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NiuTrans
Toy-MT-Introduction
Commits
e10537de
Commit
e10537de
authored
May 27, 2020
by
曹润柘
Browse files
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合并分支 'caorunzhe' 到 'master'
Caorunzhe 查看合并请求
!273
parents
35ddc010
b64ef0db
隐藏空白字符变更
内嵌
并排
正在显示
6 个修改的文件
包含
325 行增加
和
306 行删除
+325
-306
Book/Chapter6/Figures/figure-example-of-context-vector-calculation-process.tex
+1
-1
Section01-Introduction/section01.tex
+4
-4
Section03-Word-Based-Models/section03.tex
+218
-218
Section04-Phrasal-and-Syntactic-Models/section04.tex
+18
-18
Section05-Neural-Networks-and-Language-Modeling/section05.tex
+16
-0
Section06-Neural-Machine-Translation/section06.tex
+68
-65
没有找到文件。
Book/Chapter6/Figures/figure-example-of-context-vector-calculation-process.tex
查看文件 @
e10537de
...
@@ -104,7 +104,7 @@
...
@@ -104,7 +104,7 @@
%\visible<3->
%\visible<3->
{
{
% coverage score formula node
% coverage score formula node
\node
[anchor=north west] (formula) at ([xshift=-0.3
\hnode
,yshift=-1.5
\hnode
]attn11.south)
{
\small
{
不同
$
\textbf
{
C
}_
i
$
所对应的源语言词的权重是不同的
}}
;
\node
[anchor=north west] (formula) at ([xshift=-0.3
\hnode
,yshift=-1.5
\hnode
]attn11.south)
{
\small
{
不同
$
\textbf
{
C
}_
j
$
所对应的源语言词的权重是不同的
}}
;
\node
[anchor=north west] (example) at (formula.south west)
{
\footnotesize
{$
\textbf
{
C
}_
2
=
0
.
4
\times
\textbf
{
h
}
(
\textrm
{
``你''
}
)
+
0
.
4
\times
\textbf
{
h
}
(
\textrm
{
``什么''
}
)
+
$}}
;
\node
[anchor=north west] (example) at (formula.south west)
{
\footnotesize
{$
\textbf
{
C
}_
2
=
0
.
4
\times
\textbf
{
h
}
(
\textrm
{
``你''
}
)
+
0
.
4
\times
\textbf
{
h
}
(
\textrm
{
``什么''
}
)
+
$}}
;
\node
[anchor=north west] (example2) at ([yshift=0.4em]example.south west)
{
\footnotesize
{$
\ \ \ \ \ \ \ \
0
\times
\textbf
{
h
}
(
\textrm
{
``都''
}
)
+
0
.
1
\times
\textbf
{
h
}
(
\textrm
{
`` 没''
}
)
+
..
$}}
;
\node
[anchor=north west] (example2) at ([yshift=0.4em]example.south west)
{
\footnotesize
{$
\ \ \ \ \ \ \ \
0
\times
\textbf
{
h
}
(
\textrm
{
``都''
}
)
+
0
.
1
\times
\textbf
{
h
}
(
\textrm
{
`` 没''
}
)
+
..
$}}
;
}
}
...
...
Section01-Introduction/section01.tex
查看文件 @
e10537de
...
@@ -304,8 +304,8 @@
...
