ \hline {\em error} & The calculated error. \\ \hline {\em gradient} & The calculated gradient. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a0f1f4e6d93472d83852731a96c8c3f59}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Gradient@{Gradient}} \index{Gradient@{Gradient}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Gradient()\hspace{0.1cm}{\footnotesize\ttfamily [2/3]}} {\footnotesize\ttfamily Output\+Data\+Type const\& Gradient (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the gradient. Definition at line 129 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a19abce4739c3b0b658b612537e21956a}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Gradient@{Gradient}} \index{Gradient@{Gradient}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Gradient()\hspace{0.1cm}{\footnotesize\ttfamily [3/3]}} {\footnotesize\ttfamily Output\+Data\+Type\& Gradient (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the gradient. Definition at line 131 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a0ee21c2a36e5abad1e7a9d5dd00849f9}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Output\+Parameter@{Output\+Parameter}} \index{Output\+Parameter@{Output\+Parameter}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Output\+Parameter()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily Output\+Data\+Type const\& Output\+Parameter (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the output parameter. Definition at line 119 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a21d5f745f02c709625a4ee0907f004a5}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Output\+Parameter@{Output\+Parameter}} \index{Output\+Parameter@{Output\+Parameter}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Output\+Parameter()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily Output\+Data\+Type\& Output\+Parameter (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the output parameter. Definition at line 121 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_aa530552c7ef915c952fbacc77b965c90}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Parameters@{Parameters}} \index{Parameters@{Parameters}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Parameters()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily Output\+Data\+Type const\& Parameters (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the parameters. Definition at line 114 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a9c5c5900772a689d5a6b59778ec67120}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Parameters@{Parameters}} \index{Parameters@{Parameters}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Parameters()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily Output\+Data\+Type\& Parameters (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the parameters. Definition at line 116 of file flexible\+\_\+relu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_a372de693ad40b3f42839c8ec6ac845f4}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!Reset@{Reset}} \index{Reset@{Reset}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{Reset()} {\footnotesize\ttfamily void Reset (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})} Reset the layer parameter. \mbox{\label{classmlpack_1_1ann_1_1FlexibleReLU_af0dd9205158ccf7bcfcd8ff81f79c927}} \index{mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}!serialize@{serialize}} \index{serialize@{serialize}!mlpack\+::ann\+::\+Flexible\+Re\+LU@{mlpack\+::ann\+::\+Flexible\+Re\+LU}} \subsubsection{serialize()} {\footnotesize\ttfamily void serialize (\begin{DoxyParamCaption}\item[{Archive \&}]{ar, }\item[{const unsigned}]{int }\end{DoxyParamCaption})} Serialize the layer. Referenced by Flexible\+Re\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$\+::\+Alpha(). The documentation for this class was generated from the following file\+:\begin{DoxyCompactItemize} \item /var/www/mlpack.\+ratml.\+org/mlpack.\+org/\+\_\+src/mlpack-\/3.\+3.\+1/src/mlpack/methods/ann/layer/\textbf{ flexible\+\_\+relu.\+hpp}\end{DoxyCompactItemize}