Merge branch 'master' of http://62.234.201.16/hao/AAAI21_Emergent_language

AAAI2021/tex/experiments.tex

@@ -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.
@@ -99,7 +127,7 @@ capacity.
 
 \begin{figure*}[t]
   \centering
-  \includegraphics[width=1.8\columnwidth]{fig/Figure9.pdf}
+  \includegraphics[width=\textwidth]{fig/Figure9.pdf}
   \caption{Accuracy of Listeners when varying $h_{size}$ from 1 to 8. Each curve
     represents an average accuracy trend from 50 repeated training, with the
     range of [$\mu - \sigma$, $\mu + \sigma$], where $\mu$ is the average

AAAI2021/tex/relatedwork.tex

@@ -5,14 +5,15 @@
 %external environmental factors
 Previous works focus on the external environmental factors that impact the
 compositionality of emerged symbolic language. 
+Some significant works on studying the external environmental factor on the compositionality of emergent language are summarized on Table~\ref{tab:rel}.
 For example, ~\citet{kirby2015compression} explored how the pressures for expressivity and compressibility lead the structured language.
 ~\citet{kottur-etal-2017-natural} constrained the vocabulary size and whether the listener has memory to coax the compositionality of the emergent language.
 ~\citet{lazaridou2018emergence} showed that the degree of structure found in the input data affects the emergence of the symbolic language.
 ~\citet{li2019ease} studied how the pressure, ease of teaching, impact on the iterative language of the population regime.
 ~\citet{evtimova2018emergent} designed a novel multi-modal scenarios, which the speaker and the listener should access to different modalities of the input object, to explore the language emergence.
 Such factors are deliberately designed, which are too ideal to be true in
-the real world. None of these works realizes the importance of model capacity of
-agent itself. \rmk{this should be largely emphasized.}
+the real world. 
+In this paper, these handcrafted inductions above are all removed, and the high compostional language is leaded only by the agent capacity. 
 
 
 

AAAI2021/tex/theory.tex

@@ -38,8 +38,8 @@ 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
@@ -87,7 +87,7 @@ 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 $\pi_L$.
@@ -100,9 +100,9 @@ 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}
 
@@ -119,8 +119,8 @@ 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 $\pi_{old}^S\leftarrow \pi^S$
@@ -134,8 +134,8 @@ 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

@@ -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}