217 lines
5.3 KiB
TeX
217 lines
5.3 KiB
TeX
\documentclass[11pt]{report}
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\usepackage{setspace}
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\doublespacing
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\usepackage[toc,page]{appendix}
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\usepackage{pdfpages}
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\usepackage[]{amsmath}
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\usepackage[]{amsthm}
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\usepackage{mathtools}
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\numberwithin{equation}{section}
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\usepackage[]{amssymb}
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\usepackage[margin=1in]{geometry}
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\usepackage[]{soul}
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\usepackage[]{bbm}
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\usepackage[]{cancel}
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\usepackage[]{xcolor}
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\usepackage[]{enumitem}
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\usepackage{mathrsfs}
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\usepackage{graphicx}
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\usepackage{subfigure}
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\usepackage{booktabs}
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\usepackage{hyperref}
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\hypersetup{
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pdfauthor={Shakil Rafi},
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pdftitle={Dissertation},
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pdfkeywords={neural-networks, stochastic-processes},
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colorlinks = true,
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filecolor = magenta,
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urlcolor = cyan
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}
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\usepackage[capitalise]{cleveref}
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\usepackage{natbib}
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\usepackage{neuralnetwork}
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\usepackage{witharrows}
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\usepackage{stmaryrd}
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\usepackage{stackengine,amssymb,graphicx}
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\usepackage{listings}
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\usepackage{xcolor}
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\definecolor{codegreen}{rgb}{0,0.6,0}
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\definecolor{codegray}{rgb}{0.5,0.5,0.5}
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\definecolor{codepurple}{rgb}{0.58,0,0.82}
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\definecolor{backcolor}{rgb}{0.95,0.95,0.92}
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% Define R language settings
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\lstdefinestyle{rstyle}{
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language=R,
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basicstyle=\ttfamily\footnotesize,
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backgroundcolor = \color{backcolor},
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commentstyle=\color{codegreen},
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keywordstyle=\color{magenta},
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numberstyle=\ttfamily\tiny\color{codegray},
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numbers=left,
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stepnumber=1,
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frame=single,
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breaklines=true,
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numbersep = 5pt,
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breakatwhitespace=false,
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tabsize=4,
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morekeywords={install.packages, library, ggplot, aes, geom_bar}
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}
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\usepackage{fontspec}
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\setmonofont{Fira Code}
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\usepackage{graphicx}
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\DeclareMathAlphabet{\mymathbb}{U}{BOONDOX-ds}{m}{n}
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% \usepackage[]{enumerate}
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\setlength\parindent{0pt}
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\DeclareMathOperator{\Trace}{Trace}
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\DeclareMathOperator{\Hess}{Hess}
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\DeclareMathOperator{\supp}{supp}
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\DeclareMathOperator{\domain}{Domain}
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\DeclareMathOperator{\lip}{Lip}
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\DeclareMathOperator{\var}{Var}
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\DeclareMathOperator{\cov}{Cov}
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\DeclareMathOperator{\unif}{Unif}
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\DeclareMathOperator{\dropout}{Dropout}
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\DeclareMathOperator{\bern}{Bern}
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\DeclareMathOperator{\norm}{Norm}
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\DeclareMathOperator{\diag}{diag}
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\usepackage{tikz-cd}
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\DeclareMathOperator{\rect}{\mathfrak{r}}
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\DeclareMathOperator{\param}{\mathsf{P}}
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\DeclareMathOperator{\inn}{\mathsf{I}}
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\DeclareMathOperator{\out}{\mathsf{O}}
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\DeclareMathOperator{\neu}{\mathsf{NN}}
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\DeclareMathOperator{\hid}{\mathsf{H}}
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\DeclareMathOperator{\lay}{\mathsf{L}}
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\DeclareMathOperator{\dep}{\mathsf{D}}
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\DeclareMathOperator{\we}{Weight}
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\DeclareMathOperator{\bi}{Bias}
