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