Commit 5bd3d3e0 authored by Loïc Barrault's avatar Loïc Barrault
Browse files

ie

parent 139c5369
...@@ -90,7 +90,7 @@ Why doing \myemph{information extraction}? ...@@ -90,7 +90,7 @@ Why doing \myemph{information extraction}?
The \textbf{structured form} can be implemented either as a database or form (slot filling) or by using XML tags (tagging) The \textbf{structured form} can be implemented either as a database or form (slot filling) or by using XML tags (tagging)
\vfill \vfill
\todo{ADD A GRAPHIC WITH OBAMA, events = president start, end... WIFE = michelle etc...} %\todo{ADD A GRAPHIC WITH OBAMA, events = president start, end... WIFE = michelle etc...}
\end{frame} \end{frame}
...@@ -330,7 +330,7 @@ Identify all assertions of relations between entities %usually binary ...@@ -330,7 +330,7 @@ Identify all assertions of relations between entities %usually binary
May be divided into two subtasks: May be divided into two subtasks:
\begin{itemize} \begin{itemize}
\item \textbf{Relation detection}: find pairs of entities between which a relation holds \item \textbf{Relation detection}: find pairs of entities between which a relation holds
\item \textbf{Relation classification}: determine the type of a previously extracted relation \item \textbf{Relation classification}: determine the type of a previously detected relation
\end{itemize} \end{itemize}
\vfill \vfill
...@@ -385,7 +385,7 @@ Example: ...@@ -385,7 +385,7 @@ Example:
\begin{frame} \begin{frame}
\frametitle{Information Extraction: Event extraction} \frametitle{Information Extraction: Event extraction}
\begin{block}{\textbf{Relation Extraction}} \begin{block}{\textbf{Event Extraction}}
Identify all reports of event instances, typically of a small set of classes Identify all reports of event instances, typically of a small set of classes
\end{block} \end{block}
......
...@@ -910,6 +910,31 @@ the \myemph{Ashoka} mentioned is likely to be in Sheffield, while the Sheffield ...@@ -910,6 +910,31 @@ the \myemph{Ashoka} mentioned is likely to be in Sheffield, while the Sheffield
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: NER: Conclusion}
\textbf{Named Entity Recognition} (NER) is a core IE technology
\begin{itemize}
\item detect and classify all mentions of NE of a given set of entity types within a given text
\item now relatively mature and at “usable” performance levels
\end{itemize}
\textbf{Techniques used have included:}
\begin{itemize}
\item knowledge engineering approaches
\item supervised learning approaches, e.g. BIO sequence labelling
\end{itemize}
\textbf{Open challenges include:}
\begin{itemize}
\item reducing the amount of training data needed via, e.g. bootstrapping techniques
\item exploiting existing structured data sources to generate “weakly labelled” training data (aka distant supervision)
\item expanding the classes of entities addressed
\item developing NERs for languages other than English
\end{itemize}
\end{frame}
......