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\DeclareMathOperator{\aff}{\mathsf{Aff}}
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\DeclareMathOperator{\act}{\mathfrak{a}}
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\DeclareMathOperator{\real}{\mathfrak{I}}
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\DeclareMathOperator{\id}{\mathsf{Id}}
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\DeclareMathOperator{\mult}{Mult}
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\DeclareMathOperator{\wid}{\mathsf{W}}
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\DeclareMathOperator{\sm}{\mathsf{Sum}}
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\DeclareMathOperator{\trn}{Trn}
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\DeclareMathOperator{\tun}{\mathsf{Tun}}
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\DeclareMathOperator{\cpy}{\mathsf{Cpy}}
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\DeclareMathOperator{\ex}{\mathfrak{E}}
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\DeclareMathOperator{\lin}{Lin}
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\DeclareMathOperator{\relu}{\mathsf{ReLU}}
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\DeclareMathOperator{\zero}{Zr}
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\DeclareMathOperator{\sqr}{\mathsf{Sqr}}
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\DeclareMathOperator{\prd}{\mathsf{Prd}}
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\DeclareMathOperator{\pwr}{\mathsf{Pwr}}
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\DeclareMathOperator{\xpn}{\mathsf{Xpn}}
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\DeclareMathOperator{\rem}{\mathsf{Rem}}
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\DeclareMathOperator{\tay}{\mathsf{Tay}}
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\DeclareMathOperator{\G}{\mathsf{G}}
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\DeclareMathOperator{\F}{\mathsf{F}}
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\DeclareMathOperator{\U}{\mathsf{U}}
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\DeclareMathOperator{\sP}{\mathsf{P}}
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\DeclareMathOperator{\linn}{\mathsf{Lin}}
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\DeclareMathOperator{\nrm}{\mathsf{Nrm}}
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\DeclareMathOperator{\mxm}{\mathsf{Mxm}}
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\DeclareMathOperator{\trp}{\mathsf{Trp}}
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\DeclareMathOperator{\etr}{\mathsf{Etr}}
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\DeclareMathOperator{\lc}{\left\lceil}
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\DeclareMathOperator{\rc}{\right\rceil}
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\DeclareMathOperator{\csn}{\mathsf{Csn}}
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\DeclareMathOperator{\sne}{\mathsf{Sne}}
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\DeclareMathOperator{\pln}{\mathsf{Pln}}
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\DeclareMathOperator{\pnm}{\mathsf{Pnm}}
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\DeclareMathOperator{\inst}{\mathfrak{I}}
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\DeclareMathOperator{\rows}{rows}
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\DeclareMathOperator{\columns}{columns}
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\DeclareMathOperator{\va}{Var}
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\DeclareMathOperator{\obj}{obj}
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\DeclareMathOperator{\dom}{dom}
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\DeclareMathOperator{\cod}{cod}
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\newcommand{\bbP}{\mathbb{P}}
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\newcommand{\E}{\mathbb{E}}
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\newcommand{\R}{\mathbb{R}}
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\newcommand{\Z}{\mathbb{Z}}
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\newcommand{\N}{\mathbb{N}}
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\newcommand{\p}{\mathfrak{p}}
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\newcommand{\mft}{\mathfrak{t}}
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\newcommand{\f}{\mathfrak{f}}
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\newcommand{\C}{\mathfrak{C}}
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\newcommand{\n}{\mathscr{N}}
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\newcommand{\lp}{\left(}
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\newcommand{\rp}{\right)}
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\newcommand{\rb}{\right]}
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\newcommand{\lb}{\left[}
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\newcommand{\lv}{\left|}
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\newcommand{\rv}{\right|}
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\newcommand{\la}{\langle}
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\newcommand{\ra}{\rangle}
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\newcommand{\ve}{\varepsilon}
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\newcommand{\les}{\leqslant}
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\newcommand{\ges}{\geqslant}
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\newcommand\dplus{\ensurestackMath{%
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\stackengine{.5pt}{\Diamond}{\scalebox{.75}[1]{$+$}}{O}{c}{F}{F}{L}}}
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\newcommand{\DDiamond}{%
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\begin{tikzpicture}[baseline={(0,-0.2ex)}]
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\draw[rotate=45] (0,0) rectangle (0.2,0.2);
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\draw[rotate=45] (0,0.2) -- (0.2,0);
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\end{tikzpicture}%
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}
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% Input layer neurons number
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\newcommand{\inputnum}{3}
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% Hidden layer neurons number
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\newcommand{\hiddennum}{5}
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% Output layer neurons number
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\newcommand{\outputnum}{2}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{corollary}{Corollary}[theorem]
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{remark}[theorem]{Remark}
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\newtheorem{claim}[theorem]{Claim}
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