From ba105985b3e8414fb186dbe43cf73f8a3132d421 Mon Sep 17 00:00:00 2001 From: lukas-heiligenbrunner Date: Wed, 24 Apr 2024 12:14:44 +0200 Subject: [PATCH] move most stuff to outline section add cross entropy loss infos add text to 4 different methods --- src/conclusionandoutlook.tex | 4 +- src/implementation.tex | 73 --- src/introduction.tex | 89 ++- src/llncs.cls | 1189 ++++++++++++++++++++++++++++++++++ src/main.tex | 36 +- src/materialandmethods.tex | 15 +- 6 files changed, 1323 insertions(+), 83 deletions(-) create mode 100644 src/llncs.cls diff --git a/src/conclusionandoutlook.tex b/src/conclusionandoutlook.tex index c88904e..8c6c026 100644 --- a/src/conclusionandoutlook.tex +++ b/src/conclusionandoutlook.tex @@ -2,4 +2,6 @@ \subsection{Conclusion}\label{subsec:conclusion} -\subsection{Outlook}\label{subsec:outlook} \ No newline at end of file +\subsection{Outlook}\label{subsec:outlook} + +Results might be different with a multiclass classification task and segmentation tasks. \ No newline at end of file diff --git a/src/implementation.tex b/src/implementation.tex index c45a063..fb04878 100644 --- a/src/implementation.tex +++ b/src/implementation.tex @@ -1,74 +1 @@ \section{Implementation}\label{sec:implementation} -The model is defined as $g(\pmb{x};\pmb{w})$ where $\pmb{w}$ are the model weights and $\mathcal{X}$ the input samples. -We define two hyperparameters, the batch size $\mathcal{B}$ and the sample size $\mathcal{S}$ where $\mathcal{B} < \mathcal{S}$. -In every active learning loop iteration we sample $\mathcal{S}$ random samples~\eqref{eq:batchdef} from our total unlabeled sample set $\mathcal{X}_U \subset \mathcal{X}$. - -\begin{equation} - \label{eq:batchdef} - \pmb{x} \coloneqq (\pmb{x}_0,\dots,\pmb{x}_\mathcal{S}) \sim \mathcal{X}_U -\end{equation} - -The model with the weights of the current loop iteration predicts pseudo predictions. - -\begin{equation}\label{eq:equation2} - z = g(\pmb{x};\pmb{w}) -\end{equation} - -Those predictions might have any numerical value and have to be squeezed into a proper distribution which sums up to 1. -The Softmax function has exactly this effect: $\sum^\mathcal{S}_{i=1}\sigma(z)_i=1$. -Since we have a two class problem the Softmax results in two result values, the two probabilities of how certain one class is a match. -We want to calculate the distance to the class center and the more far away a prediction is from the center the more certain it is. -Vice versa, the more centered the predictions are the more uncertain the prediction is. -Labels $0$ and $1$ result in a class center of $\frac{0+1}{2}=\frac{1}{2}$. -That means taking the absolute value of the prediction minus the class center results in the certainty of the sample~\eqref{eq:certainty}. - -\begin{align} - \label{eq:certainty} - S(z) = | 0.5 - \sigma(\mathbf{z})_0| \; \textit{or} \; \arg\max_j \sigma(\mathbf{z}) -\end{align} - -\cite{activelearning} - -With the help of this metric the pseudo predictions can be sorted by the score $S(z)$. -We define $\text{min}_n(S)$ and $\text{max}_n(S)$ respectively in~\ref{eq:minnot} and~\ref{eq:maxnot} to define a short form of taking a subsection of the minimum or maximum of a set. - -\begin{equation}\label{eq:minnot} - \text{min}_n(S) \coloneqq a \subset S \mid \text{where } a \text{ are the } n \text{ smallest numbers of } S -\end{equation} - -\begin{equation}\label{eq:maxnot} - \text{max}_n(S) \coloneqq a \subset S \mid \text{where } a \text{ are the } n \text{ largest numbers of } S -\end{equation} - -This notation helps to define which subsets of samples to give the user for labeling. -There are different ways how this subset can be chosen. -In this PW we do the obvious experiments with High-Certainty first~\ref{subsec:low-certainty-first}, Low-Certainty first~\ref{subsec:high-certainty-first}. -Furthermore, the two mixtures between them, halt-high and half-low certain and only the middle section of the sorted certainty scores. - -\subsection{Low certainty first}\label{subsec:low-certainty-first} -We take the samples with the lowest certainty score first and give it to the user for labeling. - -\begin{equation} - \text{min}_\mathcal{B}(S(z)) -\end{equation} - -\subsection{High certainty first}\label{subsec:high-certainty-first} -We take the samples with the highest certainty score first and give it to the user for labeling. - -\begin{equation} - \text{max}_\mathcal{B}(S(z)) -\end{equation} - -\subsection{Low and High certain first} - -We take half the batch-size $\mathcal{B}$ of low certainty and the other half with high certainty samples. - -\begin{equation} - \text{max}_{\mathcal{B}/2}(S(z)) \cup \text{max}_{\mathcal{B}/2}(S(z)) -\end{equation} - -\subsection{Mid certain first} - -\begin{equation} - S(z) \setminus (\text{min}_{\mathcal{S}/2 - \mathcal{B}/2}(S(z)) \cup \text{max}_{\mathcal{S}/2 - \mathcal{B}/2}(S(z))) -\end{equation} \ No newline at end of file diff --git a/src/introduction.tex b/src/introduction.tex index 1fb010c..4fee1d7 100644 --- a/src/introduction.tex +++ b/src/introduction.tex @@ -18,4 +18,91 @@ Is combining Dagster with Label-Studio a good match for building scalable and re \subsubsection{Does balancing the learning samples improve performance?