Commit 2800c9e4 by haoyifan

hfa

parent 24ebf3bf
\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}
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