@@ -304,8 +304,8 @@
\visible
<3->
{
\visible
<3->
{
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=south west, fill=red, minimum width=1.5cm, minimum height=2.3cm] (mt) at (1,0)
{{
\color
{
white
}
\textbf
{
机器
}}}
;
\node
[anchor=south west, fill=red
!50
, minimum width=1.5cm, minimum height=2.3cm] (mt) at (1,0)
{{
\color
{
white
}
\textbf
{
机器
}}}
;
\node
[anchor=south west, fill=
ugreen
, minimum width=1.5cm, minimum height=2.7cm] (human) at ([xshift=0.5cm]mt.south east)
{{
\color
{
white
}
\textbf
{
人
}}}
;
\node
[anchor=south west, fill=
blue!50
, minimum width=1.5cm, minimum height=2.7cm] (human) at ([xshift=0.5cm]mt.south east)
{{
\color
{
white
}
\textbf
{
人
}}}
;
\node
[anchor=south] (mtscore) at (mt.north)
{
3.9
}
;
\node
[anchor=south] (mtscore) at (mt.north)
{
3.9
}
;
\node
[anchor=south] (humanscore) at (human.north)
{
4.7
}
;
\node
[anchor=south] (humanscore) at (human.north)
{
4.7
}
;
\draw
[->,thick] ([xshift=-0.5cm]mt.south west) -- ([xshift=0.5cm]human.south east);
\draw
[->,thick] ([xshift=-0.5cm]mt.south west) -- ([xshift=0.5cm]human.south east);
...
@@ -321,8 +321,8 @@
...
@@ -321,8 +321,8 @@
\visible
<4->
{
\visible
<4->
{
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=south west, fill=red, minimum width=1.5cm, minimum height=1.5cm] (mt) at (1,0)
{{
\color
{
white
}
\textbf
{
机器
}}}
;
\node
[anchor=south west, fill=red
!50
, minimum width=1.5cm, minimum height=1.5cm] (mt) at (1,0)
{{
\color
{
white
}
\textbf
{
机器
}}}
;
\node
[anchor=south west, fill=
ugreen
, minimum width=1.5cm, minimum height=2.7cm] (human) at ([xshift=0.5cm]mt.south east)
{{
\color
{
white
}
\textbf
{
人
}}}
;
\node
[anchor=south west, fill=
blue!50
, minimum width=1.5cm, minimum height=2.7cm] (human) at ([xshift=0.5cm]mt.south east)
{{
\color
{
white
}
\textbf
{
人
}}}
;
\node
[anchor=south] (mtscore) at (mt.north)
{
47
\%
}
;
\node
[anchor=south] (mtscore) at (mt.north)
{
47
\%
}
;
\node
[anchor=south] (humanscore) at (human.north)
{
100
\%
}
;
\node
[anchor=south] (humanscore) at (human.north)
{
100
\%
}
;
\draw
[->,thick] ([xshift=-0.5cm]mt.south west) -- ([xshift=0.5cm]human.south east);
\draw
[->,thick] ([xshift=-0.5cm]mt.south west) -- ([xshift=0.5cm]human.south east);
...
...
Section03-Word-Based-Models/section03.tex
查看文件 @
e10537de
...
@@ -775,7 +775,7 @@
...
@@ -775,7 +775,7 @@
\end{pgfonlayer}
\end{pgfonlayer}
}
}
\node
[anchor=west,ugreen] (P) at ([xshift=4em,yshift=-0.7em]corpus.east)
{
P(
$
t|s
$
)
}
;
\node
[anchor=west,ugreen] (P) at ([xshift=4em,yshift=-0.7em]corpus.east)
{
P(
$
\mathbf
{
t
}
|
\mathbf
{
s
}
$
)
}
;
\node
[anchor=south] (modellabel) at (P.north)
{{
\color
{
ublue
}
{
\scriptsize
\textbf
{
翻译模型
}}}}
;
\node
[anchor=south] (modellabel) at (P.north)
{{
\color
{
ublue
}
{
\scriptsize
\textbf
{
翻译模型
}}}}
;
\begin{pgfonlayer}
{
background
}
\begin{pgfonlayer}
{
background
}
...
@@ -808,18 +808,18 @@
...