} The sample-selection metric might select samples just from one class by chance. Does balancing this distribution help the model performance? -\subsection{Outline}\label{subsec:outline} \ No newline at end of file +\subsection{Outline}\label{subsec:outline} + +The model is defined as $g(\pmb{x};\pmb{w})$ where $\pmb{w}$ are the model weights and $\mathcal{X}$ the input samples. +We define two hyperparameters, the batch size $\mathcal{B}$ and the sample size $\mathcal{S}$ where $\mathcal{B} < \mathcal{S}$. +In every active learning loop iteration we sample $\mathcal{S}$ random samples~\eqref{eq:batchdef} from our total unlabeled sample set $\mathcal{X}_U \subset \mathcal{X}$. + +\begin{equation} + \label{eq:batchdef} + \pmb{x} \coloneqq (\pmb{x}_0,\dots,\pmb{x}_\mathcal{S}) \sim \mathcal{X}_U +\end{equation} + +The model with the weights of the current loop iteration predicts pseudo predictions. + +\begin{equation}\label{eq:equation2} +z = g(\pmb{x};\pmb{w}) +\end{equation} + +Those predictions might have any numerical value and have to be squeezed into a proper distribution which sums up to 1. +The Softmax function has exactly this effect: $\sum^\mathcal{S}_{i=1}\sigma(z)_i=1$. +Since we have a two class problem the Softmax results in two result values, the two probabilities of how certain one class is a match. +We want to calculate the distance to the class center and the more far away a prediction is from the center the more certain it is. +Vice versa, the more centered the predictions are the more uncertain the prediction is. +Labels $0$ and $1$ result in a class center of $\frac{0+1}{2}=\frac{1}{2}$. +That means taking the absolute value of the prediction minus the class center results in the certainty of the sample~\eqref{eq:certainty}. + +\begin{align} + \label{eq:certainty} + S(z) = | 0.5 - \sigma(\mathbf{z})_0| \; \textit{or} \; S(z) = \max \sigma(\mathbf{z}) - 0.5 +\end{align} + +\cite{activelearning} + +With the help of this metric the pseudo predictions can be sorted by the score $S(z)$. +We define $\text{min}_n(S)$ and $\text{max}_n(S)$ respectively in~\ref{eq:minnot} and~\ref{eq:maxnot} to define a short form of taking a subsection of the minimum or maximum of a set. + +\begin{equation}\label{eq:minnot} +\text{min}_n(S) \coloneqq a \subset S \mid \text{where } a \text{ are the } n \text{ smallest numbers of } S +\end{equation} + +\begin{equation}\label{eq:maxnot} +\text{max}_n(S) \coloneqq a \subset S \mid \text{where } a \text{ are the } n \text{ largest numbers of } S +\end{equation} + +This notation helps to define which subsets of samples to give the user for labeling. +There are different ways how this subset can be chosen. +In this PW we do the obvious experiments with High-Certainty first~\ref{subsec:low-certainty-first}, Low-Certainty first~\ref{subsec:high-certainty-first}. +Furthermore, the two mixtures between them, half-high and half-low certain and only the middle section of the sorted certainty scores. + +\subsubsection{Low certainty first}\label{subsec:low-certainty-first} +We take the samples with the lowest certainty score first and give it to the user for labeling. +This is the most intuitive way to do active learning and might also be the most beneficial. + +\begin{equation} + \mathcal{X}_t = \text{min}_\mathcal{B}(S(z)) +\end{equation} + +\subsubsection{High certainty first}\label{subsec:high-certainty-first} +We take the samples with the highest certainty score first and give it to the user for labeling. +The idea behind this is that the model is already very certain about the prediction and the user can confirm this. +This might help ignoring labels which are irrelevant for the model. + +\begin{equation} + \mathcal{X}_t =\text{max}_\mathcal{B}(S(z)) +\end{equation} + +\subsubsection{Low and High certain first} + +We take half the batch-size $\mathcal{B}$ of low certainty and the other half with high certainty samples. +Benefit from both, low and high certainty samples. + +\begin{equation} + \mathcal{X}_t =\text{max}_{\mathcal{B}/2}(S(z)) \cup \text{max}_{\mathcal{B}/2}(S(z)) +\end{equation} + +\subsubsection{Mid certain first} + +We take the middle section of the certainty scores. +To close the gap and have also the fourth variation included in the experiments. +This is expected to perform the worst but might still be better than random sampling in some cases. + +\begin{equation} + \mathcal{X}_t =S(z) \setminus (\text{min}_{\mathcal{S}/2 - \mathcal{B}/2}(S(z)) \cup \text{max}_{\mathcal{S}/2 - \mathcal{B}/2}(S(z))) +\end{equation} + +\subsubsection{Model training} +So now we have defined the samples we want to label with $\mathcal{X}_t$ and the user starts labeling this samples. +After labelling the model $g(\pmb{x};\pmb{w})$ is trained with the new samples and the weights $\pmb{w}$ are updated with the labeled samples $\mathcal{X}_t$. +The loop starts again with the new model and draws new unlabeled samples from $\mathcal{X}_U$. diff --git a/src/llncs.cls b/src/llncs.cls new file mode 100644 index 0000000..29e505e --- /dev/null +++ b/src/llncs.cls @@ -0,0 +1,1189 @@ +% LLNCS DOCUMENT CLASS -- version 2.13 (28-Jan-2002) +% Springer Verlag LaTeX2e support for Lecture Notes in Computer Science +% +%% +%% \CharacterTable +%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +%% Digits \0\1\2\3\4\5\6\7\8\9 +%% Exclamation \! Double quote \" Hash (number) \# +%% Dollar \$ Percent \% Ampersand \& +%% Acute accent \' Left paren \( Right paren \) +%% Asterisk \* Plus \+ Comma \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +%% +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{llncs}[2002/01/28 v2.13 +^^J LaTeX document class for Lecture Notes in Computer Science] +% Options +\let\if@envcntreset\iffalse +\DeclareOption{envcountreset}{\let\if@envcntreset\iftrue} +\DeclareOption{citeauthoryear}{\let\citeauthoryear=Y} +\DeclareOption{oribibl}{\let\oribibl=Y} +\let\if@custvec\iftrue +\DeclareOption{orivec}{\let\if@custvec\iffalse} +\let\if@envcntsame\iffalse +\DeclareOption{envcountsame}{\let\if@envcntsame\iftrue} +\let\if@envcntsect\iffalse +\DeclareOption{envcountsect}{\let\if@envcntsect\iftrue} +\let\if@runhead\iffalse +\DeclareOption{runningheads}{\let\if@runhead\iftrue} + +\let\if@openbib\iffalse +\DeclareOption{openbib}{\let\if@openbib\iftrue} + +% languages +\let\switcht@@therlang\relax +\def\ds@deutsch{\def\switcht@@therlang{\switcht@deutsch}} +\def\ds@francais{\def\switcht@@therlang{\switcht@francais}} + +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}} + +\ProcessOptions + +\LoadClass[twoside]{article} +\RequirePackage{multicol} % needed for the list of participants, index + +\setlength{\textwidth}{12.2cm} +\setlength{\textheight}{19.3cm} +\renewcommand\@pnumwidth{2em} +\renewcommand\@tocrmarg{3.5em} +% +\def\@dottedtocline#1#2#3#4#5{% + \ifnum #1>\c@tocdepth \else + \vskip \z@ \@plus.2\p@ + {\leftskip #2\relax \rightskip \@tocrmarg \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \parindent #2\relax\@afterindenttrue + \interlinepenalty\@M + \leavevmode + \@tempdima #3\relax + \advance\leftskip \@tempdima \null\nobreak\hskip -\leftskip + {#4}\nobreak + \leaders\hbox{$\m@th + \mkern \@dotsep mu\hbox{.