% !TEX root = text_processing.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{}
\vfill
\centering
\Huge{\edinred{[Information Extraction]\\Relation Extraction}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Overview}
\begin{itemize}
\item \gray{Introduction to Information Extraction}
\begin{itemize}
\item \gray{Definition + contrast with IR}
\item \gray{Example Applications}
\item \gray{Overview of Tasks}
\item \gray{Overview of Approaches}
\item \gray{Evaluation + Shared Task Challenges}
\item \gray{Brief(est) history of IE}
\end{itemize}
\item \gray{Named Entity Recognition}
\begin{itemize}
\item \gray{Task}
\item \gray{Approaches: Rule-based, Supervised Learning}
\item \gray{Entity Linking}
\end{itemize}
\item \textbf{Relation Extraction}
\begin{itemize}
\item \textbf{Task}
\item \textbf{Approaches: Rule-based, Supervised Learning, Bootstrapping, Distant Supervision}
\end{itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Overview}
\textbf{Relation Extraction}
\begin{itemize}
\item Task definition
\end{itemize}
\textbf{Approaches to Relation Extraction}
\begin{itemize}
\item Knowledge-engineering approaches to RE
\item Supervised learning approaches to RE
\item Bootstrapping Approaches to RE
\item Distant Supervision Approaches to RE
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction - recap}
\begin{block}{\textbf{Relation Extraction (RE)}}
Task: Identify all \myemph{assertions of relations} holding between \myemph{entities} in a text $T$\\
\begin{itemize}
\item the entities are identified in previous entity extraction step
\item The set of possible relations $\mathbf{R}$ is determined in advance
\end{itemize}
\end{block}
\textbf{Note:}
\begin{itemize}
\item relations in $\mathbf{R}$ are usually binary
\item the entity classes involved in a relation in $\mathbf{R}$ are assumed to be a subset of those identified in the entity extraction process
\end{itemize}
\textbf{Generally divided into two subtasks:}
\begin{enumerate}
\item \myemph{Relation detection}: find pairs of entities between which a relation holds
\item \myemph{Relation classification}: determine the type of a previously detected relation
\end{enumerate}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Examples}
\textbf{Some examples}
\begin{itemize}
\item \textsc{location\_of} holding between:
\begin{itemize}
\item \textsc{organisation} and \textsc{geopolitical\_location}
\item medical \textsc{investigation} and \textsc{ body\_part}
\item \textsc{gene} and \textsc{chromosome\_location}
\end{itemize}
\item \textsc{employee\_of} holding between \textsc{person} and \textsc{organisation}\\
\item \textsc{product\_of} holding between \textsc{artifact} and \textsc{organisation}\\
\item \textsc{is\_exposed\_to} holding between \textsc{organisation} and \textsc{risk}\\
\item \textsc{is\_associated\_with} holding between \textsc{drug} and \textsc{side\_effect}\\
\item \textsc{interaction} holding between \textsc{protein} and \textsc{protein}\\
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Challenges}
\textbf{Challenges for Relation Extraction}
\begin{enumerate}
\item<1-> Many different ways to express the same relation
\begin{itemize}
\item \myemph{Canonical}: \annot{Microsoft}{ORG} \textbf{\underline{is located in}} \annot{Redmond}{LOC}
\item \myemph{Synonyms}: \annot{Microsoft}{ORG} \textbf{\underline{is located/based/headquartered in}} \annot{Redmond}{LOC}
\item \myemph{Syntactic variations}:
\begin{itemize}
\item \annot{Microsoft}{ORG}, the software giant and ... , \textbf{\underline{is based in}} \annot{Redmond}{LOC}
\item \annot{Redmond}{LOC}\textbf{\underline{-based}} \annot{Microsoft}{ORG} ...
\item \annot{Redmond}{LOC}\textbf{\underline{'s}} \annot{Microsoft}{ORG} ...
\item \annot{Redmond}{LOC} software giant \annot{Microsoft}{ORG} ...
\end{itemize}
\end{itemize}
\item<2-> Relations often involve coreference links\\
\small{
\myemph{\annot{Bill Gates}{PER}} \textbf{\underline{is co-founder, technology advisor and board member}} of \annot{Microsoft}{ORG}. \myemph{\annot{He}{PER}} \textbf{\underline{served as chairman of the board}} until Feb. 4, 2014. On June 27, 2008, \myemph{\annot{Gates}{PER}} \textbf{\underline{transitioned out}} of a day-to-day role in the company to spend more time on his global health and education work at the \annot{Bill \& Melinda Gates Foundation}{ORG}.
