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Merge pull request #9 from Kautenja/bn
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Bn
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@Kautenja
Kautenja authored Feb 16, 2018
2 parents 813621c + 401e13a commit f70bf1b
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110 changes: 76 additions & 34 deletions tex/presentation.tex
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Original file line number Diff line number Diff line change
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\documentclass{beamer}
\usepackage{amsmath}
\usepackage{apacite}
\usepackage{caption}
\usepackage[font=small, labelfont=bf]{subcaption}
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\usetikzlibrary{shadows.blur}
\usetikzlibrary{shapes.symbols}

% a new command for a four quadrant slide
% a new command for a four quadrant slide mardas
\newcommand\FourQuad[4]{%
\begin{minipage}[b][.35\textheight][t]{.47\textwidth}#1\end{minipage}\hfill%
\begin{minipage}[b][.35\textheight][t]{.47\textwidth}#2\end{minipage}\\[0.5em]
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\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{img/vgg19/classification}
\caption{VGG19 Image Classification Architecture}
\caption*{VGG19 Image Classification Architecture}
\end{figure}
\end{frame}

\begin{frame}{VGG19}
\begin{figure}[H]
\centering
\includegraphics[width=.9\textwidth]{img/vgg19/feature-extraction}
\caption{VGG19 Image Feature Extraction Architecture}
\caption*{VGG19 Image Feature Extraction Architecture}
\end{figure}
\end{frame}

\begin{frame}{VGG19}
\begin{figure}[H]
\centering
\includegraphics[width=.9\textwidth]{img/vgg19/synthesis}
\caption{Gatys et al. VGG19 Image Synthesis Architecture}
\caption*{Gatys et al. VGG19 Image Synthesis Architecture}
\end{figure}
\end{frame}

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\begin{figure}[ht]
\begin{minipage}[b]{0.45\linewidth}
\centering
\caption{white noise image $\mathbf{x}$}
\caption*{white noise image $\mathbf{x}$}
\includegraphics[width=\textwidth]{img/content/noise}
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[b]{0.45\linewidth}
\centering
\caption{content image $\mathbf{p}$}
\caption*{content image $\mathbf{p}$}
\includegraphics[width=\textwidth]{img/content/tubingen}
\end{minipage}
\end{figure}
Expand All @@ -225,15 +226,15 @@
\begin{figure}[ht]
\centering
\includegraphics[width=0.8\textwidth]{img/vgg19/content/block1_conv1}
\caption{Block 1 Conv 1}
\caption*{Block 1 Conv 1}
\end{figure}
\end{frame}

\begin{frame}{Content Reconstruction}
\begin{figure}[ht]
\centering
\includegraphics[width=.9\textwidth]{img/content/block1_conv1.png}
\caption{Block 1 Conv 1}
\caption*{Block 1 Conv 1}
\end{figure}
\end{frame}

Expand All @@ -242,14 +243,14 @@
\begin{figure}[ht]
\centering
\includegraphics[width=0.9\textwidth]{img/vgg19/content/block2_conv1}
\caption{Block 2 Conv 1}
\caption*{Block 2 Conv 1}
\end{figure}
\end{frame}
\begin{frame}{Content Reconstruction}
\begin{figure}[ht]
\centering
\includegraphics[width=.9\textwidth]{img/content/block2_conv1.png}
\caption{Block 2 Conv 1}
\caption*{Block 2 Conv 1}
\end{figure}
\end{frame}

Expand All @@ -258,14 +259,14 @@
\begin{figure}[ht]
\centering
\includegraphics[width=0.9\textwidth]{img/vgg19/content/block3_conv1}
\caption{Block 3 Conv 1}
\caption*{Block 3 Conv 1}
\end{figure}
\end{frame}
\begin{frame}{Content Reconstruction}
\begin{figure}[ht]
\centering
\includegraphics[width=\textwidth]{img/content/block3_conv1.png}
\caption{Block 3 Conv 1}
\caption*{Block 3 Conv 1}
\end{figure}
\end{frame}