}\mkern \@dotsep + mu$}\hfill + \nobreak + \hb@xt@\@pnumwidth{\hfil\normalfont \normalcolor #5}% + \par}% + \fi} +% +\def\switcht@albion{% +\def\abstractname{Abstract.} +\def\ackname{Acknowledgement.} +\def\andname{and} +\def\lastandname{\unskip, and} +\def\appendixname{Appendix} +\def\chaptername{Chapter} +\def\claimname{Claim} +\def\conjecturename{Conjecture} +\def\contentsname{Table of Contents} +\def\corollaryname{Corollary} +\def\definitionname{Definition} +\def\examplename{Example} +\def\exercisename{Exercise} +\def\figurename{Fig.} +\def\keywordname{{\bf Key words:}} +\def\indexname{Index} +\def\lemmaname{Lemma} +\def\contriblistname{List of Contributors} +\def\listfigurename{List of Figures} +\def\listtablename{List of Tables} +\def\mailname{{\it Correspondence to\/}:} +\def\noteaddname{Note added in proof} +\def\notename{Note} +\def\partname{Part} +\def\problemname{Problem} +\def\proofname{Proof} +\def\propertyname{Property} +\def\propositionname{Proposition} +\def\questionname{Question} +\def\remarkname{Remark} +\def\seename{see} +\def\solutionname{Solution} +\def\subclassname{{\it Subject Classifications\/}:} +\def\tablename{Table} +\def\theoremname{Theorem}} +\switcht@albion +% Names of theorem like environments are already defined +% but must be translated if another language is chosen +% +% French section +\def\switcht@francais{%\typeout{On parle francais.}% + \def\abstractname{R\'esum\'e.}% + \def\ackname{Remerciements.}% + \def\andname{et}% + \def\lastandname{ et}% + \def\appendixname{Appendice} + \def\chaptername{Chapitre}% + \def\claimname{Pr\'etention}% + \def\conjecturename{Hypoth\`ese}% + \def\contentsname{Table des mati\`eres}% + \def\corollaryname{Corollaire}% + \def\definitionname{D\'efinition}% + \def\examplename{Exemple}% + \def\exercisename{Exercice}% + \def\figurename{Fig.}% + \def\keywordname{{\bf Mots-cl\'e:}} + \def\indexname{Index} + \def\lemmaname{Lemme}% + \def\contriblistname{Liste des contributeurs} + \def\listfigurename{Liste des figures}% + \def\listtablename{Liste des tables}% + \def\mailname{{\it Correspondence to\/}:} + \def\noteaddname{Note ajout\'ee \`a l'\'epreuve}% + \def\notename{Remarque}% + \def\partname{Partie}% + \def\problemname{Probl\`eme}% + \def\proofname{Preuve}% + \def\propertyname{Caract\'eristique}% +%\def\propositionname{Proposition}% + \def\questionname{Question}% + \def\remarkname{Remarque}% + \def\seename{voir} + \def\solutionname{Solution}% + \def\subclassname{{\it Subject Classifications\/}:} + \def\tablename{Tableau}% + \def\theoremname{Th\'eor\`eme}% +} +% +% German section +\def\switcht@deutsch{%\typeout{Man spricht deutsch.}% + \def\abstractname{Zusammenfassung.}% + \def\ackname{Danksagung.}% + \def\andname{und}% + \def\lastandname{ und}% + \def\appendixname{Anhang}% + \def\chaptername{Kapitel}% + \def\claimname{Behauptung}% + \def\conjecturename{Hypothese}% + \def\contentsname{Inhaltsverzeichnis}% + \def\corollaryname{Korollar}% +%\def\definitionname{Definition}% + \def\examplename{Beispiel}% + \def\exercisename{\"Ubung}% + \def\figurename{Abb.}% + \def\keywordname{{\bf Schl\"usselw\"orter:}} + \def\indexname{Index} +%\def\lemmaname{Lemma}% + \def\contriblistname{Mitarbeiter} + \def\listfigurename{Abbildungsverzeichnis}% + \def\listtablename{Tabellenverzeichnis}% + \def\mailname{{\it Correspondence to\/}:} + \def\noteaddname{Nachtrag}% + \def\notename{Anmerkung}% + \def\partname{Teil}% +%\def\problemname{Problem}% + \def\proofname{Beweis}% + \def\propertyname{Eigenschaft}% +%\def\propositionname{Proposition}% + \def\questionname{Frage}% + \def\remarkname{Anmerkung}% + \def\seename{siehe} + \def\solutionname{L\"osung}% + \def\subclassname{{\it Subject Classifications\/}:} + \def\tablename{Tabelle}% +%\def\theoremname{Theorem}% +} + +% Ragged bottom for the actual page +\def\thisbottomragged{\def\@textbottom{\vskip\z@ plus.0001fil +\global\let\@textbottom\relax}} + +\renewcommand\small{% + \@setfontsize\small\@ixpt{11}% + \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@ + \abovedisplayshortskip \z@ \@plus2\p@ + \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@ + \def\@listi{\leftmargin\leftmargini + \parsep 0\p@ \@plus1\p@ \@minus\p@ + \topsep 8\p@ \@plus2\p@ \@minus4\p@ + \itemsep0\p@}% + \belowdisplayskip \abovedisplayskip +} + +\frenchspacing +\widowpenalty=10000 +\clubpenalty=10000 + +\setlength\oddsidemargin {63\p@} +\setlength\evensidemargin {63\p@} +\setlength\marginparwidth {90\p@} + +\setlength\headsep {16\p@} + +\setlength\footnotesep{7.7\p@} +\setlength\textfloatsep{8mm\@plus 2\p@ \@minus 4\p@} +\setlength\intextsep {8mm\@plus 2\p@ \@minus 2\p@} + +\setcounter{secnumdepth}{2} + +\newcounter {chapter} +\renewcommand\thechapter {\@arabic\c@chapter} + +\newif\if@mainmatter \@mainmattertrue +\newcommand\frontmatter{\cleardoublepage + \@mainmatterfalse\pagenumbering{Roman}} +\newcommand\mainmatter{\cleardoublepage + \@mainmattertrue\pagenumbering{arabic}} +\newcommand\backmatter{\if@openright\cleardoublepage\else\clearpage\fi + \@mainmatterfalse} + +\renewcommand\part{\cleardoublepage + \thispagestyle{empty}% + \if@twocolumn + \onecolumn + \@tempswatrue + \else + \@tempswafalse + \fi + \null\vfil + \secdef\@part\@spart} + +\def\@part[#1]#2{% + \ifnum \c@secnumdepth >-2\relax + \refstepcounter{part}% + \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}% + \else + \addcontentsline{toc}{part}{#1}% + \fi + \markboth{}{}% + {\centering + \interlinepenalty \@M + \normalfont + \ifnum \c@secnumdepth >-2\relax + \huge\bfseries \partname~\thepart + \par + \vskip 20\p@ + \fi + \Huge \bfseries #2\par}% + \@endpart} +\def\@spart#1{% + {\centering + \interlinepenalty \@M + \normalfont + \Huge \bfseries #1\par}% + \@endpart} +\def\@endpart{\vfil\newpage + \if@twoside + \null + \thispagestyle{empty}% + \newpage + \fi + \if@tempswa + \twocolumn + \fi} + +\newcommand\chapter{\clearpage + \thispagestyle{empty}% + \global\@topnum\z@ + \@afterindentfalse + \secdef\@chapter\@schapter} +\def\@chapter[#1]#2{\ifnum \c@secnumdepth >\m@ne + \if@mainmatter + \refstepcounter{chapter}% + \typeout{\@chapapp\space\thechapter.