}
\end{enumerate}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Challenges}
\textbf{Challenges for Relation Extraction}
\begin{enumerate}
\setcounter{enumi}{2}
\item The information required may be spread across multiple sentences
\item The information may be implied by the text rather than explicitly asserted \ra\ \myemphb{inference}
\end{enumerate}
\textbf{Ex1.:}
\myemph{\annot{Dirk Ruthless}{PER}} of \annot{MegaCorp}{ORG} made a stunning announcement today. In September \myemph{\annot{he}{PER}} will be stepping down as \annot{Chief Executive Officer}{POS} to spend more time with his pet piranhas.
\begin{itemize}
\item[\Ra] resolve \textbf{pronominal anaphor} \myemph{Dirk Ruthless} \Lra\ \myemph{he} to determine the corporate \textsc{position}
\item[\Ra] In Ex1.: no explicit statement that \myemph{Dirk Ruthless} \textbf{is} CEO of MegaCorp
\begin{itemize}
\item "\myemph{\annot{Dirk Ruthless}{PER}} of \annot{MegaCorp}{ORG}" + "will be stepping down as \annot{Chief Executive Officer}{POS}" = \myemph{\annot{Dirk Ruthless}{PER}} is CEO of \annot{MegaCorp}{ORG}
\end{itemize}
\item Solving RE may imply solving \myemphb{textual entailment}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Overview}
\gray{Relation Extraction}
\begin{itemize}
\item \gray{Task definition}
\end{itemize}
\textbf{Approaches to Relation Extraction}
\begin{itemize}
\item \textbf{Knowledge-engineering approaches to RE}
\item Supervised learning approaches to RE
\item Bootstrapping Approaches to RE
\item Distant Supervision Approaches to RE
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Knowledge-engineering}
\colorbox{liumlightgray}{
\parbox{.99\textwidth}{
\annot{Mr. \tikzmark{a} Wright}{PER}, \textbf{\underline{\annot{executive vice president}{POSITION}}} of \annot{Merrill Lynch \tikzmark{b} Canada Inc.}{ORG}\\
\begin{tikzpicture}[overlay,remember picture]
\draw [very thick, color=carminered] ($({pic cs:a})+(0ex,-1ex)$) -- ($({pic cs:a})+(0ex,-3ex)$);
\draw [very thick, color=carminered] ($({pic cs:a})+(0ex,-3ex)$) -- ($({pic cs:b})+(0ex,-3ex)$) node [midway, below, color=carminered] {is-employed-by};
\draw [very thick, color=carminered] ($({pic cs:b})+(0ex,-3ex)$) -- ($({pic cs:b})+(0ex,-1ex)$);
\end{tikzpicture}
}}
\vfill
Such systems use manually authored rules and can be divided into
\begin{itemize}
\item<1-> “\myemph{shallow}”: systems engineered to the IE task, typically using \myemphb{pattern-action} rules
\begin{center}
\begin{tabular}{ll}
Pattern: & \textbf{"\$Person, \$Position of \$Organization"} \\
Action: & \textbf{add-relation(is-employed-by(\$Person,\$Organization))} \\
\end{tabular}
\end{center}
\vspace{.5cm}
\item<2-> “\myemph{deep}”: linguistically inspired language understanding systems
\end{itemize}
\vfill
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Knowledge-engineering}
\begin{itemize}
\item\myemph{deep}”: linguistically inspired language understanding systems
\begin{itemize}
\item parse input to identify key grammatical relations (e.g. subject, object)
\item use transduction rules on parser output to extract relations
\item[\ra] more powerful than regex on NE tags alone
\end{itemize}
\end{itemize}
\vspace{3.5cm}
\only<2->{
\begin{itemize}
\item Ex. parse trees:
\begin{itemize}
\item Multiple surface forms share underlying syntactic structure
\item \textsc{subject} = PER, \textsc{object} = ORG and \textsc{verb} = \textbf{works for}
\end{itemize}
\end{itemize}
\begin{textblock*}{50mm}[0,0](115mm,25mm)
\includegraphics[height=.45\textheight]{syntaxtree1}
\end{textblock*}
\begin{textblock*}{50mm}[0,0](55mm,25mm)
\includegraphics[height=.45\textheight]{syntaxtree2}
\end{textblock*}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Knowledge-engineering}
\textbf{Strengths}
\begin{itemize}
\item High precision
\item Interpretable results \ra\ system behaviour is human-comprehensible
\end{itemize}
\textbf{Weaknesses}
\begin{itemize}
\item The writing of rules has no end
\item New rules needed for every new domain
\begin{itemize}
\item pattern action rules for shallow approaches
\item transduction rules for deep approaches
\end{itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Overview}
\gray{Relation Extraction}
\begin{itemize}
\item \gray{Task definition}
\end{itemize}
\textbf{Approaches to Relation Extraction}
\begin{itemize}
\item \gray{Knowledge-engineering approaches to RE}
\item \textbf{Supervised learning approaches to RE}
\item Bootstrapping Approaches to RE
\item Distant Supervision Approaches to RE
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Supervised learning}
\textbf{Question: what is to be learned?}
Answer 1: \myemph{rules}
\begin{itemize}
\item to match \textbf{relation bearing sentences}
\item capture the \textbf{relation arguments} in the matched text
\end{itemize}
Answer 2: \myemph{binary classifier}
\begin{itemize}
\item Classifies a sentence as to whether it bears a specific relation between some entity types
\item Specialized binary classifier
\item Can be divided in two stages:
\begin{itemize}
\item \myemph{relation detection}: determines whether a sentence expresses a relation (binary)
\item \myemph{relation classification}: determines the relation (multi-way)
\end{itemize}
\item Rule learning popular until early 2000's. Then classifier approach.