Expand All @@ -274,29 +275,29 @@
\begin{figure}[ht]
\centering
\includegraphics[width=0.9\textwidth]{img/vgg19/content/block4_conv1}
\caption{Block 4 Conv 1}
\caption*{Block 4 Conv 1}
\end{figure}
\end{frame}
\begin{frame}{Content Reconstruction}
\begin{figure}[ht]
\centering
\includegraphics[width=\textwidth]{img/content/block4_conv1.png}
\caption{Block 4 Conv 1}
\caption*{Block 4 Conv 1}
\end{figure}
\end{frame}

% 5:1
\begin{frame}{Content Reconstruction}
\begin{figure}[ht]
\centering
\caption{Block 5 Conv 1}
\caption*{Block 5 Conv 1}
\includegraphics[width=0.9\textwidth]{img/vgg19/content/block5_conv1}
\end{figure}
\end{frame}
\begin{frame}{Content Reconstruction}
\begin{figure}[ht]
\centering
\caption{Block 5 Conv 1}
\caption*{Block 5 Conv 1}
\includegraphics[width=\textwidth]{img/content/block5_conv1.png}
\end{figure}
\end{frame}
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\begin{figure}[ht]
\begin{minipage}[b]{0.45\linewidth}
\centering
\caption{white noise image $\mathbf{x}$}
\caption*{white noise image $\mathbf{x}$}
\includegraphics[width=\textwidth]{img/style/noise.png}
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[b]{0.45\linewidth}
\centering
\caption{artwork image $\mathbf{a}$}
\caption*{artwork image $\mathbf{a}$}
\includegraphics[width=\textwidth]{img/style/starry_night.png}
\end{minipage}
\end{figure}
Expand All @@ -388,14 +389,14 @@
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1}
\caption*{Conv 1 of Block 1}
\includegraphics[width=0.9\textwidth]{img/vgg19/style/block1_conv1}
\end{figure}
\end{frame}
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1}
\caption*{Conv 1 of Block 1}
\includegraphics[width=\textwidth]{img/style/block1_conv1.png}
\end{figure}
\end{frame}
Expand All @@ -404,14 +405,14 @@
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1, 2}
\caption*{Conv 1 of Block 1, 2}
\includegraphics[width=0.9\textwidth]{img/vgg19/style/block2_conv1}
\end{figure}
\end{frame}
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1, 2}
\caption*{Conv 1 of Block 1, 2}
\includegraphics[width=\textwidth]{img/style/block2_conv1.png}
\end{figure}
\end{frame}
Expand All @@ -420,14 +421,14 @@
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1, 2, 3}
\caption*{Conv 1 of Block 1, 2, 3}
\includegraphics[width=0.9\textwidth]{img/vgg19/style/block3_conv1}
\end{figure}
\end{frame}
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1, 2, 3}
\caption*{Conv 1 of Block 1, 2, 3}
\includegraphics[width=\textwidth]{img/style/block3_conv1.png}
\end{figure}
\end{frame}
Expand All @@ -436,14 +437,14 @@
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1, 2, 3, 4}
\caption*{Conv 1 of Block 1, 2, 3, 4}
\includegraphics[width=0.9\textwidth]{img/vgg19/style/block4_conv1}
\end{figure}
\end{frame}
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1, 2, 3, 4}
\caption*{Conv 1 of Block 1, 2, 3, 4}
\includegraphics[width=\textwidth]{img/style/block4_conv1.png}
\end{figure}
\end{frame}
Expand All @@ -452,14 +453,14 @@
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1, 2, 3, 4, 5}
\caption*{Conv 1 of Block 1, 2, 3, 4, 5}
\includegraphics[width=0.9\textwidth]{img/vgg19/style/block5_conv1}
\end{figure}
\end{frame}
\begin{frame}{Style Reconstruction}
\begin{figure}[ht]
\centering
\caption{Conv 1 of Block 1, 2, 3, 4, 5}
\caption*{Conv 1 of Block 1, 2, 3, 4, 5}
\includegraphics[width=\textwidth]{img/style/block5_conv1.png}
\end{figure}
\end{frame}
Expand All @@ -480,22 +481,63 @@

where $\alpha$ and $\beta$ are the arbitrary weighting factors of the content
and style loss respectively. Gatys et al. find the best results using a ratio
of $\alpha / \beta \in [5*10^{-4}, 5*10^{-3}]$.
of $\alpha, \beta \in [5\times10^{-4}, 5\times10^{-3}]$.
\end{frame}

\begin{frame}[allowframebreaks]{Note on Optimization methods}

\begin{center}
$\mathbf{g}_k = \nabla f_{\theta}(\theta_k) $ \hspace{10mm}
$\mathbf{H}_k = \nabla^{2} f_{\theta}(\theta_k)$
\end{center}

