259 lines
7.3 KiB
TeX
259 lines
7.3 KiB
TeX
\documentclass[12pt,a4paper,oneside,onecolumn]{book}
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% remove unnecessary warnings
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\usepackage{silence}
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\WarningFilter{caption}{Unknown document class}
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% Hebrew + English via XeLaTeX:
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\usepackage{fontspec}
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\usepackage{polyglossia}
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\setmainlanguage{english}
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\setotherlanguage{hebrew}
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% Culmus OpenType fonts for Hebrew (exact fc family names)
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\newfontfamily\hebrewfont[Script=Hebrew]{Frank Ruehl CLM}
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\newfontfamily\hebrewfontsf[Script=Hebrew]{Miriam CLM}
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\newfontfamily\hebrewfonttt[Script=Hebrew]{Miriam Mono CLM}
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% Set page numbering with no headers (according to guidelines):
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\usepackage{fancyhdr}
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\pagestyle{fancy}
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\lhead{}
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\chead{\thepage}
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\rhead{}
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\lfoot{}
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\cfoot{}
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\rfoot{}
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\renewcommand{\headrulewidth}{0pt}
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\fancypagestyle{plain}{\pagestyle{fancy}}
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\setlength{\headheight}{15pt}
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% Sub-figures/tables parenthesis:
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% For parenthesis in sub-figure reference
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\usepackage[labelformat=simple]{subcaption}
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\renewcommand\thesubfigure{(\alph{subfigure})}
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% For parenthesis before sub-table caption
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\renewcommand\thesubtable{(\alph{subtable})}
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% Misc packages:
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\usepackage{textcomp} %loaded before "gensymb" to avoid annoying warnings
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\usepackage{gensymb} %Degree symbol
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\usepackage{mathtools} %cases*
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\usepackage{amssymb} %Math letters
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\usepackage[shortlabels]{enumitem}
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\usepackage[multiple]{footmisc}
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%theorem, corollary and lemma definitions:
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\usepackage[amsmath, thmmarks]{ntheorem}
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\newtheorem{theorem}{Theorem}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{observation}[theorem]{Observation}
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\newtheorem{assumption}[theorem]{Assumption}
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\newtheorem{remark}[theorem]{Remark}
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%proof definition:
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\theoremstyle{nonumberplain}
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\theoremheaderfont{\itshape}
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\theorembodyfont{\normalfont}
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\theoremseparator{.}
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\theoremsymbol{\ensuremath{\square}}
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\newtheorem{proof}{Proof}
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% Change back to default values - needed to repeat assumptions
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\theoremstyle{plain}
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\theoremheaderfont{\normalfont\bfseries}
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\theorembodyfont{\itshape}
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\theoremseparator{}
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\theoremsymbol{}
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\usepackage{chngcntr}
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\counterwithin{theorem}{chapter}
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% Misc:
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\DeclareMathOperator*{\argmax}{arg\,max}
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\usepackage[ruled,vlined,algochapter]{algorithm2e}
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\usepackage{csquotes}
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% Show numbers also for subsubsection
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\setcounter{secnumdepth}{4}
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% bibliography:
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\usepackage[numbers,sort,compress,square]{natbib}
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\bibliographystyle{bibliography/unsrtnat_adjusted_for_bgu_thesis}
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%add bib to toc
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\usepackage[nottoc]{tocbibind}
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%add command for citation with possessive apostrophe
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\newcommand\citepossessive [1]{\citeauthor{#1}'s\ \cite{#1}}
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%Natbib cites cannot be broken to two lines
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\makeatletter
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\def\NAT@spacechar{~}% NEW
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\makeatother
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% paragraph settings:
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\setlength{\parindent}{0pt}
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\setlength{\parskip} {5pt}
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% drawing and graphics:
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\usepackage{tikz}
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\usetikzlibrary{matrix,positioning}
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\usepackage{float} %Not sure it will be needed
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\usepackage{graphicx}
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\graphicspath{ {content/images/} }
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\usepackage{booktabs}
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\usepackage{titling}
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\usepackage[titletoc]{appendix}
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% Code listings:
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\usepackage{listings}
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\lstset{
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basicstyle=\ttfamily\footnotesize,
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breaklines=true,
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breakatwhitespace=false,