\item[\ra] Details on classifier approach only
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Supervised Learning}
Classification approaches to relation extraction:
\begin{itemize}
\item Assume entities are already tagged \ra\ output of NER
\item Use an algorithm to learn binary classifiers to distinguish instances where
\begin{itemize}
\item entities co-occur and relation holds (positive instances)
\item entities co-occur and relation does not hold (negative instances)
\end{itemize}
\end{itemize}
Key issue: what \textbf{features} to use to represent instances?
\begin{itemize}
\item 3 broad classes:
\begin{itemize}
\item Features of the Named Entities
\item Features from the words in the text
\begin{itemize}
\item words between the two NE
\item words surrounding the candidates (left of 1st word and right of 2nd word)
\end{itemize}
\item Features about the entity pair within the sentence, e.g.
\begin{itemize}
\item distance between the entities (in words or constituents)
\item is there a NE in between them?
\item clues from the syntactic structure of the sentence (parse tree)
\end{itemize}
\end{itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Supervised Learning: Example}
Ex.: \annot{American Airlines}{ORG}, a unit of \annot{AMR Inc.}{ORG}, immediately matched the move, spokesman \annot{Tim Wagner}{PER} said. \source{Jurafsky and Martin, 2nd ed., p. 730}
Features extracted from this example:
\scriptsize{
\begin{center}
\setlength\extrarowheight{-3pt}
\begin{tabular}{ll}
\toprule
\textbf{Features} & \textbf{Value} \\
\midrule
\MC{2}{l}{\textbf{Entity-based features} }\\
~~~~~~~~Entity$_1$ type & ORG\\
~~~~~~~~Entity$_1$ head & \textit{airlines}\\
~~~~~~~~Entity$_2$ type & PERS \\
~~~~~~~~Entity$_2$ head & \textit{Wagner}\\
~~~~~~~~Concatenated types & ORGPERS \\ %\midrule
\MC{2}{l}{\textbf{Word-based features} }\\
~~~~~~~~Between-entity BOW & \{ \textit{a, unit, of, AMR, Inc., immediately, matched, the, move, spokesman} \}\\
~~~~~~~~Word(s) before Entity$_1$ & NONE\\
~~~~~~~~Word(s) before Entity$_2$ & \textit{said}\\ %\midrule
\MC{2}{l}{\textbf{Syntactic features} }\\
~~~~~~~~Constituent path & NP \ua\ NP \ua\ S \ua\ S \da\ NP\\
~~~~~~~~Base syntactic chunk path & NP \ra\ NP \ra\ PP \ra\ NP \ra\ VP \ra\ NP \ra\ NP \\
~~~~~~~~Typed-dependency path & \textit{Airlines} \la\ $_{subj}$ \textit{matched} \la\ $_{comp}$ \textit{said} \ra\ $_{subj}$ \textit{Wagner} \\
\bottomrule
\end{tabular}
\source{Jurafsky and Martin, 2nd ed., p. 730}
\end{center}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: RE: Supervised Learning}
\textbf{Strengths}
\begin{itemize}
\item No need to write extensive/complex rule sets for each domain
\item System can adapt to any new domain \ra\ provided that training data is supplied
\item[\ra] beware of data sparsity!