}% + \addcontentsline{toc}{chapter}% + {\protect\numberline{\thechapter}#1}% + \else + \addcontentsline{toc}{chapter}{#1}% + \fi + \else + \addcontentsline{toc}{chapter}{#1}% + \fi + \chaptermark{#1}% + \addtocontents{lof}{\protect\addvspace{10\p@}}% + \addtocontents{lot}{\protect\addvspace{10\p@}}% + \if@twocolumn + \@topnewpage[\@makechapterhead{#2}]% + \else + \@makechapterhead{#2}% + \@afterheading + \fi} +\def\@makechapterhead#1{% +% \vspace*{50\p@}% + {\centering + \ifnum \c@secnumdepth >\m@ne + \if@mainmatter + \large\bfseries \@chapapp{} \thechapter + \par\nobreak + \vskip 20\p@ + \fi + \fi + \interlinepenalty\@M + \Large \bfseries #1\par\nobreak + \vskip 40\p@ + }} +\def\@schapter#1{\if@twocolumn + \@topnewpage[\@makeschapterhead{#1}]% + \else + \@makeschapterhead{#1}% + \@afterheading + \fi} +\def\@makeschapterhead#1{% +% \vspace*{50\p@}% + {\centering + \normalfont + \interlinepenalty\@M + \Large \bfseries #1\par\nobreak + \vskip 40\p@ + }} + +\renewcommand\section{\@startsection{section}{1}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {12\p@ \@plus 4\p@ \@minus 4\p@}% + {\normalfont\large\bfseries\boldmath + \rightskip=\z@ \@plus 8em\pretolerance=10000 }} +\renewcommand\subsection{\@startsection{subsection}{2}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {8\p@ \@plus 4\p@ \@minus 4\p@}% + {\normalfont\normalsize\bfseries\boldmath + \rightskip=\z@ \@plus 8em\pretolerance=10000 }} +\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {-0.5em \@plus -0.22em \@minus -0.1em}% + {\normalfont\normalsize\bfseries\boldmath}} +\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}% + {-12\p@ \@plus -4\p@ \@minus -4\p@}% + {-0.5em \@plus -0.22em \@minus -0.1em}% + {\normalfont\normalsize\itshape}} +\renewcommand\subparagraph[1]{\typeout{LLNCS warning: You should not use + \string\subparagraph\space with this class}\vskip0.5cm +You should not use \verb|\subparagraph| with this class.\vskip0.5cm} + +\DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00} +\DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01} +\DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02} +\DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03} +\DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04} +\DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05} +\DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06} +\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07} +\DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08} +\DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09} +\DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A} + +\let\footnotesize\small + +\if@custvec +\def\vec#1{\mathchoice{\mbox{\boldmath$\displaystyle#1$}} +{\mbox{\boldmath$\textstyle#1$}} +{\mbox{\boldmath$\scriptstyle#1$}} +{\mbox{\boldmath$\scriptscriptstyle#1$}}} +\fi + +\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}} +\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil +\penalty50\hskip1em\null\nobreak\hfil\squareforqed +\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi} + +\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr\gets\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +\gets\cr\to\cr}}}}} +\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +<\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr +>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.8pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.3pt}<\cr}}}}} +\def\bbbr{{\rm I\!R}} %reelle Zahlen +\def\bbbm{{\rm I\!M}} +\def\bbbn{{\rm I\!N}} %natuerliche Zahlen +\def\bbbf{{\rm I\!F}} +\def\bbbh{{\rm I\!H}} +\def\bbbk{{\rm I\!K}} +\def\bbbp{{\rm I\!P}} +\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l} +{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}} +\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}} +\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbs{{\mathchoice +{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}} +\def\bbbz{{\mathchoice {\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}} +{\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}} +{\hbox{$\mathsf\scriptstyle Z\kern-0.3em Z$}} +{\hbox{$\mathsf\scriptscriptstyle Z\kern-0.2em Z$}}}} + +\let\ts\, + +\setlength\leftmargini {17\p@} +\setlength\leftmargin {\leftmargini} +\setlength\leftmarginii {\leftmargini} +\setlength\leftmarginiii {\leftmargini} +\setlength\leftmarginiv {\leftmargini} +\setlength \labelsep {.5em} +\setlength \labelwidth{\leftmargini} +\addtolength\labelwidth{-\labelsep} + +\def\@listI{\leftmargin\leftmargini + \parsep 0\p@ \@plus1\p@ \@minus\p@ + \topsep 8\p@ \@plus2\p@ \@minus4\p@ + \itemsep0\p@} +\let\@listi\@listI +\@listi +\def\@listii {\leftmargin\leftmarginii + \labelwidth\leftmarginii + \advance\labelwidth-\labelsep + \topsep 0\p@ \@plus2\p@ \@minus\p@} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii + \advance\labelwidth-\labelsep + \topsep 0\p@ \@plus\p@\@minus\p@ + \parsep \z@ + \partopsep \p@ \@plus\z@ \@minus\p@} + +\renewcommand\labelitemi{\normalfont\bfseries --} +\renewcommand\labelitemii{$\m@th\bullet$} + +\setlength\arraycolsep{1.4\p@} +\setlength\tabcolsep{1.4\p@} + +\def\tableofcontents{\chapter*{\contentsname\@mkboth{{\contentsname}}% + {{\contentsname}}} + \def\authcount##1{\setcounter{auco}{##1}\setcounter{@auth}{1}} + \def\lastand{\ifnum\value{auco}=2\relax + \unskip{} \andname\ + \else + \unskip \lastandname\ + \fi}% + \def\and{\stepcounter{@auth}\relax + \ifnum\value{@auth}=\value{auco}% + \lastand + \else + \unskip, + \fi}% + \@starttoc{toc}\if@restonecol\twocolumn\fi} + +\def\l@part#1#2{\addpenalty{\@secpenalty}% + \addvspace{2em plus\p@}% % space above part line + \begingroup + \parindent \z@ + \rightskip \z@ plus 5em + \hrule\vskip5pt + \large % same size as for a contribution heading + \bfseries\boldmath % set line in boldface + \leavevmode % TeX command to enter horizontal mode. + #1\par + \vskip5pt + \hrule + \vskip1pt + \nobreak % Never break after part entry + \endgroup} + +\def\@dotsep{2} + +\def\hyperhrefextend{\ifx\hyper@anchor\@undefined\else +{chapter.