Github user njayaram2 commented on a diff in the pull request:

    https://github.com/apache/incubator-madlib/pull/162#discussion_r132340750
  
    --- Diff: doc/design/modules/neural-network.tex ---
    @@ -197,3 +207,44 @@ \subsubsection{The $\mathit{Gradient}$ Function}
         \State \Return $\delta$
     \end{algorithmic}
     \end{algorithm}
    +
    +\begin{algorithm}[mlp-train-iteration$(X, Y, \eta)$] 
\label{alg:mlp-train-iteration}
    +\alginput{
    +start vectors $X_{i...m} \in \mathbb{R}^{n_0}$,\\
    +end vectors $Y_{i...m} \in \mathbb{R}^{n_N}$,\\
    +learning rate $\eta$,\\}
    +\algoutput{Coefficients $u = \{ u_{k-1}^{sj} \; | \; k = 1,...,N, \: s = 
0,...,n_{k-1}, \: j = 1,...,n_k\}$}
    +\begin{algorithmic}[1]
    +    \State \texttt{Randomnly initialize u}
    +    \For{$i = 1,...,m$}
    +        \State $\nabla f(u) \set \texttt{mlp-gradient}(u,X_i,Y_i)$
    +        \State $u \set u - (\eta \nabla f(u) u + \lambda u)$
    +    \EndFor
    +    \State \Return $u$
    +\end{algorithmic}
    +\end{algorithm}
    +
    +\begin{algorithm}[mlp-train-parallel$(X, Y, \eta, s, t)$] 
\label{alg:mlp-train-parallel}
    +\alginput{
    +start vectors $X_{i...m} \in \mathbb{R}^{n_0}$,\\
    +end vectors $Y_{i...m} \in \mathbb{R}^{n_N}$,\\
    +learning rate $\eta$,\\
    +segments $s$,\\
    +iterations $t$,\\}
    +\algoutput{Coefficients $u = \{ u_{k-1}^{sj} \; | \; k = 1,...,N, \: s = 
0,...,n_{k-1}, \: j = 1,...,n_k\}$}
    +\begin{algorithmic}[1]
    +    \State \texttt{Randomnly initialize u}
    +    \For{$j = 1,...,s$}
    +        \State $X_j \set \texttt{subset-of-X}$
    +        \State $Y_j \set \texttt{subset-of-Y}$
    +    \EndFor
    +    \For{$i = 1,...,t$}
    +        \For{$j = 1,...,s$}
    +            \State $u_j \set copy(u)$
    +            \State $u_j \set \texttt{mlp-train-iteration}(X_j, Y_j, \eta)$
    +        \EndFor
    +        \State $u \set \texttt{weighted-avg}(u_{1...s})$
    +    \EndFor
    +    \State \Return $u$
    --- End diff --
    
    Just the `return u` shows up in a new page in the pdf, see if you can avoid 
that.


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