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\caption{The distribution of compositionality for 100 emerged symbolic
\caption{The distribution of compositionality for 100 emergent
languages without
languages without
any induction. It can be observed that high compositional symbolic language
any induction. It can be observed that high compositional language
seldom emerged (e.g., $<5\%$ for compositionality $>0.99$). Moreover, varying
seldom emerged (e.g., $<5\%$ for compositionality $>0.99$). Moreover, varying
the vocabulary size does not affect the compositionality notably.}
the vocabulary size does not affect the compositionality notably.}
\label{fig:induction}
\label{fig:induction}
...
@@ -71,32 +71,34 @@ vocabulary can express almost infinite concepts.}
...
@@ -71,32 +71,34 @@ vocabulary can express almost infinite concepts.}
\end{tabular}
\end{tabular}
\end{table*}
\end{table*}
Prior studies focus on achieving high compositional symbolic language
Prior studies focus on achieving high compositional language
through \emph{deliberately handcrafted} inductions, e.g., small vocabulary
through \emph{deliberately handcrafted} inductions, e.g., additional rewards~\cite{},
sizes~\cite{}, memoryless~\cite{}, additional rewards~\cite{}, constructed loss functions~\cite{}, and
constructed loss functions~\cite{}, structural input data~\cite{},
ease-of-teaching~\cite{}. \note{Such optimization methodologies are driven by the challenges to generate high compositional symbolic without induction in an existing multi-agent environment.}
memoryless~\cite{}, and ease-of-teaching~\cite{}.
\note{Such optimization methodologies are driven by the challenges to generate high compositional language without induction in an existing multi-agent environment.}
Figure~\ref{fig:induction} reports the compositionality when training two agents
Figure~\ref{fig:induction} reports the compositionality when training two agents
in the widely-used listener-speaker referential game for emerging 100 symbolic
in the widely-used listener-speaker referential game~\cite{} for emerging 100
languages, and it can be observed that \note{the compositionality
languages, and it can be observed that \note{the compositionality
of emerged symbolic language is extremely low without any induction. Moreover, varying
of emergent language is seldom high (e.g., $<5\%$ for compositionality $>0.99$)
without any induction. Moreover, varying
the vocabulary size does not affect the compositionality notably.}
the vocabulary size does not affect the compositionality notably.}
Though such unnatural inductions are useful, they prevent us from better understanding the mystery of
Though such unnatural inductions are useful, they prevent us from better understanding the mystery of
the emergence of language and even intelligence among our pre-human ancestors.
the emergence of language and even intelligence among our pre-human ancestors.
Yet, few works investigate the emergence of high compositional symbolic language
Yet, few works investigate the emergence of high compositional language
\emph{naturally}, i.e., without handcrafted inductions.
\emph{naturally}, i.e., without handcrafted inductions.
In other words, it is never clear whether \emph{natural}
In other words, it is never clear whether \emph{natural}
environment and agents are sufficient for achieving high compositionality.
environment and agents are sufficient for achieving high compositionality.
This paper is the first one to achieve high compositional
This paper is the first one to achieve high compositional
symbolic language without any deliberately handcrafted induction. The key observation
language without any deliberately handcrafted induction. The key observation
is that the internal \emph{agent capacity} plays a crucial role in the
is that the internal \emph{agent capacity} plays a crucial role in the
compositionality of symbolic language.
compositionality of emergent language.
%by thoroughly
%by thoroughly
%analyzing the compositionality after removing the inductions in
%analyzing the compositionality after removing the inductions in
%the most widely-used listener-speaker referential game framework.
%the most widely-used listener-speaker referential game framework.
Concretely, the relationship between the agent capacity and the compositionality
Concretely, the relationship between the agent capacity and the compositionality
of symbolic language is characterized, with a novel mutual information-based
of emergent language is characterized, with a novel mutual information-based
metric for the compositionality.
metric for the compositionality.
%both theoretically and experimentally.
%both theoretically and experimentally.
%theoretically
%theoretically
...
@@ -106,16 +108,16 @@ Regarding the theoretical analysis, we propose
...
