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haoyifan
AAAI21_Emergent_language
Commits
37549f10
Commit
37549f10
authored
Sep 10, 2020
by
YZhao
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AAAI2021/fig/Figure5_An_emergent_language.pdf
+0
-0
AAAI2021/tex/experiments.tex
+37
-9
AAAI2021/tex/relatedwork.tex
+0
-4
AAAI2021/tex/theory.tex
+9
-9
AAAI2021/tex/theory2.tex
+1
-1
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AAAI2021/fig/Figure5_An_emergent_language.pdf
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37549f10
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AAAI2021/tex/experiments.tex
View file @
37549f10
...
...
@@ -18,14 +18,42 @@
\label
{
fig:exp2
}
\end{figure}
\begin{figure}
[t]
%\begin{figure}[t]
% \centering
% \includegraphics[width=0.99\columnwidth]{fig/Figure10_p_value.pdf}
% \caption{The Chi-square test between high-compositionality and agent
% capacity. (a) $MIS>0.99$. (b)
% $MIS>0.9$.}
% \label{fig:exp10}
%\end{figure}
\begin{table}
[b]
\centering
\includegraphics
[width=0.99\columnwidth]
{
fig/Figure10
_
p
_
value.pdf
}
\caption
{
The Chi-square test between high-compositionality and agent
capacity. (a)
$
MIS>
0
.
99
$
. (b)
$
MIS>
0
.
9
$
.
}
\label
{
fig:exp10
}
\end{figure}
\caption
{
The Chi-square test between high-compositionality and agent capacity.
}
\label
{
tab:exp10
}
\begin{tabular}
{
cccc
}
\toprule
\multicolumn
{
4
}{
c
}{$
H
_
0
$
:
$
\mathit
{
MIS
}
>
0
.
90
$
is independent with
$
h
_{
\mathit
{
size
}}$}
\\
\midrule
Vocabulary size
&
$
\chi
^
2
$
&
$
df
$
&
$
p
$
-value
\\
\midrule
4
&
22.20
&
10
&
$
1
.
41
\times
10
^{
-
2
}$
\\
6
&
27.52
&
10
&
$
2
.
16
\times
10
^{
-
3
}$
\\
10
&
64.46
&
10
&
$
5
.
14
\times
10
^{
-
10
}$
\\
\bottomrule
\multicolumn
{
4
}{
c
}{
\vspace
{
1em
}}
\\
\toprule
\multicolumn
{
4
}{
c
}{$
H
_
0
$
:
$
\mathit
{
MIS
}
>
0
.
99
$
is independent with
$
h
_{
\mathit
{
size
}}$}
\\
\midrule
Vocabulary size
&
$
\chi
^
2
$
&
$
df
$
&
$
p
$
-value
\\
\midrule
4
&
30.19
&
10
&
$
7
.
97
\times
10
^{
-
4
}$
\\
6
&
25.96
&
10
&
$
3
.
80
\times
10
^{
-
3
}$
\\
10
&
33.80
&
10
&
$
2
.
00
\times
10
^{
-
4
}$
\\
\bottomrule
\end{tabular}
\end{table}
\begin{figure}
[t]
\centering
...
...
@@ -84,8 +112,8 @@ more meanings, for the constraint from low capacity.
Additionally, we also perform
$
\chi
^
2
$
test to check the statistical
significance between the high compositionality and agent
capacity.
Figure~
\ref
{
fig
:exp10
}
reports the
$
\chi
^
2
$
test results for
$
MIS>
0
.
99
$
and
$
MIS>
0
.
9
$
in (a) and (b)
, respectively. It can be observed that
capacity.
Table~
\ref
{
tab
:exp10
}
reports the
$
\chi
^
2
$
test results for
$
\mathit
{
MIS
}
>
0
.
99
$
and
$
\mathit
{
MIS
}
>
0
.
9
$
, respectively. It can be observed that
for different vocabulary size, the p-value is always less than 0.05, which means
the high compositionality has statistical significance related to agent
capacity.
...
...
