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AAAI2021/tex/appendix.tex

@@ -40,33 +40,18 @@ i.e., hidden layer size ($h_{size}$), from 6 to 100.
 
 Figure~\ref{fig:exp1} reports the supplementally experimental results. Consistent with 
 previous experiments, it can be observed that the mean value of MIS decreases as the value 
-of $h_{size}$ increases, no matter what configuration we take.
- Taking the
-configuration of vocabulary size $|V|=10$ as an example, the mean value of MIS
-is around 0.8 when $h_{size}\le 20$; MIS significantly decreases to 0.75 when
-$h_{size}$ increases from 20 to 40; MIS further reduces to 0.7 when $h_{size}$
-increases from 40 to 100.
-For different vocabulary sizes, the MIS shares the
-similar behavior.
-It is because symbols in low-compositional languages carry semantic information
-about more concepts. As a result, higher capacity is required to characterize the
-complex semantic information for low-compositional language to emerge.
-In summary, lower agent capacity improves the possibility of
-emerging high compositional symbolic language.
-
-
-\subsection{Ratio of high compositional language.}
-We further breakdown our results to investigate the importance of agent capacity
-to the compositionality of symbolic language. Figure~\ref{fig:exp2} reports the
-ratio of high compositional symbolic language in all emerged languages,
-Figure~\ref{fig:exp2} (a) and (b) for $\mathit{MIS}>0.99$ and $\mathit{MIS}>0.9$, respectively. It
-can be observed that the ratio of high compositional symbolic languages
-decreases drastically with the increase of $h_{size}$.
-Taking vocabulary size $|V|=4$ as an example, symbolic languages with
-compositionality $\mathit{MIS}>0.99$ take $>$10\% mainly over all the emerged symbolic
-languages, when $h_{size}<20$; the ratio reduces to 0\%$\sim$5\% when $h_{size}$
-increases to 40; the ratio reduces around 3\% when $h_{size}$ goes beyond 40. 
-$\mathit{MIS}>0.9$ reports similar results.
+of $h_{size}$ increases, no matter what configuration we take. MIS significantly decreases
+from around 0.8 to less than 0.7 when $h_{size}$ increases from 6 to 100.
+
+
+Just like we do in the \emph{Experiment} section, we further breakdown our results to show the importance 
+of agent capacity for emerging a symbolic language with high compositionality. Figure~\ref{fig:exp2} reports 
+the ratio of high compositional symbolic language in all emerged languages,
+Figure~\ref{fig:exp2} (a) and (b) for $\mathit{MIS}>0.99$ and $\mathit{MIS}>0.9$, respectively. 
+Under these two supplementary configuration, we also find that the ratio of high compositional symbolic languages
+decreases drastically with the increase of $h_{size}$, and such ratio would be closed to zero when agent capacity
+comes too large (i.e., $h_{size} > 80$).
+
 Notably, when $h_{size}$ is large enough (e.g., $>40$), high compositional
 symbolic language is hard to emerge in a natural referential game, for
 easy-to-emerge low compositional symbolic language is sufficient in scenarios of