@@ -106,16 +108,16 @@ Regarding the theoretical analysis, we propose
a novel mutual information-based metric to measure the compositionality quantitatively.
a novel mutual information-based metric to measure the compositionality quantitatively.
%experimentally
%experimentally
Regarding the experimental validation, we exploit the relationship between agent
Regarding the experimental validation, we exploit the relationship between agent
capacity and the compositionality of symbolic language that emerged
capacity and the compositionality of \emph{naturally} emergent language
\emph{naturally}in our experiments.
in our experiments.
%two different dedicated experiments, i.e., \note{XXX and XXX, are utilized for XXX}.
%two different dedicated experiments, i.e., \note{XXX and XXX, are utilized for XXX}.
%Regarding the experimental validation, it is conducted on a listener-speaker
%Regarding the experimental validation, it is conducted on a listener-speaker
%referential game framework with eliminated unnatural inductions.
%referential game framework with eliminated unnatural inductions.
Both the theoretical analysis and experimental results lead to a counter-intuitive
Both the theoretical analysis and experimental results lead to a counter-intuitive
conclusion that \emph{lower agent capacity facilitates the emergence of symbolic language
conclusion that \emph{lower agent capacity facilitates the emergence of language
with higher compositionality}. \note{Therefore, by only reducing the agent capacity
with higher compositionality}. \note{Therefore, by only reducing the agent capacity
in such a natural environment, we
in such a natural environment, we
can generate a higher compositional symbolic language with a higher probability.}
can generate a more compositional language with a higher probability.}
%Prior studies focus on investigating how to affect the
%Prior studies focus on investigating how to affect the
...
@@ -208,16 +210,16 @@ can generate a higher compositional symbolic language with a higher probability.
...
@@ -208,16 +210,16 @@ can generate a higher compositional symbolic language with a higher probability.
In this paper, we made the following contributions:
In this paper, we made the following contributions:
\begin{itemize}[topsep=0pt,itemsep=0cm]
\begin{itemize}[topsep=0pt,itemsep=0cm]
\item To our best knowledge, we are the first work to successfully achieve
\item To our best knowledge, we are the first work to successfully achieve
high compositional symbolic
high compositional emergent
language naturally, without any deliberately handcrafted induction.
language naturally, without any deliberately handcrafted induction.
\item We analyze the compositionality of emerged symbolic language
\item We analyze the compositionality of emergent language
after removing deliberately handcrafted inductions.
after removing deliberately handcrafted inductions.
\item We propose a novel mutual information-based metric to measure the
\item We propose a novel mutual information-based metric to measure the
compositionality quantitatively, which is more reasonable.
compositionality quantitatively, which is more reasonable.
\item We experimentally exploited the relationship between agent
\item We experimentally exploited the relationship between agent
capacity. Both theoretical analysis and
capacity. Both theoretical analysis and
experimental results lead to a counter-intuitive conclusion that lower agent
experimental results lead to a counter-intuitive conclusion that lower agent
capacity facilitates the emergence of symbolic language with higher
capacity facilitates the emergence of language with higher
compositionality.
compositionality.
\end{itemize}
\end{itemize}
...
@@ -227,6 +229,6 @@ Section~\ref{sec:relatedwork} summarizes the related works.
...
@@ -227,6 +229,6 @@ Section~\ref{sec:relatedwork} summarizes the related works.
Section~\ref{sec:thory}
Section~\ref{sec:thory}
introduces the experimental setup used in this study. Section~\ref{sec:mis}
introduces the experimental setup used in this study. Section~\ref{sec:mis}
describes our proposed novel mutual-information-based metric for measuring
describes our proposed novel mutual-information-based metric for measuring
the compositionality of symbolic language. Section~\ref{sec:exp} gives the
the compositionality of emergent language. Section~\ref{sec:exp} gives the
experimental results of the exploration for the relationship between agent
experimental results of the exploration for the relationship between agent
capacity and compositionality. Section~\ref{sec:con} concludes this paper.
capacity and compositionality. Section~\ref{sec:con} concludes this paper.