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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]
\begin{table}
[b]
\centering
\centering
\small
\small
...
@@ -48,15 +29,19 @@
...
@@ -48,15 +29,19 @@
\section
{
Appendix
}
\section
{
Appendix
}
\label
{
sec:exp
}
\label
{
sec:exp
}
We exploit the relationship between agent capacity and the compositionality of
We add two sets of experimental results to further verify the relationship between
symbolic language that emerged in our natural referential game.
agent capacity and the compositionality of symbolic language that emerged in our natural referential game.
For various configuration of
As a supplement to the
\emph
{
Experiments
}
section, these two sets of data (coresponding to two
vocabulary size, we fix
$
|M
_
0
|
=
|M
_
1
|
=
3
$
and train the speaker-listener agents to emerge symbolic
kinds of configuration) are used to prove that the relationship is independent of configuration.
language when varying the agent capacities, i.e., hidden layer size
Specifically, with the configuration of: a)
$
|M
_
0
|
=
5
,|M
_
1
|
=
3
,|V|
=
10
$
and b)
$
|M
_
0
|
=
4
,|M
_
1
|
=
4
,|V|
=
10
$
,
(
$
h
_{
size
}$
), from 6 to 100.
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
Figure~
\ref
{
fig:exp1
}
reports the supplementally experimental results. Consistent with
the mean value of MIS decreases as the value of
$
h
_{
size
}$
increases. Taking the
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
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
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
}$
$
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
...
@@ -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
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
the high compositionality has a statistical significance related to agent
capacity.
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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