\documentclass[11pt]{article} \usepackage[a4paper,left=25mm,right=25mm,top=24mm,bottom=25mm,headheight=14pt]{geometry} \usepackage{amsmath,amssymb,amsthm,booktabs,float,algorithm,algpseudocode} \usepackage{graphicx,array,microtype,placeins,needspace} \usepackage[T1]{fontenc} \usepackage{mathpazo,titlesec,fancyhdr,caption,enumitem,etoolbox} \linespread{1.045} \setlength{\parindent}{1.2em} \setlength{\parskip}{2pt} \titleformat{\section}{\Large\sffamily\bfseries}{\thesection}{0.65em}{} \titleformat{\subsection}{\normalsize\sffamily\bfseries}{\thesubsection}{0.65em}{} \titlespacing*{\section}{0pt}{3.0ex plus 1ex minus .2ex}{1.1ex} \titlespacing*{\subsection}{0pt}{2.2ex plus .5ex}{0.7ex} \captionsetup{font=small,labelfont=bf,labelsep=period,skip=8pt} \setlist[enumerate]{leftmargin=1.8em,itemsep=4pt,topsep=6pt} \pagestyle{fancy} \fancyhf{} \fancyhead[L]{\small\itshape SGD with vanishing correlated gradient errors} \fancyfoot[C]{\small\thepage} \renewcommand{\headrulewidth}{0pt} \AtBeginEnvironment{thebibliography}{\small} \renewcommand{\maketitle}{% \thispagestyle{plain}% \begingroup\raggedright {\fontsize{22}{26}\selectfont\bfseries SGD with Vanishing\\Correlated Gradient Errors\par} \vspace{5pt}{\large (technique notes)\par} \vspace{12pt}\hrule\vspace{14pt} \endgroup} \renewenvironment{abstract} {\small\noindent\textbf{Abstract.}\enspace\ignorespaces} {\par\vspace{10pt}} \usepackage[hidelinks]{hyperref} \floatstyle{ruled}\restylefloat{algorithm} \setlength{\tabcolsep}{4pt} \setlength{\emergencystretch}{1em} \raggedbottom \numberwithin{equation}{section} \newtheoremstyle{emphasizedplain} {13pt plus 2pt minus 1pt}{9pt plus 2pt minus 1pt} {\itshape}{}{\bfseries}{.}{0.6em} {\thmname{#1}\thmnumber{ #2}\thmnote{\textbf{ (#3)}}} \newtheoremstyle{emphasizeddefinition} {9pt plus 2pt minus 1pt}{9pt plus 2pt minus 1pt} {\normalfont}{}{\bfseries}{.}{0.6em} {\thmname{#1}\thmnumber{ #2}\thmnote{\textbf{ (#3)}}} \theoremstyle{emphasizedplain} \newtheorem{theorem}{Theorem} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \theoremstyle{emphasizeddefinition} \newtheorem{assumption}{Assumption} \title{SGD with Vanishing Correlated Gradient Errors (technique notes)} \author{} \date{} \hypersetup{pdftitle={SGD with Vanishing Correlated Gradient Errors (technique notes)}, pdfsubject={Technical note: weighted historical errors in stochastic gradient descent}} \begin{document} \maketitle \input{abstract} \input{introduction} \input{related_work} \input{main_results} \input{variance_lower_bound} \input{experiments} \FloatBarrier \input{references} \appendix \input{appendix_proofs} \end{document}