@@ -808,18 +808,18 @@
\end{tikzpicture}
\end{tikzpicture}
\item
<3->
\textbf
{
步骤1
}
：构建单词翻译表 - 翻译词典
\\
\item
<3->
\textbf
{
步骤1
}
：构建单词翻译表 - 翻译词典
\\
\small
{
对于任意的源语言单词
$
x
$
，要获得它所有可能的译文
$
Y
$
。给定一个互译句对
$
(
s,t
)
$
，对于
$
y
\in
Y
$
，定义
$
\textrm
{
P
}
(
x
\leftrightarrow
y; s, t
)
$
表示
$
x
$
和
$
y
$
在
$
(
x,y
)
$
中互译的概率，我们用
$
x
$
和
$
y
$
的联合概率表示：
\small
{
对于任意的源语言单词
$
x
$
，要获得它所有可能的译文
$
Y
$
。给定一个互译句对
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
，对于
$
y
\in
Y
$
，定义
$
\textrm
{
P
}
(
x
\leftrightarrow
y;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
表示
$
x
$
和
$
y
$
在
$
(
x,y
)
$
中互译的概率，我们用
$
x
$
和
$
y
$
的联合概率表示：
\vspace
{
-2.0em
}
\vspace
{
-2.0em
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
P
}
(x
\leftrightarrow
y;
s,t)
&
\equiv
&
\textrm
{
P
}
(x,y;s,t
)
\nonumber
\\
\textrm
{
P
}
(x
\leftrightarrow
y;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
&
\equiv
&
\textrm
{
P
}
(x,y;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
\nonumber
\\
&
=
&
\frac
{
c(x,y;
s,t)
}{
\sum
_{
x',y'
}
c(x',y';s,t
)
}
\nonumber
&
=
&
\frac
{
c(x,y;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
}{
\sum
_{
x',y'
}
c(x',y';
\mathbf
{
s
}
,
\mathbf
{
t
}
)
}
\nonumber
\end{eqnarray}
\end{eqnarray}
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
$
c
(
x,y;
s,t
)
$
表示
$
(
x,y
)
$
在
$
(
s,t
)
$
中共现的次数;
$
\sum
_{
x',y'
}
c
(
x',y';s,t
)
$
表示
$
(
s,t
)
$
中任意源/译文单词共现的总次数
$
c
(
x,y;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
表示
$
(
x,y
)
$
在
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
中共现的次数;
$
\sum
_{
x',y'
}
c
(
x',y';
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
表示
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
中任意源/译文单词共现的总次数
}
}
\end{itemize}
\end{itemize}
...
@@ -831,7 +831,7 @@
...
@@ -831,7 +831,7 @@
\begin{frame}
{
实现一个简单的机器翻译系统：学习单词翻译概率(2)
}
\begin{frame}
{
实现一个简单的机器翻译系统：学习单词翻译概率(2)
}
\vspace
{
-1em
}
\vspace
{
-1em
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
P
}
(x,y;
s,t)
&
=
&
\frac
{
c(x,y;s,t)
}{
\sum
_{
x',y'
}
c(x',y';s,t
)
}
\nonumber
\textrm
{
P
}
(x,y;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
&
=
&
\frac
{
c(x,y;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
}{
\sum
_{
x',y'
}
c(x',y';
\mathbf
{
s
}
,
\mathbf
{
t
}
)
}
\nonumber
\end{eqnarray}
\end{eqnarray}
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
...
@@ -839,7 +839,7 @@
...
@@ -839,7 +839,7 @@
\begin{flushleft}
\begin{flushleft}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (s) at (0,0)
{$
s
=
$}
;
\node
[anchor=west] (s) at (0,0)
{$
\mathbf
{
s
}
=
$}
;
\node
[anchor=center] (sw1) at ([xshift=1em]s.east)
{
机器
}
;
\node
[anchor=center] (sw1) at ([xshift=1em]s.east)
{
机器
}
;
\visible
<1,4->
{
\visible
<1,4->
{
\node
[anchor=center] (sw2) at ([xshift=1.3em]sw1.east)
{
翻译
}
;
\node
[anchor=center] (sw2) at ([xshift=1.3em]sw1.east)
{
翻译
}
;
...
@@ -849,7 +849,7 @@
...