AAAI2021/tex/relatedwork.tex
View file @
37549f10
<<<<<<< HEAD
\section
{
Related works
}
\label
{
sec:relatedwork
}
\begin{table*}
[b]
=======
\begin{table*}
[htbp]
>>>>>>> 013236e0637a916d76a342113079f93be73ec3a7
\centering
\small
\caption
{
Handcrafted inductions in related works.
}
...
...
AAAI2021/tex/theory.tex
View file @
37549f10
...
...
@@ -29,8 +29,8 @@ to finish the game in a cooperative manner. In each round, once received an
input object
$
t
$
, Speaker
$
S
$
speaks a symbol sequence
$
s
$
to Listener
$
L
$
;
Listener
$
L
$
reconstruct the predicted result
$
\hat
{
t
}$
based on the listened
sequence
$
s
$
; if
$
t
=
\hat
{
t
}$
, agents win this game and receive positive rewards
(
$
R
(
t,
\hat
{
t
}
)=
1
$
); otherwise agents fail this game and receive negative rewards
(
$
R
(
t,
\hat
{
t
}
)=-
1
$
).
(
$
r
(
t,
\hat
{
t
}
)=
1
$
); otherwise agents fail this game and receive negative rewards
(
$
r
(
t,
\hat
{
t
}
)=-
1
$
).
Precisely, during the game, Speaker
$
S
$
receives an input object
$
t
$
, which is
an expression with two words from the vocabulary set
$
V
$
, i.e., two
...
...
@@ -84,7 +84,7 @@ Algorithm~\ref{al:learning}, we train the separate Speaker $S$ and Listener $L$
Stochastic Policy Gradient methodology in a tick-tock manner, i.e, training one
agent while keeping the other one. Roughly, when training the Speaker, the
target is set to maximize the expected reward
$
J
(
\theta
_
S,
\theta
_
L
)=
E
_{
\pi
_
S,
\pi
_
L
}
[
R
(
t,
\hat
{
t
}
)]
$
by adjusting the parameter
$
J
(
\theta
_
S,
\theta
_
L
)=
E
_{
\pi
_
S,
\pi
_
L
}
[
r
(
t,
\hat
{
t
}
)]
$
by adjusting the parameter
$
\theta
_
S
$
, where
$
\theta
_
S
$
is the neural network parameters of Speaker
$
S
$
with learned output probability distribution
$
\pi
_
S
$
, and
$
\theta
_
L
$
is the
neural network parameters of Listener with learned probability distribution
$
\pi
_
L
$
.
...
...
@@ -97,9 +97,9 @@ use the predict result $\hat{t}$ of the listener agent as the
evidence of whether giving the positive rewards. Then, the gradients of the
expected reward
$
J
(
\theta
_
S,
\theta
_
L
)
$
can be calculated as follows:
\begin{align}
\nabla
_{
\theta
^
S
}
J
&
=
\mathbb
{
E
}_{
\pi
^
S,
\pi
^
L
}
\left
[
R
(
\hat
{
t
}
, t)
\cdot
\nabla
_{
\theta
^
S
}
J
&
=
\mathbb
{
E
}_{
\pi
^
S,
\pi
^
L
}
\left
[
r
(
\hat
{
t
}
, t)
\cdot
\nabla
_{
\theta
^
S
}
\log
{
\pi
^
S(s
_
0, s
_
1 | t)
}
\right
]
\\
\nabla
_{
\theta
^
L
}
J
&
=
\mathbb
{
E
}_{
\pi
^
S,
\pi
^
L
}
\left
[
R
(
\hat
{
t
}
, t)
\cdot
\nabla
_{
\theta
^
L
}
J
&
=
\mathbb
{
E
}_{
\pi
^
S,
\pi
^
L
}
\left
[
r
(
\hat
{
t
}
, t)
\cdot
\nabla
_{
\theta
^
L
}
\log
{
\pi
^
S(
\hat
{
t
}
| s
_
0, s
_
1)
}
\right
]
\end{align}
...
...