\textbf{Methods}:
\begin{enumerate}
\item \textbf{Gradient}: $\boldsymbol{\theta}_{k+1} =
\boldsymbol{\theta}_k - \eta_k \mathbf{g}_k$
\item \textbf{Hessian}: $\boldsymbol{\theta}_{k+1} = \boldsymbol{\theta}_k - d_k$
where $\mathbf{d}_k = \mathbf{H}_k^{-1} \mathbf{g}_k$ \\
Rather than computing $\mathbf{d}_k = \mathbf{H}_k^{-1} \mathbf{g}_k$ directly,
we can solve the linear systems of equations
$\mathbf{H}_k \mathbf{d}_k = -\mathbf{g}_k$ for $\mathbf{d}_k$.
\end{enumerate}
\newpage
\begin{center}
$\mathbf{s}_k = \mathbf {x} _{k+1}-\mathbf {x} _{k}$ and
\end{center}
However calculating $H^{-1}_k$ is extensive both in terms of computation and
memory. Approximation methods have been proposed:
\begin{enumerate}
\item Imposing quasi-newtonian condition: \\
$H_{k+1}(\mathbf{s}_k)=y_k$\\
and $\mathbf{y}_k = \nabla f(\mathbf {x} _{k+1})-
\nabla f(\mathbf {x} _{k})
= \mathbf{g}_{k+1} - \mathbf{g}_{k}$. \\
\item \textbf{BFGS}: After some math magic we have:
$H_{k+1}=H_{k}+{\frac {\mathbf {y} _{k}\mathbf {y} _{k}
^{\mathrm {T} }}{\mathbf {y} _{k}^{\mathrm {T} }
\mathbf {s} _{k}}}-{\frac {H_{k}\mathbf {s} _{k}\mathbf {s} _{k}^
{\mathrm {T} }H_{k}^{\mathrm {T} }}{\mathbf {s} _{k}^
{\mathrm {T} }H_{k}\mathbf {s} _{k}}}$\\
$H^{-1}_{k+1}=(I-\rho _{k}s_{k}y_{k}^{\top })
H^{-1}_{k}(I-\rho _{k}y_{k}s_{k}^{\top })+\rho _{k}s_{k}s_{k}^{\top }$\\
where $\rho_k = \rho_k = \frac{1}{y^{\rm T}_k s_k} $.
\end{enumerate}

\end{frame}
% VGG19 for style transfer
\begin{frame}{Style Transfer}
\begin{figure}[ht]
\centering
\caption{Content and Style Loss Layers for Style Transfer}
\caption*{Content and Style Loss Layers for Style Transfer}
\includegraphics[width=0.9\textwidth]{img/vgg19/transfer/layers}
\end{figure}
\end{frame}
% Gatys et al. visualize of network passes
\begin{frame}{Style Transfer}
\begin{figure}[ht]
\centering
\caption{Style Transfer Architecture}
\caption*{Style Transfer Architecture}
\includegraphics[width=\textwidth]{img/style-transfer}
\end{figure}
\end{frame}
Expand All @@ -504,7 +546,7 @@
\begin{frame}{Style Transfer}
\begin{figure}[H]
\centering
\caption{Content Image \textbf{p}, Tubingen Germany}
\caption*{Content Image \textbf{p}, Tubingen Germany}
\includegraphics[width=\textwidth]{img/content/tubingen}
\end{figure}
\end{frame}
Expand All @@ -513,7 +555,7 @@
\begin{frame}{Style Transfer}
\begin{figure}
\centering
\caption{Artwork Image \textbf{a}}
\caption*{Artwork Image \textbf{a}}
\FourQuad{
\begin{figure}[ht]
\centering
Expand Down Expand Up @@ -547,7 +589,7 @@
\begin{frame}{Style Transfer}
\begin{figure}
\centering
\caption{Stylized Image \textbf{x}}
\caption*{Stylized Image \textbf{x}}
\FourQuad{
\begin{figure}[ht]
\centering
Expand Down

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