@@ -849,7 +849,7 @@
\node
[anchor=center] (sw4) at ([xshift=1.0em]sw3.east)
{
翻译
}
;
\node
[anchor=center] (sw4) at ([xshift=1.0em]sw3.east)
{
翻译
}
;
}
}
\node
[anchor=north west] (t) at (s.south west)
{$
t
=
$}
;
\node
[anchor=north west] (t) at (s.south west)
{$
\mathbf
{
t
}
=
$}
;
\node
[anchor=center] (tw1) at ([xshift=1.8em]t.east)
{
machine
}
;
\node
[anchor=center] (tw1) at ([xshift=1.8em]t.east)
{
machine
}
;
\visible
<1,3,5->
{
\visible
<1,3,5->
{
\node
[anchor=center] (tw2) at ([xshift=2.2em]tw1.east)
{
translation
}
;
\node
[anchor=center] (tw2) at ([xshift=2.2em]tw1.east)
{
translation
}
;
...
@@ -880,8 +880,8 @@
...
@@ -880,8 +880,8 @@
\begin{itemize}
\begin{itemize}
\item
$
c
(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
;
s,t
)=
\only
<
1
>
{
?
}
\visible
<
2
-
>
{
1
}
\visible
<
3
-
>
{
+
1
}
\visible
<
4
-
>
{
+
1
}
\visible
<
5
-
>
{
+
1
=
4
}$
\item
$
c
(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
;
\mathbf
{
s
}
,
\mathbf
{
t
}
)=
\only
<
1
>
{
?
}
\visible
<
2
-
>
{
1
}
\visible
<
3
-
>
{
+
1
}
\visible
<
4
-
>
{
+
1
}
\visible
<
5
-
>
{
+
1
=
4
}$
\item
<6->
$
\sum
_{
x',y'
}
c
(
x',y';
s,t
)=
\textrm
{
使劲数...
}
=
63
\visible
<
7
-
>
{
=
9
\times
7
=
|s|
\times
|t
|
}$
\item
<6->
$
\sum
_{
x',y'
}
c
(
x',y';
\mathbf
{
s
}
,
\mathbf
{
t
}
)=
\textrm
{
使劲数...
}
=
63
\visible
<
7
-
>
{
=
9
\times
7
=
|
\mathbf
{
s
}
|
\times
|
\mathbf
{
t
}
|
}$
\vspace
{
0.3em
}
\vspace
{
0.3em
}
\begin{itemize}
\begin{itemize}
\item
<7->
$
|
\cdot
|
$
表示句子长度
\item
<7->
$
|
\cdot
|
$
表示句子长度
...
@@ -889,14 +889,14 @@
...
@@ -889,14 +889,14 @@
\vspace
{
0.3em
}
\vspace
{
0.3em
}
\item
<8-> '翻译'和'translation'的互译概率为
\item
<8-> '翻译'和'translation'的互译概率为
\begin{displaymath}
\begin{displaymath}
\textrm
{
P
}
(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
;
s,t
) = 4/63
\textrm
{
P
}
(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
;
\mathbf
{
s
}
,
\mathbf
{
t
}
) = 4/63
\end{displaymath}
\end{displaymath}
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
类似的
类似的
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
P
}
(
\textrm
{
'机器'
}
,
\textrm
{
'translation'
}
;
s,t
)
&
=
&
2/63
\nonumber
\\
\textrm
{
P
}
(
\textrm
{
'机器'
}
,
\textrm
{
'translation'
}
;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
&
=
&
2/63
\nonumber
\\
\textrm
{
P
}
(
\textrm
{
'机器'
}
,
\textrm
{
'look'
}
;
s,t
)
&
=
&
0/63
\nonumber
\textrm
{
P
}
(
\textrm
{
'机器'
}
,
\textrm
{
'look'
}
;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
&
=
&
0/63
\nonumber
\end{eqnarray}
\end{eqnarray}
\end{itemize}
\end{itemize}
...
@@ -909,12 +909,12 @@
...