\thechapter}\fi} + +\def\addnumcontentsmark#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{\protect\numberline + {\thechapter}#3}{\thepage}\hyperhrefextend}} +\def\addcontentsmark#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{#3}{\thepage}\hyperhrefextend}} +\def\addcontentsmarkwop#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{#3}{0}\hyperhrefextend}} + +\def\@adcmk[#1]{\ifcase #1 \or +\def\@gtempa{\addnumcontentsmark}% + \or \def\@gtempa{\addcontentsmark}% + \or \def\@gtempa{\addcontentsmarkwop}% + \fi\@gtempa{toc}{chapter}} +\def\addtocmark{\@ifnextchar[{\@adcmk}{\@adcmk[3]}} + +\def\l@chapter#1#2{\addpenalty{-\@highpenalty} + \vskip 1.0em plus 1pt \@tempdima 1.5em \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip + {\large\bfseries\boldmath#1}\ifx0#2\hfil\null + \else + \nobreak + \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern + \@dotsep mu$}\hfill + \nobreak\hbox to\@pnumwidth{\hss #2}% + \fi\par + \penalty\@highpenalty \endgroup} + +\def\l@title#1#2{\addpenalty{-\@highpenalty} + \addvspace{8pt plus 1pt} + \@tempdima \z@ + \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip + #1\nobreak + \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern + \@dotsep mu$}\hfill + \nobreak\hbox to\@pnumwidth{\hss #2}\par + \penalty\@highpenalty \endgroup} + +\def\l@author#1#2{\addpenalty{\@highpenalty} + \@tempdima=\z@ %15\p@ + \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima %\hskip -\leftskip + \textit{#1}\par + \penalty\@highpenalty \endgroup} + +\setcounter{tocdepth}{0} +\newdimen\tocchpnum +\newdimen\tocsecnum +\newdimen\tocsectotal +\newdimen\tocsubsecnum +\newdimen\tocsubsectotal +\newdimen\tocsubsubsecnum +\newdimen\tocsubsubsectotal +\newdimen\tocparanum +\newdimen\tocparatotal +\newdimen\tocsubparanum +\tocchpnum=\z@ % no chapter numbers +\tocsecnum=15\p@ % section 88. plus 2.222pt +\tocsubsecnum=23\p@ % subsection 88.8 plus 2.222pt +\tocsubsubsecnum=27\p@ % subsubsection 88.8.8 plus 1.444pt +\tocparanum=35\p@ % paragraph 88.8.8.8 plus 1.666pt +\tocsubparanum=43\p@ % subparagraph 88.8.8.8.8 plus 1.888pt +\def\calctocindent{% +\tocsectotal=\tocchpnum +\advance\tocsectotal by\tocsecnum +\tocsubsectotal=\tocsectotal +\advance\tocsubsectotal by\tocsubsecnum +\tocsubsubsectotal=\tocsubsectotal +\advance\tocsubsubsectotal by\tocsubsubsecnum +\tocparatotal=\tocsubsubsectotal +\advance\tocparatotal by\tocparanum} +\calctocindent + +\def\l@section{\@dottedtocline{1}{\tocchpnum}{\tocsecnum}} +\def\l@subsection{\@dottedtocline{2}{\tocsectotal}{\tocsubsecnum}} +\def\l@subsubsection{\@dottedtocline{3}{\tocsubsectotal}{\tocsubsubsecnum}} +\def\l@paragraph{\@dottedtocline{4}{\tocsubsubsectotal}{\tocparanum}} +\def\l@subparagraph{\@dottedtocline{5}{\tocparatotal}{\tocsubparanum}} + +\def\listoffigures{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn + \fi\section*{\listfigurename\@mkboth{{\listfigurename}}{{\listfigurename}}} + \@starttoc{lof}\if@restonecol\twocolumn\fi} +\def\l@figure{\@dottedtocline{1}{0em}{1.5em}} + +\def\listoftables{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn + \fi\section*{\listtablename\@mkboth{{\listtablename}}{{\listtablename}}} + \@starttoc{lot}\if@restonecol\twocolumn\fi} +\let\l@table\l@figure + +\renewcommand\listoffigures{% + \section*{\listfigurename + \@mkboth{\listfigurename}{\listfigurename}}% + \@starttoc{lof}% + } + +\renewcommand\listoftables{% + \section*{\listtablename + \@mkboth{\listtablename}{\listtablename}}% + \@starttoc{lot}% + } + +\ifx\oribibl\undefined +\ifx\citeauthoryear\undefined +\renewenvironment{thebibliography}[1] + {\section*{\refname} + \def\@biblabel##1{##1.} + \small + \list{\@biblabel{\@arabic\c@enumiv}}% + {\settowidth\labelwidth{\@biblabel{#1}}% + \leftmargin\labelwidth + \advance\leftmargin\labelsep + \if@openbib + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + \fi + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{\@arabic\c@enumiv}}% + \if@openbib + \renewcommand\newblock{\par}% + \else + \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% + \fi + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.=\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} +\def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw + {\let\protect\noexpand\immediate + \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces} +\newcount\@tempcntc +\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do + {\@ifundefined + {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries + ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% + {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}% + \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne + \@citea\def\@citea{,}\hbox{\csname b@\@citeb\endcsname}% + \else + \advance\@tempcntb\@ne + \ifnum\@tempcntb=\@tempcntc + \else\advance\@tempcntb\m@ne\@citeo + \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}} +\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else + \@citea\def\@citea{,\,\hskip\z@skip}% + \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else + {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else + \def\@citea{--}\fi + \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi} +\else +\renewenvironment{thebibliography}[1] + {\section*{\refname} + \small + \list{}% + {\settowidth\labelwidth{}% + \leftmargin\parindent + \itemindent=-\parindent + \labelsep=\z@ + \if@openbib + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + \fi + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{}}% + \if@openbib + \renewcommand\newblock{\par}% + \else + \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% + \fi + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.