cleanup remaining TODO blocks

tex/review.nlo

@@ -0,0 +1,8 @@
+\nomenclatureentry{P$c$@[{$c$}]\begingroup Speed of light in a vacuum inertial system\nomeqref {0}|nompageref}{1}
+\nomenclatureentry{P$h$@[{$h$}]\begingroup Plank Constant\nomeqref {0}|nompageref}{1}
+\nomenclatureentry{P$g$@[{$g$}]\begingroup Gravitational Constant\nomeqref {0}|nompageref}{1}
+\nomenclatureentry{N$\mathbb{R}$@[{$\mathbb{R}$}]\begingroup Real Numbers\nomeqref {0}|nompageref}{1}
+\nomenclatureentry{N$\mathbb{C}$@[{$\mathbb{C}$}]\begingroup Complex Numbers\nomeqref {0}|nompageref}{1}
+\nomenclatureentry{N$\mathbb{H}$@[{$\mathbb{H}$}]\begingroup Quaternions\nomeqref {0}|nompageref}{1}
+\nomenclatureentry{O$V$@[{$V$}]\begingroup Constant Volume\nomeqref {0}|nompageref}{1}
+\nomenclatureentry{O$\rho$@[{$\rho$}]\begingroup Friction Index\nomeqref {0}|nompageref}{1}

tex/review.tex

@@ -22,9 +22,6 @@
 \begin{document}
 \title{Review: A Neural Algorithm of Artistic Style}
 
-%% TODO: notations section?
-%% TODO: clarify notations for both content and styl representation (N_l etc.)
-
 \author{
     James C. Kauten \\
     Department of Software Engineering \\
@@ -59,7 +56,7 @@ \section{Paper Summary}
 T\"{u}bingen, Germany in the style of Claude Monet's \textit{Houses of
 Parliament}.
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{Style Transfer from $\textbf{a}$ to $\textbf{p}$ via $\textbf{x}$}
 \label{basic-example}
@@ -98,11 +95,10 @@ \subsection{Content Representation}
 $\frac{1}{2}$ to simplify the formulation of the analytical gradient in Eq.
 \ref{eq:content-grad}.
 
-% TODO: note the M_l and N_l variables in the above paragraph
 \begin{equation}
 \label{eq:content-loss}
 \mathcal{L}_{content}(\mathbf{p}, \mathbf{x}, l) =
-\frac{1}{2} \sum_{i=1}^{N_l}\sum_{j=1}^{M_l}{(F^l_{ij} - P^l_{ij})^2}
+\frac{1}{2} \sum_{i,j}{(F^l_{ij} - P^l_{ij})^2}
 \end{equation}
 
 \begin{equation}
@@ -134,7 +130,7 @@ \subsubsection{Content Reconstruction}
 this looser representation allows the content to blend more smoothly with
 other images while still preserving the global features of the content.
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{Content Reconstruction of \textit{T\"{u}bingen, Germany}}
 \label{fig:content-reconstruction}
@@ -173,12 +169,16 @@ \subsection{Style Representation}
 feature responses of particular layers in the \ac{CNN}. However, this
 representation uses a different feature space. Converting each activation
 map to a \textit{gram matrix} allows the extraction of just the texture from
-a given image. It does so by computing the correlations between different
-filters in an arbitrary convolutional layer $l$. Simply put, the gram matrix
-$G^l$ for an activation map is the inner product of feature maps:
+a given image. It does so by computing the correlations between $N_l$
+different filters in an arbitrary convolutional layer $l$. Simply put, the
+gram matrix $G^l$ for an activation map is the inner product of feature maps.
+Eq. \ref{eq:gram-matrix} shows a formulation of the gram matrix. Note that
+$F$ is flattened about the height and width dimension. This reduces the two
+dimensions to a new dimension of length $M_l = height * width$.
 
 \begin{equation}
-G_{i j}^l = \sum_{k}^{M_l} F_{i k}^l F_{j k}^l
+\label{eq:gram-matrix}
+G_{i j}^l = \sum_{k}^{N_l} F_{i k}^l F_{j k}^l
 \end{equation}
 
 With a new feature space representation of raw texture,
@@ -188,13 +188,12 @@ \subsection{Style Representation}
 for $\textbf{a}$ and $\textbf{x}$ are transformed to their respective gram
 matrices $A^l$, and $G^l$. Then, much like the content loss, we define
 the style loss for a given layer as the squared euclidean distance between the
-gram matrices $A^l$, and $G^l$:
+gram matrices $A^l$, and $G^l$. Eq. \ref{eq:style-loss-single-layer} shows the
+formulation of the style loss for a single layer $l$.
 
 \begin{equation}
-E_l =
-\frac{1}{4 N_l^2 M_l^2}
-\sum_{i=1}^{N_l}\sum_{j=1}^{M_l}
-(G^l_{ij} - A^l_{ij})^2
+\label{eq:style-loss-single-layer}
+E_l = \frac{1}{4 N_l^2 M_l^2} \sum_{i,j} (G^l_{ij} - A^l_{ij})^2
 \end{equation}
 
 \cite{2015arXiv150806576G} incorporate multiple layers in the style loss using
@@ -241,7 +240,7 @@ \subsubsection{Style Reconstruction}
 $\textbf{a}$. As more layers contribute to the loss, the details of the
 texture spread and smoothen across the noise image $\textbf{x}$.
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{Style Reconstruction of Vincent Van Gogh's \textit{A Starry Night}}
 \label{fig:style-reconstruction}
@@ -399,7 +398,7 @@ \section{Questions \& Answers}
 layers in the style loss. We see that the additional layers do in fact help
 transfer more of the style.
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{Samford Hall Styled as Pablo Picasso's \textit{Seated Nude} Using
 Different Style Loss Layer Sets}
@@ -442,7 +441,7 @@ \section{Questions \& Answers}
 somewhere between these. That said, "optimal" depends on the viewers' taste in
 images.
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{Samford Hall Styled as Pablo Picasso's \textit{Seated Nude} Using
 Different Content Loss Layers}
@@ -485,7 +484,7 @@ \section{Questions \& Answers}
 portrays how the algorithm can use a photo of New York at night to style a
 photo of Atlanta at day, resulting in a new image of Atlanta at dusk.
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{Photo-realistic Style Transfer}
 \label{fig:photo-realistic-style-transfer}
@@ -513,7 +512,7 @@ \section{Questions \& Answers}
 from VGG19, the AlexNet results hardly resembles either image, let alone a
 transfer of style from one to another.
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{Style Transfer Using AlexNet}
 \label{fig:alex-net-transfer}
@@ -536,7 +535,7 @@ \section{Questions \& Answers}
 \ref{fig:deep-dream} shows Vincent Van Gogh's \textit{The Starry Night}
 styled in a "deep dream".
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{\textit{Deep Dream}: Style Transfer Using Inception Net}
 \label{fig:deep-dream}
@@ -625,6 +624,7 @@ \section{Questions \& Answers}
 
 % MARK: bibliography
 %% print the bibliography using the custom NIPS bib style
+\clearpage
 \bibliographystyle{my-unsrtnat}
 \bibliography{references}
 
@@ -633,7 +633,7 @@ \section{Questions \& Answers}
 % MARK: appendix
 % \appendix
 
-\begin{figure}[htp]
+\begin{figure}
 \centering
 \caption{Style Transfer}
 \label{fig:style-transfer}