\end{itemize}
\textbf{Weaknesses}
\begin{itemize}
\item Quality of relation extraction dependent on quality and quantity of training data
\item[\ra] can be difficult, costly and time consuming to generate
\item Feature extractors can be noisy (e.g. parsers) \ra\ reduce overall performance
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Overview}
\gray{Relation Extraction}
\begin{itemize}
\item \gray{Task definition}
\end{itemize}
\textbf{Approaches to Relation Extraction}
\begin{itemize}
\item \gray{Knowledge-engineering approaches to RE}
\item \gray{Supervised learning approaches to RE}
\item \textbf{Bootstrapping Approaches to RE}
\item Distant Supervision Approaches to RE
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Bootstrapping}
\textbf{Motivation}: reduce the number of manually labelled examples needed to build a system
\textbf{Requirements}:
\begin{enumerate}
\item a document collection $\mathcal{D}$
\item set of trusted tuples \textbf{T}, also called \myemph{seed tuples}
\item set of trusted patterns \textbf{P}, also called \myemph{seed patterns}
\end{enumerate}
\textbf{Principle}:
\begin{enumerate}
%\setcounter{enumi}{3}
\item Find tuples from \textbf{T} in $\mathcal{D}$ \Ra\ extract patterns, add them to \textbf{P}
\item Match patterns \textbf{P} in $\mathcal{D}$ \Ra\ extract tuples, add them to \textbf{T}
\item[\ra] Rinse, repeat
\end{enumerate}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Bootstrapping}
\begin{center}
\includegraphics[width=.55\textwidth]{pattern_based_RE}
\source{Jurafsky and Martin, 2nd ed., p. 740}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Bootstrapping - DIPRE}
\myemphb{DIPRE} Dual Iterative Pattern Relation Expansion – proposed by Sergie Brin (1999)
\vfill
\textbf{Aim}: to extract useful relational tuples from the Web, of the form (\textsc{person}, \textsc{book\_title})
Ex.: (\textsc{Leo Tolstoy}, \textsc{War and Peace})
\vfill
\textbf{Method}:
\begin{itemize}
\item Exploit duality of patterns and relations
\begin{itemize}
\item Good tuples help find good patterns
\item Good patterns help find good tuples
\end{itemize}
\item Use the bootstrapping method starting with user-supplied tuples
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Information Extraction: Relation Extraction: Bootstrapping - DIPRE}
Main loop in DIPRE is the following:
\begin{enumerate}
\item $\mathcal{R}'$ \la\ Sample
\begin{itemize}
\item[] $\mathcal{R}'$ is a set of tuples \ra\ approximation of target relation
\item[] Sample is the seed tuples (e.g. 5 author-title pairs)
\end{itemize}
\item $\mathcal{O}$ \la\ FindOccurrences($\mathcal{R}'$, $\mathcal{D}$)
\begin{itemize}
\item[] $\mathcal{O}$ contains all occurrences of tuples in $\mathcal{R}'$ appearing in $\mathcal{D}$
\end{itemize}
\item $\mathcal{P}$ \la\ GenPatterns($\mathcal{O}$)
\begin{itemize}
\item[] $\mathcal{P}$ contains the patterns generated based on the occurrences
\item[] Seek for low error rate patterns, ideally having high coverage
\end{itemize}
\item $\mathcal{R}'$ \la\ $M_{\mathcal{D}}(\mathcal{P})$
\begin{itemize}
\item[] Update $\mathcal{R}'$ with the tuples from $\mathcal{D}$ matching patterns in $\mathcal{P}$
\end{itemize}
\item Stop if $\mathcal{R}'$ is large enough, otherwise go to \circled{2}{black}
\end{enumerate}
\end{frame}