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showstringspaces=false,
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frame=single,
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numbers=left,
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numberstyle=\tiny\ttfamily,
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numbersep=6pt,
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xleftmargin=18pt,
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framexleftmargin=18pt,
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tabsize=4,
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captionpos=b,
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keepspaces=true,
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columns=flexible,
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}
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%Not included since 'hyperref' and 'bookmark' are too problematic with Hebrew
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% \usepackage[hidelinks]{hyperref}
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% \usepackage{bookmark}
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% cleveref:
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\usepackage[capitalise]{cleveref}
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%Workaround for babel and cleveref (for citing few equations)
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\makeatletter
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\def\@@number#1{#1}
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\makeatother
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\Crefname{observation}{Observation}{Observations}
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\Crefname{assumption}{Assumption}{Assumptions}
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\Crefname{remark}{Remark}{Remarks}
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%set spacing between lines
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\usepackage{setspace}
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\doublespacing
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%Title and names for the article
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\newcommand{\thesistitle}{\textbf{Noise-Robust Gradient-Based Learning Utilizing Rate Optimized Likelihood Loss}}
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\newcommand{\thesistitlehe}{\textbf{למידה עמידה לרעש מבוססת גרדיאנט תוך שימוש בפונקציית הפסד קירוב-הסתברות}}
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\newcommand{\thesisauthorname}{\textbf{Aner Zakobar}}
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\newcommand{\thesisauthornamehe}{\textbf{ענר זקובר}}
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\newcommand{\thesissupervisername}{\textbf{Prof. Lior Rokach, Prof. Aryeh Kontorovich}}
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\newcommand{\thesissupervisernamehe}{\textbf{פרופ. ליאור רוקח, פרופ. אריה קונטורוביץ}}
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\newcommand{\thesismonth}{\textbf{September}}
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\newcommand{\thesismonthhe}{\textbf{ספטמבר}}
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\newcommand{\thesisyear}{\textbf{2026}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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\begin{titlepage}
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\centering
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\vspace*{3cm}
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{\LARGE\bfseries Noise-Robust Gradient-Based Learning\\[0.5em]
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Utilizing Rate Optimized Likelihood Loss}\\[2.5em]
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{\large Aner Zakobar}\\[0.5em]
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{\normalsize Supervised by: Prof.\ Lior Rokach, Prof.\ Aryeh Kontorovich}\\[3em]
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\rule{0.5\textwidth}{0.4pt}\\[1em]
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{\large\itshape Excerpt: Chapter~3 \& Appendices A, C--F, I}\\[0.5em]
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{\normalsize Note: cross-references to omitted chapters appear as \textbf{??}}\\[1em]
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\rule{0.5\textwidth}{0.4pt}
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\vfill
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{\large September 2026}
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\end{titlepage}
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\tableofcontents
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\clearpage
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\mainmatter
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%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%
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\setcounter{chapter}{2}
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\chapter{Method}
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\label{chapter:method}
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\input{content/method/method}
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%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%
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\begin{appendices}
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\setcounter{chapter}{0}
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\chapter{Gaussian ROLL: Forward Pass and Gradient Derivation}
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\label{appendix:gauss-grad}
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\input{content/appendixs/appendix_gauss_grad}
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\setcounter{chapter}{2}
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\chapter{KDE ROLL: Gradient Derivation}
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\label{appendix:kde-grad}
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\input{content/appendixs/appendix_kde_grad}
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\setcounter{chapter}{3}
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\chapter{KDE ROLL: Sigmoid Kernel -- Explicit Equations}
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\label{appendix:kde-sigmoid}
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\input{content/appendixs/appendix_kde_sigmoid}
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\setcounter{chapter}{4}
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\chapter{KDE ROLL: Bisection for CDF Inversion}
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\label{appendix:kde-bisection}
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\input{content/appendixs/appendix_kde_bisection}
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\setcounter{chapter}{5}
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\chapter{KDE ROLL: Newton--Raphson Inversion (Superseded)}
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\label{appendix:kde-nr}
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\input{content/appendixs/appendix_kde_nr}
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\setcounter{chapter}{8}
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\chapter{Proof of the Gradient Balance Proposition}
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\label{appendix:grad-balance}
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\input{content/appendixs/appendix_grad_balance}
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\end{appendices}
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%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%
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\bibliography{bibliography/thesis}
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\end{document}
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