@@ -909,12 +909,12 @@
\begin{itemize}
\begin{itemize}
\item
很多时候，我们有多个互译句对
$
(
s
^{
[
1
]
}
,t
^{
[
1
]
}
)
,...,
(
s
^{
[
n
]
}
,t
^{
[
n
]
}
)
$
，称之为
\alert
{
双语平行数据(语料)
}
。翻译概率可以被定义为
\item
很多时候，我们有多个互译句对
$
(
\mathbf
{
s
}^{
[
1
]
}
,
\mathbf
{
t
}^{
[
1
]
}
)
,...,
(
\mathbf
{
s
}^{
[
n
]
}
,
\mathbf
{
t
}
^{
[
n
]
}
)
$
，称之为
\alert
{
双语平行数据(语料)
}
。翻译概率可以被定义为
\vspace
{
-1em
}
\vspace
{
-1em
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
P
}
(x,y)
&
=
&
\frac
{
\sum
_{
i=1
}^{
n
}
c(x,y;
s
^{
[i]
}
,t
^{
[i]
}
)
}{
\sum
_{
i=1
}^{
n
}
\sum
_{
x',y'
}
c(x',y';s
^{
[i]
}
,t
^{
[i]
}
)
}
\nonumber
\textrm
{
P
}
(x,y)
&
=
&
\frac
{
\sum
_{
i=1
}^{
n
}
c(x,y;
\mathbf
{
s
}^{
[i]
}
,
\mathbf
{
t
}^{
[i]
}
)
}{
\sum
_{
i=1
}^{
n
}
\sum
_{
x',y'
}
c(x',y';
\mathbf
{
s
}^{
[i]
}
,
\mathbf
{
t
}
^{
[i]
}
)
}
\nonumber
\end{eqnarray}
\end{eqnarray}
\item
<2-> 说白了就是计算
$
(
x,y
)
$
的频次时，在每个句子上累加
\item
<2-> 说白了就是计算
$
(
x,y
)
$
的频次时，在每个句子上累加
...
@@ -922,11 +922,11 @@
...
@@ -922,11 +922,11 @@
\begin{flushleft}
\begin{flushleft}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (s1) at (0,0)
{$
s
_
1
=
$
机器 翻译 就 是 用 计算机 进行 翻译
}
;
\node
[anchor=west] (s1) at (0,0)
{$
\mathbf
{
s
}^
1
=
$
机器 翻译 就 是 用 计算机 进行 翻译
}
;
\node
[anchor=north west] (t1) at ([yshift=0.4em]s1.south west)
{$
t
_
1
=
$
Machine translation is just translation by computer
}
;
\node
[anchor=north west] (t1) at ([yshift=0.4em]s1.south west)
{$
\mathbf
{
t
}^
1
=
$
Machine translation is just translation by computer
}
;
\node
[anchor=north west] (s2) at (t1.south west)
{$
s
_
2
=
$
那 人工 翻译 呢 ?
}
;
\node
[anchor=north west] (s2) at (t1.south west)
{$
\mathbf
{
s
}^
2
=
$
那 人工 翻译 呢 ?
}
;
\node
[anchor=north west] (t2) at ([yshift=0.4em]s2.south west)
{$
t
_
2
=
$
So , what is human translation ?
}
;
\node
[anchor=north west] (t2) at ([yshift=0.4em]s2.south west)
{$
\mathbf
{
t
}^
2
=
$
So , what is human translation ?
}
;
\end{tikzpicture}
\end{tikzpicture}
\end{flushleft}
\end{flushleft}
...
@@ -936,8 +936,8 @@
...
