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haoyifan
AAAI21_Emergent_language
Commits
2800c9e4
Commit
2800c9e4
authored
Sep 17, 2020
by
haoyifan
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AAAI2021/tex/appendix.tex
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2800c9e4
\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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