~

AAAI2021/tex/theory.tex

@@ -24,35 +24,22 @@ In this paper, the task is xxxx.
 \textbf{Game rules} In our referential game, agents follow the following rules
 to finish the game in a cooperatively manner. In each round，once received an
 input object $t$, Speaker $S$ speaks a symbol sequence $s$ to Listener $L$ ;
-Listener $L$ reconstruct the predict result $\hat{t}$ based on the listened
+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
 ($R(t,\hat{t})=-1$).
 
-Precisely, 
-
-
-An input object t is a concept sequence with fixed length, denoted
-$t=(c_0,c_1)$.
-
-The concept $c_0(shape)$ and $c_1(color)$ are indicated as a
-one-hot vector respectively.
-The length of each one-hot vector ranges from 3 to 6.
-These two vectors are concatenated to denote the input object t.
-Each symbol sequence s contains two words, denoted $(s_0,s_1)$. Each word $s_i$
-is chosen in the vocabulary set $V$. In this game, let the card $|V|$ range from
-4 to 10, and the inequation $|V|^2\geq|M_1||M_1|$ is satisfied to ensure the
-symbol sequence $(s_0,s_1)$ can be used to denote all the input object t. The
-one-hot vector with the length $|V|$ is used to indicate the word $s_0$ and
-$s_1$ respectively. Then, the two one-hot vectors are concatenated to denote the
-symbol sequence s.
-The predict result $\hat{t}$ is denoted as a one-hot vector with the length
-$|M_0||M_1|$. Each bit of the one-hot vector denotes one input object. If the
-predict result $\hat{t}[i*|M_1|+j]=1$, the one-hot vector of each predict
-concept $\hat{c}_0$ and $\hat{c}_1$ respectively satisfied $\hat{c}_0[i]=1$ and
-$\hat{c}_1[j]=1$.
-If $(c_0,c_1)$ is equal to $(\hat{c}_0,\hat{c}_1)$, the input object and the
-predict result indicate the same object.
+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
+one-hot vector representing shape and color, respectively. Based on the $t$,
+Speaker $S$ speaks a symbol sequence $s$, which similarly contains two words
+from $V$. The Listener $L$ receives $s$ and output predicted result $\hat{t}$,
+a single word (one-hot vector) selected from the Cartesian product of set two $V$s
+($V\times V$), which representing all the meanings of two combined words from $V$.
+Please note that since $t$ and $\hat{t}$ have different length, we say
+$t=\hat{t}$ if $t$ expresses the same meaning as $\hat{t}$, e.g.,
+$t={[0,0,1],[0,1,0]}$ would be equal to $\hat{t}=[0,0,0,0,0,1]$ if they both mean ``red
+circle''.