@@ -936,8 +936,8 @@
{
\footnotesize
{
\footnotesize
\begin{eqnarray}
\begin{eqnarray}
&
&
\textrm
{
P
}
(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
)
\nonumber
\\
&
&
\textrm
{
P
}
(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
)
\nonumber
\\
&
=
&
\frac
{
c(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
;
s
^{
[1]
}
,t
^{
[1]
}
)+c(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
;s
^{
[2]
}
,t
^{
[2]
}
)
}{
\sum
_{
x',y'
}
c(x',y';s
^{
[1]
}
,t
^{
[1]
}
) +
\sum
_{
x',y'
}
c(x',y';s
^{
[2]
}
,t
^{
[2]
}
)
}
\nonumber
\\
&
=
&
\frac
{
c(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
;
\mathbf
{
s
}^{
[1]
}
,
\mathbf
{
t
}^{
[1]
}
)+c(
\textrm
{
'翻译'
}
,
\textrm
{
'translation'
}
;
\mathbf
{
s
}^{
[2]
}
,
\mathbf
{
t
}^{
[2]
}
)
}{
\sum
_{
x',y'
}
c(x',y';
\mathbf
{
s
}^{
[1]
}
,
\mathbf
{
t
}^{
[1]
}
) +
\sum
_{
x',y'
}
c(x',y';
\mathbf
{
s
}^{
[2]
}
,
\mathbf
{
t
}
^{
[2]
}
)
}
\nonumber
\\
\visible
<3->
{&
=
&
\frac
{
4 + 1
}{
|
s
^{
[1]
}
|
\times
|t
^{
[1]
}
| + |s
^{
[2]
}
|
\times
|t
^{
[2]
}
|
}
=
\frac
{
4 + 1
}{
9
\times
7 + 5
\times
7
}
=
\frac
{
5
}{
98
}}
\nonumber
\visible
<3->
{&
=
&
\frac
{
4 + 1
}{
|
\mathbf
{
s
}^{
[1]
}
|
\times
|
\mathbf
{
t
}^{
[1]
}
| + |
\mathbf
{
s
}^{
[2]
}
|
\times
|
\mathbf
{
t
}
^{
[2]
}
|
}
=
\frac
{
4 + 1
}{
9
\times
7 + 5
\times
7
}
=
\frac
{
5
}{
98
}}
\nonumber
\end{eqnarray}
\end{eqnarray}
}
}
...
@@ -964,7 +964,7 @@
...
@@ -964,7 +964,7 @@
\end{pgfonlayer}
\end{pgfonlayer}
}
}
\node
[anchor=west,ugreen] (P) at ([xshift=4em,yshift=-0.7em]corpus.east)
{
P(
$
t|s
$
)
}
;
\node
[anchor=west,ugreen] (P) at ([xshift=4em,yshift=-0.7em]corpus.east)
{
P(
$
\mathbf
{
t
}
|
\mathbf
{
s
}
$
)
}
;
\node
[anchor=south] (modellabel) at (P.north)
{{
\color
{
ublue
}
{
\scriptsize
\textbf
{
翻译模型
}}}}
;
\node
[anchor=south] (modellabel) at (P.north)
{{
\color
{
ublue
}
{
\scriptsize
\textbf
{
翻译模型
}}}}
;
\begin{pgfonlayer}
{
background
}
\begin{pgfonlayer}
{
background
}
...
@@ -992,14 +992,14 @@
...
@@ -992,14 +992,14 @@
\end{center}
\end{center}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
步骤2
}
: 对任意的句对
$
(
s,t
)
$
计算句子级翻译概率
$
\textrm
{
P
}
(
t|s
)
$
\\
\item
\textbf
{
步骤2
}
: 对任意的句对
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
计算句子级翻译概率
$
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
)
$
\\
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\visible
<2->
{
\visible
<2->
{
用一种比较简单的思路：定义
$
(
s,t
)
$
上的一种分数
$
g
(
s,t
)
$
用一种比较简单的思路：定义
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
上的一种分数
$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
\begin{itemize}
\begin{itemize}
\item
$
g
(
s,t
)
$
的值越大翻译质量越好
\item
$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
的值越大翻译质量越好
\item
$
g
(
s,t
)
$
的值越小翻译质量越差
\item
$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
的值越小翻译质量越差
\end{itemize}
\end{itemize}
}
}
...
@@ -1009,10 +1009,10 @@
...
