The emergence of human language has always been an important and controversial
The emergence of symbolic language has always been an important and controversial
issue. This problem attracts attentions from a broad range of communities,
including philology~\cite{}, biology~\cite{}, and computer
science~\cite{}. Especially in computer science, efforts in recent years try to explore
the emergence of symbolic language in virtual environments, where agents are trained
to communicate with neural network based method, i.e, deep reinforcement
learning~\cite{}. For example, \note{XXXX}
the emergence of symbolic language in virtual, multi-agent environments, where
agents are trained to communicate with neural network based method, i.e., deep
reinforcement learning~\cite{}. For example, \note{XXXX}
%Such works can be roughly classified into two categories,
%referential game~\cite{} and multi-agent reinforcement learning (MARL)~\cite{}, based on
%the environment setting.
...
...
@@ -20,7 +20,7 @@ whether the meaning of a complex expression (e.g, phase), which is assembled out
given set of simple components (e.g., symbols), can be determined by its
constituent components and the rules that combines them~\cite{}.
\note{For example, the expression "AAAI is a conference'' consists of two
meaningful words ``AAAI'' and ``conference'', and a rule of definition (``is'').}
meaningful words ``AAAI'' and ``conference'', and a rule for definition (``is'').}
More recently, measuring the compositionality \note{xxxxx}.
...
...
@@ -41,42 +41,42 @@ More recently, measuring the compositionality \note{xxxxx}.
\label{fig:symbols}
\end{figure}
Prior studies focus on achieving high compositionality of the emergent language
through \emph{deliberately handcrafted} inductions unnaturally, e.g., small vocabulary
Prior studies focus on achieving high compositionality
through \emph{deliberately handcrafted} inductions, e.g., small vocabulary
sizes~\cite{}, memoryless~\cite{}, carefully constructed rewards~\cite{}, and
ease-of-teaching~\cite{}. \note{xxxxxxx}
However, these unnatural inductions prevent us to better understand the mystery of
However, these unnatural inductions prevent us from better understanding the mystery of
the emergence of language and even intelligence among our pre-human ancestors.
Yet, few works investigate the emergence of symbolic language with high
compositionality \emph{naturally} (i.e., without \emph{deliberately
handcrafted} inductions). As a results, it is never clear whether \emph{natural}
Yet, few works investigate the emergence of high compositional symbolic language
\emph{naturally}, i.e., without \emph{deliberately
handcrafted} inductions.
As a results, it is never clear whether \emph{natural}
environment and agent are sufficient for compositionality.
In this work, we focus on generating high compositional symbolic language
naturally without any ``human'' induction.
In this work, we focus on the natural emergence of high compositional symbolic language
naturally without any handcrafted induction.
Initially, we thoroughly analyze the compositionality of emerged symbolic
language after removing the \emph{deliberately handcrafted}
inductions. Figure~\ref{fig:comp} reports the compositionality when train two
agents in a listener-speaker referential game. It can be observed that \note{it
is challenging to achieve high compositionality without induction as xxxxxx}. Moreover,
we observe that the agent capacity plays a key role in compositionality, see
Figure xxx.
is challenging to achieve high compositionality without induction as
xxxxxx}. Moreover, we observe that the agent capacity plays a key role in
compositionality, see Figure xxx.
In this work, we reveal and characterize the quantitative relationship
We reveal and characterize the quantitative relationship
between the agent capacity and the compositionality of symbolic language both
theoretically and experimentally.
%theoretically
Regarding the theoretical analysis, it is conduct based on the MSC
(Markov Series Channel) model for the language transmission process and a
novel mutual information-based metric for the compositionality.
Regarding the theoretical analysis, we use the
Markov Series Channel (MSC)~\cite{} to model the language transmission process and a
novel mutual information-based metric to measure the compositionality quantitatively.
%experimentally
Regarding the experimental verification, it is conducted on a listener-speaker referential game framework
with eliminated unnatural inductions.
================
Regarding the experimental verification, it is conducted on a listener-speaker
referential game framework with eliminated unnatural inductions.
Both theoretical analysis and
experimental results lead to a counter-intuitive conclusion that lower agent
capacity facilitates the emergence of symbolic language with higher
compositionality.
%Prior studies focus on investigating how to affect the
...
...
@@ -90,76 +90,91 @@ with eliminated unnatural inductions.
