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AAAI2021/tex/appendix.tex

@@ -37,6 +37,24 @@ Specifically, with the configuration of: a)$|M_0|=5,|M_1|=3,|V|=10$ and b)$|M_0|
 we train the speaker-listener agents to emerge symbolic language when varying the agent capacities, 
 i.e., hidden layer size ($h_{size}$), from 6 to 100. 
 
+\begin{figure}[t]
+  \centering \includegraphics[width=0.99\columnwidth]{fig/Appendix_Figure1_MIS.pdf}
+  \caption{Compositionality of symbolic language under different parameters
+    ($[\mu-\sigma,\mu+\sigma]$, where $\mu$ is the mean value and $\sigma$ is
+    the standard deviation).}
+  \label{fig:exp1}
+\end{figure}
+
+
+
+\begin{figure}[t]
+  \centering \includegraphics[width=0.99\columnwidth]{fig/Appendix_Figure2_Ratio.pdf}
+  \caption{The ratio of high compositional language. (a) $MIS>0.99$. (b)
+    $MIS>0.9$. }
+  \label{fig:exp2}
+\end{figure}
+
+
 
 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 
@@ -44,6 +62,7 @@ of $h_{size}$ increases, no matter what configuration we take. MIS significantly
 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,
@@ -53,6 +72,7 @@ decreases drastically with the increase of $h_{size}$, and that such ratio would
 comes too large (i.e., $h_{size} > 80$).
 
 
+
 For these two supplementary sets of data, we also perform $\chi^2$ test to check the statistical
 significance between the high compositionality and agent
 capacity. Table~\ref{tab:exp10} reports the $\chi^2$ test results for
@@ -62,19 +82,6 @@ the high compositionality has a statistical significance related to agent
 capacity.
 
 
-\begin{figure}[t]
-  \centering \includegraphics[width=0.99\columnwidth]{fig/Appendix_Figure1_MIS.pdf}
-  \caption{Compositionality of symbolic language under different parameters
-    ($[\mu-\sigma,\mu+\sigma]$, where $\mu$ is the mean value and $\sigma$ is
-    the standard deviation).}
-  \label{fig:exp1}
-\end{figure}
 
 
-\begin{figure}[t]
-  \centering \includegraphics[width=0.99\columnwidth]{fig/Appendix_Figure2_Ratio.pdf}
-  \caption{The ratio of high compositional language. (a) $MIS>0.99$. (b)
-    $MIS>0.9$. }
-  \label{fig:exp2}
-\end{figure}