@@ -1009,10 +1009,10 @@
于是，我们进一步定义
于是，我们进一步定义
\begin{displaymath}
\begin{displaymath}
\textrm
{
P
}
(
t|s) =
\frac
{
g(s,t)
}{
\sum
_{
t'
}
g(s,t
')
}
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
) =
\frac
{
g(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
}{
\sum
_{
\mathbf
{
t
}
'
}
g(
\mathbf
{
s
}
,
\mathbf
{
t
}
')
}
\end{displaymath}
\end{displaymath}
实际上就是对
$
g
(
s,t
)
$
在所有可能的译文集合上做归一化，使其具有概率意义
实际上就是对
$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
在所有可能的译文集合上做归一化，使其具有概率意义
}
}
\end{itemize}
\end{itemize}
...
@@ -1030,11 +1030,11 @@
...
@@ -1030,11 +1030,11 @@
\item
两个问题
\item
两个问题
\begin{enumerate}
\begin{enumerate}
\item
如何计算
$
g
(
s,t
)
$
\visible
<2->
{
- 最关键的建模问题，马上开始
}
\item
如何计算
$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
\visible
<2->
{
- 最关键的建模问题，马上开始
}
\item
如何计算
$
\sum
_{
t'
}
g
(
s,t
'
)
$
\visible
<2->
{
- 实际上
\alert
{
不用计算
}
，后面再说
}
\item
如何计算
$
\sum
_{
\mathbf
{
t
}
'
}
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
'
)
$
\visible
<2->
{
- 实际上
\alert
{
不用计算
}
，后面再说
}
\end{enumerate}
\end{enumerate}
\item
<3->
\textbf
{
对
$
g
(
s,t
)
$
建模:
}
根据本章第一页的假设，
$
s
$
与
$
t
$
之间存在一种单词间的对应，我们称之为
\alert
{
词对齐
}
关系
\item
<3->
\textbf
{
对
$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
建模:
}
根据本章第一页的假设，
$
\mathbf
{
s
}$
与
$
\mathbf
{
t
}
$
之间存在一种单词间的对应，我们称之为
\alert
{
词对齐
}
关系
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
...
@@ -1045,7 +1045,7 @@
...
@@ -1045,7 +1045,7 @@
\node
[anchor=west] (s3) at ([xshift=0.5em]s2.east)
{
你
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (s3) at ([xshift=0.5em]s2.east)
{
你
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (s4) at ([xshift=0.5em]s3.east)
{
感到
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (s4) at ([xshift=0.5em]s3.east)
{
感到
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (s5) at ([xshift=0.5em]s4.east)
{
满意
\footnotesize
{$_
5
$}}
;
\node
[anchor=west] (s5) at ([xshift=0.5em]s4.east)
{
满意
\footnotesize
{$_
5
$}}
;
\node
[anchor=east] (s) at (s1.west)
{$
s
=
$}
;
\node
[anchor=east] (s) at (s1.west)
{$
\mathbf
{
s
}
=
$}
;
\end{scope}
\end{scope}
\begin{scope}
[yshift=-3.0em]
\begin{scope}
[yshift=-3.0em]
...
@@ -1054,7 +1054,7 @@
...
@@ -1054,7 +1054,7 @@
\node
[anchor=west] (t3) at ([xshift=0.3em,yshift=0.1em]t2.east)
{
satisfied
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (t3) at ([xshift=0.3em,yshift=0.1em]t2.east)
{
satisfied
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (t4) at ([xshift=0.3em]t3.east)
{
with
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (t4) at ([xshift=0.3em]t3.east)
{
with
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (t5) at ([xshift=0.3em,yshift=-0.2em]t4.east)
{
you
\footnotesize
{$_
5
$}}
;
\node
[anchor=west] (t5) at ([xshift=0.3em,yshift=-0.2em]t4.east)
{
you
\footnotesize
{$_
5
$}}
;
\node
[anchor=east] (t) at ([xshift=-0.3em]t1.west)
{$
t
=
$}
;
\node
[anchor=east] (t) at ([xshift=-0.3em]t1.west)
{$
\mathbf
{
t
}
=
$}
;
\end{scope}
\end{scope}
...
