Previous works focus on the \emph{deliberately handcrafted} inductions that affect the
compositionality of emergent language.
Some significant works on studying the environmental inductions on the compositionality of emergent language are summarized in Table~\ref{tab:rel}.
For example, ~\citet{kirby2015compression} explored how the pressures for expressivity and compressibility lead the structured language.
~\citet{kottur-etal-2017-natural} constrained the vocabulary size and whether the listener has memory to coax the compositionality of the emergent language.
~\citet{lazaridou2018emergence} showed that the degree of structure found in the input data affects the emergence of the symbolic language.
~\citet{li2019ease} studied how the pressure, ease of teaching, impact on the iterative language of the population regime.
~\citet{evtimova2018emergent} designed novel multi-modal scenarios, which the speaker and the listener should access to different modalities of the input object, to explore the language emergence.
For example, ~\cite{kirby2015compression} explored how the pressures for expressivity and compressibility lead the structured language.
~\cite{kottur-etal-2017-natural} constrained the vocabulary size and whether the listener has memory to coax the compositionality of the emergent language.
~\cite{lazaridou2018emergence} showed that the degree of structure found in the input data affects the emergence of the symbolic language.
~\cite{li2019ease} studied how the pressure, ease of teaching, impact on the iterative language of the population regime.
~\cite{evtimova2018emergent} designed novel multi-modal scenarios, which the speaker and the listener should access to different modalities of the input object, to explore the language emergence.
These inductions are deliberately designed, which are too ideal to be true in
the real world.
In this paper, these handcrafted inductions above are all removed, and the high compositional language is learned only by the agent capacity.
%understanding between speakers and listeners, i.e., the concept-symbol mapping
%consistency between speakers and listeners.
At the initial stage, many studies only analyzed the language compositionality qualitatively (i.e. not quantitatively).
For example, ~\citet{choi2018compositional} printed the agent messages with the letter `abcd' at some training round, and directly analyzed the compositionality on these messages.
~\citet{kottur-etal-2017-natural} introduced the dialog tree to show the evolution of language compositionality during the training process.
For example, ~\cite{choi2018compositional} printed the agent messages with the letter `abcd' at some training round, and directly analyzed the compositionality on these messages.
~\cite{kottur-etal-2017-natural} introduced the dialog tree to show the evolution of language compositionality during the training process.
Latter, some quantitative metrics are explored.
The topographic similarity\cite{lazaridou2018emergence} is introduced to measure the distances between all the possible pairs of meanings and the corresponding pairs of signals.
\citet{chaabouni2020compositionality} proposed the positional disentanglement, which measures whether symbols in a specific position relate to the specific attribute of the input object.
\cite{chaabouni2020compositionality} proposed the positional disentanglement, which measures whether symbols in a specific position relate to the specific attribute of the input object.
From Table~\ref{tab:rel}, most metrics are proposed on the sight of speaker. In our view, human beings developed the language based on a bilateral communication between the speaker and the listener. One research~\cite{choi2018compositional} considered the metric bilaterally, but it is not a quantitative metric. In this paper, we propose a novel quantitative metric from both the speaker and the listener's perspective.