=\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} + \def\@cite#1{#1}% + \def\@lbibitem[#1]#2{\item[]\if@filesw + {\def\protect##1{\string ##1\space}\immediate + \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces} + \fi +\else +\@cons\@openbib@code{\noexpand\small} +\fi + +\def\idxquad{\hskip 10\p@}% space that divides entry from number + +\def\@idxitem{\par\hangindent 10\p@} + +\def\subitem{\par\setbox0=\hbox{--\enspace}% second order + \noindent\hangindent\wd0\box0}% index entry + +\def\subsubitem{\par\setbox0=\hbox{--\,--\enspace}% third + \noindent\hangindent\wd0\box0}% order index entry + +\def\indexspace{\par \vskip 10\p@ plus5\p@ minus3\p@\relax} + +\renewenvironment{theindex} + {\@mkboth{\indexname}{\indexname}% + \thispagestyle{empty}\parindent\z@ + \parskip\z@ \@plus .3\p@\relax + \let\item\par + \def\,{\relax\ifmmode\mskip\thinmuskip + \else\hskip0.2em\ignorespaces\fi}% + \normalfont\small + \begin{multicols}{2}[\@makeschapterhead{\indexname}]% + } + {\end{multicols}} + +\renewcommand\footnoterule{% + \kern-3\p@ + \hrule\@width 2truecm + \kern2.6\p@} + \newdimen\fnindent + \fnindent1em +\long\def\@makefntext#1{% + \parindent \fnindent% + \leftskip \fnindent% + \noindent + \llap{\hb@xt@1em{\hss\@makefnmark\ }}\ignorespaces#1} + +\long\def\@makecaption#1#2{% + \vskip\abovecaptionskip + \sbox\@tempboxa{{\bfseries #1.} #2}% + \ifdim \wd\@tempboxa >\hsize + {\bfseries #1.} #2\par + \else + \global \@minipagefalse + \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}% + \fi + \vskip\belowcaptionskip} + +\def\fps@figure{htbp} +\def\fnum@figure{\figurename\thinspace\thefigure} +\def \@floatboxreset {% + \reset@font + \small + \@setnobreak + \@setminipage +} +\def\fps@table{htbp} +\def\fnum@table{\tablename~\thetable} +\renewenvironment{table} + {\setlength\abovecaptionskip{0\p@}% + \setlength\belowcaptionskip{10\p@}% + \@float{table}} + {\end@float} +\renewenvironment{table*} + {\setlength\abovecaptionskip{0\p@}% + \setlength\belowcaptionskip{10\p@}% + \@dblfloat{table}} + {\end@dblfloat} + +\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname + ext@#1\endcsname}{#1}{\protect\numberline{\csname + the#1\endcsname}{\ignorespaces #2}}\begingroup + \@parboxrestore + \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par + \endgroup} + +% LaTeX does not provide a command to enter the authors institute +% addresses. The \institute command is defined here. + +\newcounter{@inst} +\newcounter{@auth} +\newcounter{auco} +\newdimen\instindent +\newbox\authrun +\newtoks\authorrunning +\newtoks\tocauthor +\newbox\titrun +\newtoks\titlerunning +\newtoks\toctitle + +\def\clearheadinfo{\gdef\@author{No Author Given}% + \gdef\@title{No Title Given}% + \gdef\@subtitle{}% + \gdef\@institute{No Institute Given}% + \gdef\@thanks{}% + \global\titlerunning={}\global\authorrunning={}% + \global\toctitle={}\global\tocauthor={}} + +\def\institute#1{\gdef\@institute{#1}} + +\def\institutename{\par + \begingroup + \parskip=\z@ + \parindent=\z@ + \setcounter{@inst}{1}% + \def\and{\par\stepcounter{@inst}% + \noindent$^{\the@inst}$\enspace\ignorespaces}% + \setbox0=\vbox{\def\thanks##1{}\@institute}% + \ifnum\c@@inst=1\relax + \gdef\fnnstart{0}% + \else + \xdef\fnnstart{\c@@inst}% + \setcounter{@inst}{1}% + \noindent$^{\the@inst}$\enspace + \fi + \ignorespaces + \@institute\par + \endgroup} + +\def\@fnsymbol#1{\ensuremath{\ifcase#1\or\star\or{\star\star}\or + {\star\star\star}\or \dagger\or \ddagger\or + \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger + \or \ddagger\ddagger \else\@ctrerr\fi}} + +\def\inst#1{\unskip$^{#1}$} +\def\fnmsep{\unskip$^,$} +\def\email#1{{\tt#1}} +\AtBeginDocument{\@ifundefined{url}{\def\url#1{#1}}{}% +\@ifpackageloaded{babel}{% +\@ifundefined{extrasenglish}{}{\addto\extrasenglish{\switcht@albion}}% +\@ifundefined{extrasfrenchb}{}{\addto\extrasfrenchb{\switcht@francais}}% +\@ifundefined{extrasgerman}{}{\addto\extrasgerman{\switcht@deutsch}}% +}{\switcht@@therlang}% +} +\def\homedir{\~{ }} + +\def\subtitle#1{\gdef\@subtitle{#1}} +\clearheadinfo + +\renewcommand\maketitle{\newpage + \refstepcounter{chapter}% + \stepcounter{section}% + \setcounter{section}{0}% + \setcounter{subsection}{0}% + \setcounter{figure}{0} + \setcounter{table}{0} + \setcounter{equation}{0} + \setcounter{footnote}{0}% + \begingroup + \parindent=\z@ + \renewcommand\thefootnote{\@fnsymbol\c@footnote}% + \if@twocolumn + \ifnum \col@number=\@ne + \@maketitle + \else + \twocolumn[\@maketitle]% + \fi + \else + \newpage + \global\@topnum\z@ % Prevents figures from going at top of page. + \@maketitle + \fi + \thispagestyle{empty}\@thanks +% + \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}% + \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}% + \instindent=\hsize + \advance\instindent by-\headlineindent + \if!\the\toctitle!\addcontentsline{toc}{title}{\@title}\else + \addcontentsline{toc}{title}{\the\toctitle}\fi + \if@runhead + \if!\the\titlerunning!\else + \edef\@title{\the\titlerunning}% + \fi + \global\setbox\titrun=\hbox{\small\rm\unboldmath\ignorespaces\@title}% + \ifdim\wd\titrun>\instindent + \typeout{Title too long for running head. Please supply}% + \typeout{a shorter form with \string\titlerunning\space prior to + \string\maketitle}% + \global\setbox\titrun=\hbox{\small\rm + Title Suppressed Due to Excessive Length}% + \fi + \xdef\@title{\copy\titrun}% + \fi +% + \if!\the\tocauthor!