%like regrading the entropy as an item of additional rewards, may be too ideal to
%exist in the real world.
In contrast to prior work, we investigate the compositionality of emergent
language from a new perspective, i.e., the agent capacity. Different from
previous work that only considers external environmental factors, we study the
impact of agent internal capacity on the compositionality of emergent
language. Specifically, we first analyze the correlation between agent capacity
and compositionality theoretically, and propose a novel metric to evaluate
compostionality quantitatively. Then, on the basis of the theoretical analysis
and the metric proposed, we verify the relationship between agent capacity and
compostionality experimentally.
Theoretically, on the basis of mutual information theory[8], we analyse the
correlation between compostionality of the emergent language and complexity of
the semantic information carried by a symbol. Such semantic information can be
characterized in neural network-based agents and requires the certain capacity
(i.e., the count of neural nodes in the hidden layer). Specifically, we use the
MSC (Markov Series Channel)[9] to model the language transmission process and
use the probability distribution of symbols and concepts to model policies of
agents. After modelling, we use the mutual information matrix $MRI^B$ to
quantitatively represent the semantic information, and each column of $MRI^B$
correspond to information carried by one symbol. We find that each column of the
matrix should be an one-hot vector for a perfectly compositional language, cause
a symbol only transmit information of a certain concept exclusively. Therefore,
the average similarity between the columns of $MRI^B$ and a one-hot vector is
higher, indicating that the emergent language is more compostional (i.e., the
compostionality is higher). We propose the metric \emph{MIS} to measure
compositionality by calculating such average similarity
quantitatively. Different from other metrics, such as \emph{topographic
similarity}[10] and \emph{posdis}[11], \emph{MIS} is a bilateral metric
because it takes both listener and speaker's understanding of semantics into
account. Moreover, \emph{MIS} comes lower indicates that the emergent language
tends to delivery semantic information about more concepts in each symbol, so
that the complexity of semantic information carried by one symbol tend to be
higher. As a result, higher agent capacity is required to characterize the more
complex semantic information when \emph{MIS} (i.e., compositionality) is lower.
Experimentally, we verify the relationship between agent capacity and
compostionality. We build a listener-speaker referential game as experimental
framework, and train agents of Stochastic Policy Gradient Algorithm[12] with the
correctness of forecast output from the listener as the criterion (i.e.,
reward). The criterion does not imply any environmental pressures on the
agents. Therefore, we can study the impact of capacity on the compositionality
without any environmental pressures’ affection. Moreover, to study the impact of
capacity on the compositionality under a more ‘natural’ environment, the speaker
and listener are disconnected models without sharing parameters. Our first
experiment is to verify that agent need higher capacity to master an artificial
language with lower compositionality under a scenario of language
teaching. Specifically, we fabricate the speaker to output preassigned languages
with different compostionality respectively, and train the listener to interpret
the preassigned language. For all artificial language, we compare the accuracy
curve during training process of the listener with different capacity, and show
how capacity affect learning languages with different compostionality. Our
second experiment is to verify that lower agent capacity would facilitate higher
compostionality of the emergent language under a scenario of language
inducing. Specifically, we training a speaker and a listener to create a
communication protocol (i.e., emergent language), so that the listener can
select the same object which is received by the speaker. By adjusting capacity
and comparing the compositionality of emergent language, we show that the
emergent language attend to have higher compositionality when agent capacity is
restricted more stringently. As a result, these two experiments verify the
negative correlation between agent capacity and compostionality both in language
teaching and language inducing.
This paper makes the following contributions:
We propose a ‘bilateral’ metric \emph{MIS}, which takes both listener and speaker's understanding of semantics into account. Compare to previous ‘unilateral’ metrics, \emph{MIS} can handle situations where the semantics of the listener and the speaker are not exactly the same (, we discuss the problem in next section).
%In contrast to prior work, we investigate the compositionality of emergent
%language from a new perspective, i.e., the agent capacity. Different from
%previous work that only considers external environmental factors, we study the
%impact of agent internal capacity on the compositionality of emergent
%language. Specifically, we first analyze the correlation between agent capacity
%and compositionality theoretically, and propose a novel metric to evaluate
%compostionality quantitatively. Then, on the basis of the theoretical analysis
%and the metric proposed, we verify the relationship between agent capacity and
%compostionality experimentally.
