hfa

AAAI2021/tex/appendix.tex

-\documentclass[11pt,b5paper,onecolumn]{article}
-
-\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}
-
-
 \begin{table}[b]
   \centering
   \small
@@ -48,15 +29,19 @@
 \section{Appendix}
 \label{sec:exp}
 
-We exploit the relationship between agent capacity and the compositionality of
-symbolic language that emerged in our natural referential game.
-For various configuration of
-vocabulary size, we fix $|M_0|=|M_1|=3$ and 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. 
+We add two sets of experimental results to further verify the relationship between
+agent capacity and the compositionality of symbolic language that emerged in our natural referential game.
+As a supplement to the \emph{Experiments} section, these two sets of data (coresponding to two 
+kinds of configuration) are used to prove that the relationship is independent of configuration.
+Specifically, with the configuration of: a)$|M_0|=5,|M_1|=3,|V|=10$ and b)$|M_0|=4,|M_1|=4,|V|=10$,
+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. 
+
 
-Figure~\ref{fig:exp1} reports the experimental results. It can be observed that
-the mean value of MIS decreases as the value of $h_{size}$ increases. Taking the
+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 $h_{size}$
@@ -98,3 +83,21 @@ $\mathit{MIS}>0.99$ and $\mathit{MIS}>0.9$, respectively. It can be observed tha
 for different vocabulary sizes, the p-value is always less than 0.05, which means
 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}
+