\section{E\+LU$<$ Input\+Data\+Type, Output\+Data\+Type $>$ Class Template Reference} \label{classmlpack_1_1ann_1_1ELU}\index{E\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$@{E\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$}} The \doxyref{E\+LU}{p.}{classmlpack_1_1ann_1_1ELU} activation function, defined by. \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ E\+LU} () \begin{DoxyCompactList}\small\item\em Create the \doxyref{E\+LU}{p.}{classmlpack_1_1ann_1_1ELU} object. \end{DoxyCompactList}\item \textbf{ E\+LU} (const double alpha) \begin{DoxyCompactList}\small\item\em Create the \doxyref{E\+LU}{p.}{classmlpack_1_1ann_1_1ELU} object using the specified parameter. \end{DoxyCompactList}\item double const \& \textbf{ Alpha} () const \begin{DoxyCompactList}\small\item\em Get the non zero gradient. \end{DoxyCompactList}\item double \& \textbf{ Alpha} () \begin{DoxyCompactList}\small\item\em Modify the non zero gradient. \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 bool \textbf{ Deterministic} () const \begin{DoxyCompactList}\small\item\em Get the value of deterministic parameter. \end{DoxyCompactList}\item bool \& \textbf{ Deterministic} () \begin{DoxyCompactList}\small\item\em Modify the value of deterministic parameter. \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 double const \& \textbf{ Lambda} () const \begin{DoxyCompactList}\small\item\em Get the lambda parameter. \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 {\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\+::\+E\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$} The \doxyref{E\+LU}{p.}{classmlpack_1_1ann_1_1ELU} activation function, defined by. \begin{eqnarray*} f(x) &=& \left\{ \begin{array}{lr} x & : x > 0 \\ \alpha(e^x - 1) & : x \le 0 \end{array} \right. \\ f'(x) &=& \left\{ \begin{array}{lr} 1 & : x > 0 \\ f(x) + \alpha & : x \le 0 \end{array} \right. \end{eqnarray*} For more information, read the following paper\+: \begin{DoxyCode} @article\{Clevert2015, author = \{Djork\{-\}Arn\{\(\backslash\)\textcolor{stringliteral}{'\{e\}\} Clevert and Thomas Unterthiner and} \textcolor{stringliteral}{ Sepp Hochreiter\},} \textcolor{stringliteral}{ title = \{Fast and Accurate Deep Network Learning by Exponential Linear} \textcolor{stringliteral}{ Units (ELUs)\},} \textcolor{stringliteral}{ journal = \{CoRR\},} \textcolor{stringliteral}{ year = \{2015\},} \textcolor{stringliteral}{ url = \{https://arxiv.org/abs/1511.07289\}} \textcolor{stringliteral}{\}} \end{DoxyCode} The S\+E\+LU activation function is defined by \begin{eqnarray*} f(x) &=& \left\{ \begin{array}{lr} \lambda * x & : x > 0 \\ \lambda * \alpha(e^x - 1) & : x \le 0 \end{array} \right. \\ f'(x) &=& \left\{ \begin{array}{lr} \lambda & : x > 0 \\ f(x) + \lambda * \alpha & : x \le 0 \end{array} \right. \end{eqnarray*} For more information, read the following paper\+: \begin{DoxyCode} @article\{Klambauer2017, author = \{Gunter Klambauer and Thomas Unterthiner and Andreas Mayr\}, title = \{Self-Normalizing Neural Networks\}, journal = \{Advances in Neural Information Processing Systems\}, year = \{2017\}, url = \{https:\textcolor{comment}{//arxiv.org/abs/1706.02515\}} \} \end{DoxyCode} In the deterministic mode, there is no computation of the derivative. \begin{DoxyNote}{Note} During training deterministic should be set to false and during testing/inference deterministic should be set to true. Make sure to use S\+E\+LU activation function with normalized inputs and weights initialized with Lecun Normal Initialization. \end{DoxyNote} \begin{DoxyTemplParams}{Template Parameters} {\em Input\+Data\+Type} & Type of the input data (arma\+::colvec, arma\+::mat, 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 111 of file elu.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1ann_1_1ELU_ac74bf903a3d27e91aaf80e59e3812624}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!E\+LU@{E\+LU}} \index{E\+LU@{E\+LU}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}} \subsubsection{E\+L\+U()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily \textbf{ E\+LU} (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})} Create the \doxyref{E\+LU}{p.}{classmlpack_1_1ann_1_1ELU} object. N\+O\+TE\+: Use this constructor for S\+E\+LU activation function. \mbox{\label{classmlpack_1_1ann_1_1ELU_a2be97a9ea26474ca497b24ac1b1a9323}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!E\+LU@{E\+LU}} \index{E\+LU@{E\+LU}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}} \subsubsection{E\+L\+U()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily \textbf{ E\+LU} (\begin{DoxyParamCaption}\item[{const double}]{alpha }\end{DoxyParamCaption})} Create the \doxyref{E\+LU}{p.}{classmlpack_1_1ann_1_1ELU} object using the specified parameter. The non zero gradient for negative inputs can be adjusted by specifying the \doxyref{E\+LU}{p.}{classmlpack_1_1ann_1_1ELU} hyperparameter alpha (alpha $>$ 0). \begin{DoxyNote}{Note} Use this constructor for \doxyref{E\+LU}{p.