%
%
%Theoretically, on the basis of mutual information theory[8], we analyse the
%correlation between compostionality of the emergent language and complexity of
%the semantic information carried by a symbol. Such semantic information can be
%characterized in neural network-based agents and requires the certain capacity
%(i.e., the count of neural nodes in the hidden layer). Specifically, we use the
%MSC (Markov Series Channel)[9] to model the language transmission process and
%use the probability distribution of symbols and concepts to model policies of
%agents. After modelling, we use the mutual information matrix $MRI^B$ to
%quantitatively represent the semantic information, and each column of $MRI^B$
%correspond to information carried by one symbol. We find that each column of the
%matrix should be an one-hot vector for a perfectly compositional language, cause
%a symbol only transmit information of a certain concept exclusively. Therefore,
%the average similarity between the columns of $MRI^B$ and a one-hot vector is
%higher, indicating that the emergent language is more compostional (i.e., the
%compostionality is higher). We propose the metric \emph{MIS} to measure
%compositionality by calculating such average similarity
%quantitatively. Different from other metrics, such as \emph{topographic
% similarity}[10] and \emph{posdis}[11], \emph{MIS} is a bilateral metric
%because it takes both listener and speaker's understanding of semantics into
%account. Moreover, \emph{MIS} comes lower indicates that the emergent language
%tends to delivery semantic information about more concepts in each symbol, so
%that the complexity of semantic information carried by one symbol tend to be
%higher. As a result, higher agent capacity is required to characterize the more
%complex semantic information when \emph{MIS} (i.e., compositionality) is lower.
%
%Experimentally, we verify the relationship between agent capacity and
%compostionality. We build a listener-speaker referential game as experimental
%framework, and train agents of Stochastic Policy Gradient Algorithm[12] with the
%correctness of forecast output from the listener as the criterion (i.e.,
%reward). The criterion does not imply any environmental pressures on the
%agents. Therefore, we can study the impact of capacity on the compositionality
%without any environmental pressures’ affection. Moreover, to study the impact of
%capacity on the compositionality under a more ‘natural’ environment, the speaker
%and listener are disconnected models without sharing parameters. Our first
%experiment is to verify that agent need higher capacity to master an artificial
%language with lower compositionality under a scenario of language
%teaching. Specifically, we fabricate the speaker to output preassigned languages
%with different compostionality respectively, and train the listener to interpret
%the preassigned language. For all artificial language, we compare the accuracy
%curve during training process of the listener with different capacity, and show
%how capacity affect learning languages with different compostionality. Our
%second experiment is to verify that lower agent capacity would facilitate higher
%compostionality of the emergent language under a scenario of language
%inducing. Specifically, we training a speaker and a listener to create a
%communication protocol (i.e., emergent language), so that the listener can
%select the same object which is received by the speaker. By adjusting capacity
%and comparing the compositionality of emergent language, we show that the
%emergent language attend to have higher compositionality when agent capacity is
%restricted more stringently. As a result, these two experiments verify the
%negative correlation between agent capacity and compostionality both in language
%teaching and language inducing.
We analyse the relationship between compostionality and agent capacity theoretically.
We verify the negative correlation between agent capacity and compostionality both in language teaching and language inducing.
%\endsection
%
%This paper makes the following contributions:
%
%We propose a ‘bilateral’ metric \emph{MIS}, which takes both listener and speaker's understanding of semantics into account. Compare to previous ‘unilateral’ metrics, \emph{MIS} can handle situations where the semantics of the listener and the speaker are not exactly the same (, we discuss the problem in next section).
%
%We analyse the relationship between compostionality and agent capacity theoretically.
%
%We verify the negative correlation between agent capacity and compostionality both in language teaching and language inducing.
%%\endsection
In this paper, we made the following contributions:
\begin{itemize}[topsep=0pt,itemsep=0cm]
\item We are the first to successfully achieve high compositional symbolic
language naturally, without any deliberately handcrafted inductions.
\item We thoroughly analyze the compositionality of emerged symbolic language
after removing deliberately handcrafted inductions, and confirm that the agent
capacity acts as a key factor for compositionality.
\item We experimentally verified the conclusion for relationship between agent
capacity. Both theoretical analysis and
experimental results lead to a counter-intuitive conclusion that lower agent
capacity facilitates the emergence of symbolic language with higher