@@ -116,8 +116,8 @@ expected reward $ J(\theta_S, \theta_L)$ can be calculated as follows:
\STATE
Sample
$
s
_
0
$
with
$
P
(
s
_
0
|t
)
$
,
$
s
_
1
$
with
$
P
(
s
_
1
|t
)
$
\STATE
$
P
(
\hat
{
t
}
|s
)
=
\pi
^
L
(
\hat
{
t
}
|s
)
$
\STATE
Sample
$
\hat
{
t
}$
with
$
P
(
\hat
{
t
}
|s
)
$
\STATE
Get reward
$
R
(
\hat
{
t
}
,t
)
$
\STATE
$
J
(
\theta
^
S,
\theta
^
L
)=
E
_{
\pi
_{
old
}^
S,
\pi
^
L
}
[
R
(
\hat
{
t
}
,t
)
\cdot\frac
{
\pi
^
S
(
s|t
)
}{
\pi
^
S
_{
old
}
(
s|t
)
}
]
$
\STATE
Get reward
$
r
(
\hat
{
t
}
,t
)
$
\STATE
$
J
(
\theta
^
S,
\theta
^
L
)=
E
_{
\pi
_{
old
}^
S,
\pi
^
L
}
[
r
(
\hat
{
t
}
,t
)
\cdot\frac
{
\pi
^
S
(
s|t
)
}{
\pi
^
S
_{
old
}
(
s|t
)
}
]
$
\STATE
Update
$
\theta
^
S
$
by
$
\bigtriangledown
_{
\theta
^
S
}
J
$
\ENDFOR
\STATE
$
\pi
_{
old
}^
S
\leftarrow
\pi
^
S
$
...
...
@@ -131,8 +131,8 @@ expected reward $ J(\theta_S, \theta_L)$ can be calculated as follows:
\STATE
Sample
$
s
_
0
$
with
$
P
(
s
_
0
|t
)
$
,
$
s
_
1
$
with
$
P
(
s
_
1
|t
)
$
\STATE
$
P
(
\hat
{
t
}
|s
)
=
\pi
^
L
_{
old
}
(
\hat
{
t
}
|s
)
$
\STATE
Sample
$
\hat
{
t
}$
with
$
P
(
\hat
{
t
}
|s
)
$
\STATE
Get reward
$
R
(
\hat
{
t
}
,t
)
$
\STATE
$
J
(
\theta
^
S,
\theta
^
L
)=
E
_{
\pi
_{
old
}^
S,
\pi
^
L
}
[
R
(
\hat
{
t
}
,t
)
\cdot\frac
{
\pi
^
L
(
s|t
)
}{
\pi
^
L
_{
old
}
(
s|t
)
}
]
$
\STATE
Get reward
$
r
(
\hat
{
t
}
,t
)
$
\STATE
$
J
(
\theta
^
S,
\theta
^
L
)=
E
_{
\pi
_{
old
}^
S,
\pi
^
L
}
[
r
(
\hat
{
t
}
,t
)
\cdot\frac
{
\pi
^
L
(
s|t
)
}{
\pi
^
L
_{
old
}
(
s|t
)
}
]
$
\STATE
Update
$
\theta
^
L
$
by
$
\bigtriangledown
_{
\theta
^
L
}
J
$
\ENDFOR
\STATE
$
\pi
_{
old
}^
L
\leftarrow
\pi
^
L
$
...
...
AAAI2021/tex/theory2.tex
View file @
37549f10
...
...
@@ -36,7 +36,7 @@ Each column of $M$ correspond to the semantic information carried by one symbol.
\begin{figure}
[t]
\centering
\includegraphics
[width=\columnwidth]
{
fig/Figure5
_
An
_
emergent
_
language.pdf
}
\includegraphics
[width=
0.8
\columnwidth]
{
fig/Figure5
_
An
_
emergent
_
language.pdf
}
\caption
{
An emergent language that the unilateral metrics cannot measure its non-compositionality. Notice that given
$
s
_
1
=
\mathrm
{
a
}$
, the listener can neither determine the shape nor the color without the knowledge about
$
s
_
0
$
.
}
\label
{
fig:unilateral
}
\end{figure}
...
...
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