}{classmlpack_1_1ann_1_1ELU} activation function. \end{DoxyNote} \begin{DoxyParams}{Parameters} {\em alpha} & Scale parameter for the negative factor. \\ \hline \end{DoxyParams} \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1ann_1_1ELU_a21679485637bdec3078ec74d71572980}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Alpha@{Alpha}} \index{Alpha@{Alpha}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+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 non zero gradient. Definition at line 164 of file elu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1ELU_acbb0e4747a3a307bee88bad71e5eeaf1}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Alpha@{Alpha}} \index{Alpha@{Alpha}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+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 non zero gradient. Definition at line 166 of file elu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1ELU_aef8c56f1f8624bd006afec8b3bcda9d6}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Backward@{Backward}} \index{Backward@{Backward}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+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 f(x). \\ \hline {\em gy} & The backpropagated error. \\ \hline {\em g} & The calculated gradient. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1ann_1_1ELU_a797f7edb44dd081e5e2b3cc316eef6bd}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Delta@{Delta}} \index{Delta@{Delta}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+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 159 of file elu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1ELU_ad6601342d560219ce951d554e69e5e87}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Delta@{Delta}} \index{Delta@{Delta}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+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 161 of file elu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1ELU_a9f4103707f4d199ce5594d239b60443e}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Deterministic@{Deterministic}} \index{Deterministic@{Deterministic}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}} \subsubsection{Deterministic()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily bool Deterministic (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the value of deterministic parameter. Definition at line 169 of file elu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1ELU_a42d4ee3da432cff20d3a41b8b1ec801c}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Deterministic@{Deterministic}} \index{Deterministic@{Deterministic}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}} \subsubsection{Deterministic()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily bool\& Deterministic (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the value of deterministic parameter. Definition at line 171 of file elu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1ELU_a09440df0a90bdcc766e56e097d91205b}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Forward@{Forward}} \index{Forward@{Forward}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+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_1ELU_acb669457ad59e62d0fccc5bae3a6c35e}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Lambda@{Lambda}} \index{Lambda@{Lambda}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}} \subsubsection{Lambda()} {\footnotesize\ttfamily double const\& Lambda (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the lambda parameter. Definition at line 174 of file elu.\+hpp. References E\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$\+::serialize(). \mbox{\label{classmlpack_1_1ann_1_1ELU_a0ee21c2a36e5abad1e7a9d5dd00849f9}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Output\+Parameter@{Output\+Parameter}} \index{Output\+Parameter@{Output\+Parameter}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+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 154 of file elu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1ELU_a21d5f745f02c709625a4ee0907f004a5}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!Output\+Parameter@{Output\+Parameter}} \index{Output\+Parameter@{Output\+Parameter}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+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 156 of file elu.\+hpp. \mbox{\label{classmlpack_1_1ann_1_1ELU_af0dd9205158ccf7bcfcd8ff81f79c927}} \index{mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}!serialize@{serialize}} \index{serialize@{serialize}!mlpack\+::ann\+::\+E\+LU@{mlpack\+::ann\+::\+E\+LU}} \subsubsection{serialize()} {\footnotesize\ttfamily void serialize (\begin{DoxyParamCaption}\item[{Archive \&}]{ar, }\item[{const unsigned}]{int }\end{DoxyParamCaption})} Serialize the layer. Referenced by E\+L\+U$<$ Input\+Data\+Type, Output\+Data\+Type $>$\+::\+Lambda(). 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.\+2/src/mlpack/methods/ann/layer/\textbf{ elu.\+hpp}\end{DoxyCompactItemize}