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

    https://github.com/apache/incubator-madlib/pull/162#discussion_r132340137
  
    --- Diff: doc/design/modules/neural-network.tex ---
    @@ -46,41 +47,49 @@ \subsection{Formal Description}
     In the remaining part of this section, we will give a formal description 
of the derivation of objective function and its gradient.
     
     \paragraph{Objective function.}
    -We mostly follow the notations in example 1.5.3 from Bertsekas 
\cite{bertsekas1999nonlinear}, for a multilayer perceptron that has $N$ layers 
(stages), and the $k$th stage has $n_k$ activation units ($\phi : \mathbb{R} 
\to \mathbb{R}$), the objective function is given as
    -\[f_{(y, z)}(u) = \frac{1}{2} \|h(u, y) - z\|_2^2,\]
    -where $y \in \mathbb{R}^{n_0}$ is the input vector, $z \in 
\mathbb{R}^{n_N}$ is the output vector,
    +We mostly follow the notations in example 1.5.3 from Bertsekas 
\cite{bertsekas1999nonlinear}, for a multilayer perceptron that has $N$ layers 
(stages), and the $k$th stage has $n_k$ activation units ($\phi : \mathbb{R} 
\to \mathbb{R}$), the objective function for regression is given as
    +\[f_{(x, y)}(u) = \frac{1}{2} \|h(u, x) - y\|_2^2,\]
    +and for classification the objective function is given as
    +\[f_{(x, y)}(u) = \sum_i (\log(h_i(u, x)) * z_i + (1-\log(h_i(u, x))) *( 
1- z_i) ,\]
    +where $x \in \mathbb{R}^{n_0}$ is the input vector, $y \in 
\mathbb{R}^{n_N}$ is the output vector (one hot encoded for classification),
     \footnote{Of course, the objective function can be defined over a set of 
input-output vector pairs, which is simply given as the addition of the above 
$f$.}
     and the coefficients are given as
    --- End diff --
    
    Change ```classification),\n
    \footnote{```
    to ```classification),~\footnote{```
    
    Similar comment for the second footnote too.


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