\relax + {\def\and{\noexpand\protect\noexpand\and}% + \protected@xdef\toc@uthor{\@author}}% + \else + \def\\{\noexpand\protect\noexpand\newline}% + \protected@xdef\scratch{\the\tocauthor}% + \protected@xdef\toc@uthor{\scratch}% + \fi + \addcontentsline{toc}{author}{\toc@uthor}% + \if@runhead + \if!\the\authorrunning! + \value{@inst}=\value{@auth}% + \setcounter{@auth}{1}% + \else + \edef\@author{\the\authorrunning}% + \fi + \global\setbox\authrun=\hbox{\small\unboldmath\@author\unskip}% + \ifdim\wd\authrun>\instindent + \typeout{Names of authors too long for running head. Please supply}% + \typeout{a shorter form with \string\authorrunning\space prior to + \string\maketitle}% + \global\setbox\authrun=\hbox{\small\rm + Authors Suppressed Due to Excessive Length}% + \fi + \xdef\@author{\copy\authrun}% + \markboth{\@author}{\@title}% + \fi + \endgroup + \setcounter{footnote}{\fnnstart}% + \clearheadinfo} +% +\def\@maketitle{\newpage + \markboth{}{}% + \def\lastand{\ifnum\value{@inst}=2\relax + \unskip{} \andname\ + \else + \unskip \lastandname\ + \fi}% + \def\and{\stepcounter{@auth}\relax + \ifnum\value{@auth}=\value{@inst}% + \lastand + \else + \unskip, + \fi}% + \begin{center}% + \let\newline\\ + {\Large \bfseries\boldmath + \pretolerance=10000 + \@title \par}\vskip .8cm +\if!\@subtitle!\else {\large \bfseries\boldmath + \vskip -.65cm + \pretolerance=10000 + \@subtitle \par}\vskip .8cm\fi + \setbox0=\vbox{\setcounter{@auth}{1}\def\and{\stepcounter{@auth}}% + \def\thanks##1{}\@author}% + \global\value{@inst}=\value{@auth}% + \global\value{auco}=\value{@auth}% + \setcounter{@auth}{1}% +{\lineskip .5em +\noindent\ignorespaces +\@author\vskip.35cm} + {\small\institutename} + \end{center}% + } + +% definition of the "\spnewtheorem" command. +% +% Usage: +% +% \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font} +% or \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font} +% or \spnewtheorem*{env_nam}{caption}{cap_font}{body_font} +% +% New is "cap_font" and "body_font". It stands for +% fontdefinition of the caption and the text itself. +% +% "\spnewtheorem*" gives a theorem without number. +% +% A defined spnewthoerem environment is used as described +% by Lamport. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\def\@thmcountersep{} +\def\@thmcounterend{.} + +\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}} + +% definition of \spnewtheorem with number + +\def\@spnthm#1#2{% + \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}} +\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}} + +\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}\@addtoreset{#1}{#3}% + \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand + \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}% + \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spothm#1[#2]#3#4#5{% + \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}% + {\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{the#1}{\@nameuse{the#2}}% + \expandafter\xdef\csname #1name\endcsname{#3}% + \global\@namedef{#1}{\@spthm{#2}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}}} + +\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\refstepcounter{#1}% +\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}} + +\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}% + \ignorespaces} + +\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname + the#1\endcsname}{#5}{#3}{#4}\ignorespaces} + +\def\@spbegintheorem#1#2#3#4{\trivlist + \item[\hskip\labelsep{#3#1\ #2\@thmcounterend}]#4} + +\def\@spopargbegintheorem#1#2#3#4#5{\trivlist + \item[\hskip\labelsep{#4#1\ #2}]{#4(#3)\@thmcounterend\ }#5} + +% definition of \spnewtheorem* without number + +\def\@sthm#1#2{\@Ynthm{#1}{#2}} + +\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}} + +\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces} + +\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1} + {#4}{#2}{#3}\ignorespaces} + +\def\@Begintheorem#1#2#3{#3\trivlist + \item[\hskip\labelsep{#2#1\@thmcounterend}]} + +\def\@Opargbegintheorem#1#2#3#4{#4\trivlist + \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }} + +\if@envcntsect + \def\@thmcountersep{.} + \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape} +\else + \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape} + \if@envcntreset + \@addtoreset{theorem}{section} + \else + \@addtoreset{theorem}{chapter} + \fi +\fi + +%definition of divers theorem environments +\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily} +\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily} +\if@envcntsame % alle Umgebungen wie Theorem. + \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}} +\else % alle Umgebungen mit eigenem Zaehler + \if@envcntsect % mit section numeriert + \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}} + \else % nicht mit section numeriert + \if@envcntreset + \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4} + \@addtoreset{#1}{section}} + \else + \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4} + \@addtoreset{#1}{chapter}}% + \fi + \fi +\fi +\spn@wtheorem{case}{Case}{\itshape}{\rmfamily} +\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily} +\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape} +\spn@wtheorem{definition}{Definition}{\bfseries}{\itshape} +\spn@wtheorem{example}{Example}{\itshape}{\rmfamily} +\spn@wtheorem{exercise}{Exercise}{\itshape}{\rmfamily} +\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape} +\spn@wtheorem{note}{Note}{\itshape}{\rmfamily} +\spn@wtheorem{problem}{Problem}{\itshape}{\rmfamily} +\spn@wtheorem{property}{Property}{\itshape}{\rmfamily} +\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape} +\spn@wtheorem{question}{Question}{\itshape}{\rmfamily} +\spn@wtheorem{solution}{Solution}{\itshape}{\rmfamily} +\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily} + +\def\@takefromreset#1#2{% + \def\@tempa{#1}% + \let\@tempd\@elt + \def\@elt##1{% + \def\@tempb{##1}% + \ifx\@tempa\@tempb\else + \@addtoreset{##1}{#2}% + \fi}% + \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname + \expandafter\def\csname cl@#2\endcsname{}% + \@tempc + \let\@elt\@tempd} + +\def\theopargself{\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5} + \def\@Opargbegintheorem##1##2##3##4{##4\trivlist + \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }} + } + +\renewenvironment{abstract}{% + \list{}{\advance\topsep by0.35cm\relax\small + \leftmargin=1cm + \labelwidth=\z@ + \listparindent=\z@ + \itemindent\listparindent + \rightmargin\leftmargin}\item[\hskip\labelsep + \bfseries\abstractname]} + {\endlist} + +\newdimen\headlineindent % dimension for space between +\headlineindent=1.166cm % number and text of headings. + +\def\ps@headings{\let\@mkboth\@gobbletwo + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}% + \leftmark\hfil} + \def\@oddhead{\normalfont\small\hfil\rightmark\hspace{\headlineindent}% + \llap{\thepage}} + \def\chaptermark##1{}% + \def\sectionmark##1{}% + \def\subsectionmark##1{}} + +\def\ps@titlepage{\let\@mkboth\@gobbletwo + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}% + \hfil} + \def\@oddhead{\normalfont\small\hfil\hspace{\headlineindent}% + \llap{\thepage}} + \def\chaptermark##1{}% + \def\sectionmark##1{}% + \def\subsectionmark##1{}} + +\if@runhead\ps@headings\else +\ps@empty\fi + +\setlength\arraycolsep{1.4\p@} +\setlength\tabcolsep{1.4\p@} + +\endinput +%end of file llncs.cls diff --git a/src/main.tex b/src/main.tex index 7081620..586494f 100644 --- a/src/main.tex +++ b/src/main.tex @@ -1,12 +1,22 @@ +\def\ieee{1} + +\if\ieee1 \documentclass[sigconf]{acmart} +\else +\documentclass{llncs} +\fi \usepackage{amsmath} \usepackage{mathtools} +\usepackage{hyperref} \usepackage[inline]{enumitem} + +\if\ieee1 \settopmatter{printacmref=false} % Removes citation information below abstract \renewcommand\footnotetextcopyrightpermission[1]{} % removes footnote with conference information in first column \pagestyle{plain} % removes running headers +\fi %% %% \BibTeX command to typeset BibTeX logo in the docs @@ -14,7 +24,9 @@ \providecommand\BibTeX{{% \normalfont B\kern-0.5em{\scshape i\kern-0.25em b}\kern-0.8em\TeX}}} +\if\ieee1 \acmConference{Minimize labeling effort of Binary classification Tasks with Active learning}{2023}{Linz} +\fi %% %% end of the preamble, start of the body of the document source. @@ -32,14 +44,18 @@ %% "authornote" and "authornotemark" commands %% used to denote shared contribution to the research. \author{Lukas Heiligenbrunner} + + \if\ieee1 \email{k12104785@students.jku.at} \affiliation{% - \institution{Johannes Kepler University Linz} - \city{Linz} - \state{Upperaustria} - \country{Austria} - \postcode{4020} + \institution{Johannes Kepler University Linz} + \city{Linz} + \state{Upperaustria} + \country{Austria} + \postcode{4020} } + \fi + %% %% By default, the full list of authors will be used in the page @@ -47,11 +63,15 @@ %% other information printed in the page headers. This command allows %% the author to define a more concise list %% of authors' names for this purpose. - \renewcommand{\shortauthors}{Lukas Heilgenbrunner} +% \renewcommand{\shortauthors}{Lukas Heilgenbrunner} %% %% The abstract is a short summary of the work to be presented in the %% article. + \if\ieee0 + \maketitle + \fi + \begin{abstract} Active learning might result in a faster model convergence and thus less labeled samples would be required. This method might be beneficial in areas where labeling datasets is demanding and reducing computational effort is not the main objective. \end{abstract} @@ -59,7 +79,9 @@ %% %% Keywords. The author(s) should pick words that accurately describe %% the work being presented. Separate the keywords with commas. + \if\ieee1 \keywords{neural networks, ResNET, pseudo-labeling, active-learning} + \fi %\received{20 February 2007} %\received[revised]{12 March 2009} @@ -68,7 +90,9 @@ %% %% This command processes the author and affiliation and title %% information and builds the first part of the formatted document. + \if\ieee1 \maketitle + \fi \input{introduction} \input{materialandmethods} \input{implementation} diff --git a/src/materialandmethods.tex b/src/materialandmethods.tex index a8c5b28..e1981ca 100644 --- a/src/materialandmethods.tex +++ b/src/materialandmethods.tex @@ -24,7 +24,7 @@ Moreover, it can be used for clustering or downprojection. Those two techniques combined yield semi-supervised learning. Some of the labels are known, but for most of the data we have only the raw datapoints. -The basic idea is that the unlabeled data can significantly improve the model performance when used in combination with the labeled data. +The basic idea is that the unlabeled data can significantly improve the model performance when used in combination with the labeled data.\cite{Xu_2022_CVPR} \subsubsection{ROC and AUC} @@ -74,5 +74,16 @@ Its a generalization of the Sigmoid function and often used as an Activation Lay The softmax function has high similarities with the Boltzmann distribution and was first introduced in the 19$^{\textrm{th}}$ century~\cite{Boltzmann}. \subsubsection{Cross Entropy Loss} -% todo maybe remove this +Cross Entropy Loss is a well established loss function in machine learning. +\eqref{eq:crelformal} shows the formal general definition of the Cross Entropy Loss. +And~\eqref{eq:crelbinary} is the special case of the general Cross Entropy Loss for binary classification tasks. + +\begin{align} + H(p,q) &= -\sum_{x\in\mathcal{X}} p(x)\, \log q(x)\label{eq:crelformal}\\ + H(p,q) &= - (p \log q + (1-p) \log(1-q))\label{eq:crelbinary}\\ + \mathcal{L}(p,q) &= - \frac1N \sum_{i=1}^{\mathcal{B}} (p_i \log q_i + (1-p_i) \log(1-q_i))\label{eq:crelbinarybatch} +\end{align} + +$\mathcal{L}(p,q)$~\eqref{eq:crelbinarybatch} is the Binary Cross Entropy Loss for a batch of size $\mathcal{B}$ and used for model training in this PW. + \subsubsection{Adam}