From 2d2bb235d8dbfbf9acc31f1d8f64e193993265d9 Mon Sep 17 00:00:00 2001 From: rasoolianbehnam Date: Tue, 13 Feb 2018 15:10:16 -0600 Subject: [PATCH 1/2] a test commit --- tex/presentation.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tex/presentation.tex b/tex/presentation.tex index 24c3219..2f7d749 100755 --- a/tex/presentation.tex +++ b/tex/presentation.tex @@ -20,7 +20,7 @@ \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] From 401e13acd011d3d2ece3ad7a62968f92ea6603c2 Mon Sep 17 00:00:00 2001 From: rasoolianbehnam Date: Fri, 16 Feb 2018 14:01:02 -0600 Subject: [PATCH 2/2] latest tex --- tex/img/content/block4_conv2.png | Bin 347532 -> 347290 bytes tex/presentation.tex | 108 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a/tex/presentation.tex +++ b/tex/presentation.tex @@ -1,4 +1,5 @@ \documentclass{beamer} +\usepackage{amsmath} \usepackage{apacite} \usepackage{caption} \usepackage[font=small, labelfont=bf]{subcaption} @@ -155,7 +156,7 @@ \begin{figure}[H] \centering \includegraphics[width=\textwidth]{img/vgg19/classification} -\caption{VGG19 Image Classification Architecture} +\caption*{VGG19 Image Classification Architecture} \end{figure} \end{frame} @@ -163,7 +164,7 @@ \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} @@ -171,7 +172,7 @@ \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} @@ -208,13 +209,13 @@ \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} @@ -225,7 +226,7 @@ \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} @@ -233,7 +234,7 @@ \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} @@ -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} @@ -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} @@ -274,14 +275,14 @@ \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} @@ -289,14 +290,14 @@ \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} @@ -372,13 +373,13 @@ \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} @@ -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} @@ -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} @@ -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} @@ -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} @@ -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} @@ -480,14 +481,55 @@ 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} @@ -495,7 +537,7 @@ \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} @@ -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} @@ -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 @@ -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

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