@@ -1082,9 +1082,9 @@
...
@@ -1082,9 +1082,9 @@
\begin{frame}
{
实现一个简单的机器翻译系统：句子级翻译模型(3)
}
\begin{frame}
{
实现一个简单的机器翻译系统：句子级翻译模型(3)
}
\begin{itemize}
\begin{itemize}
\item
给定一个句对
$
(
s,t
)
$
，及它们之间的(最优)词对齐
$
\hat
{
A
}$
，可以定义模型得分为：
\item
给定一个句对
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
，及它们之间的(最优)词对齐
$
\hat
{
A
}$
，可以定义模型得分为：
\begin{displaymath}
\begin{displaymath}
g(
s,t
)
\equiv
\prod
_{
(j,i)
\in
\hat
{
A
}}
\textrm
{
P
}
(s
_
j,t
_
i)
g(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
\equiv
\prod
_{
(j,i)
\in
\hat
{
A
}}
\textrm
{
P
}
(s
_
j,t
_
i)
\end{displaymath}
\end{displaymath}
显然每个单词翻译概率都高，那么整句的模型得分也高
显然每个单词翻译概率都高，那么整句的模型得分也高
...
@@ -1097,7 +1097,7 @@ g(s,t) \equiv \prod_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)
...
@@ -1097,7 +1097,7 @@ g(s,t) \equiv \prod_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)
\node
[anchor=west] (s3) at ([xshift=0.5em]s2.east)
{
你
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (s3) at ([xshift=0.5em]s2.east)
{
你
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (s4) at ([xshift=0.5em]s3.east)
{
感到
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (s4) at ([xshift=0.5em]s3.east)
{
感到
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (s5) at ([xshift=0.5em]s4.east)
{
满意
\footnotesize
{$_
5
$}}
;
\node
[anchor=west] (s5) at ([xshift=0.5em]s4.east)
{
满意
\footnotesize
{$_
5
$}}
;
\node
[anchor=east] (s) at (s1.west)
{$
s
=
$}
;
\node
[anchor=east] (s) at (s1.west)
{$
\mathbf
{
s
}
=
$}
;
\end{scope}
\end{scope}
\begin{scope}
[yshift=-3.0em]
\begin{scope}
[yshift=-3.0em]
...
@@ -1106,7 +1106,7 @@ g(s,t) \equiv \prod_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)
...
@@ -1106,7 +1106,7 @@ g(s,t) \equiv \prod_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)
\node
[anchor=west] (t3) at ([xshift=0.3em,yshift=0.1em]t2.east)
{
satisfied
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (t3) at ([xshift=0.3em,yshift=0.1em]t2.east)
{
satisfied
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (t4) at ([xshift=0.3em]t3.east)
{
with
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (t4) at ([xshift=0.3em]t3.east)
{
with
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (t5) at ([xshift=0.3em,yshift=-0.2em]t4.east)
{
you
\footnotesize
{$_
5
$}}
;
\node
[anchor=west] (t5) at ([xshift=0.3em,yshift=-0.2em]t4.east)
{
you
\footnotesize
{$_
5
$}}
;
\node
[anchor=east] (t) at ([xshift=-0.3em]t1.west)
{$
t
=
$}
;
\node
[anchor=east] (t) at ([xshift=-0.3em]t1.west)
{$
\mathbf
{
t
}
=
$}
;
\end{scope}
\end{scope}
...
@@ -1122,7 +1122,7 @@ g(s,t) \equiv \prod_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)
...
@@ -1122,7 +1122,7 @@ g(s,t) \equiv \prod_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)
\vspace
{
-2.5em
}
\vspace
{
-2.5em
}
\begin{eqnarray}
\begin{eqnarray}
g(
s,t
)
&
=
&
\textrm
{
P
}
(
\textrm
{
'我','I'
}
)
\times
\textrm
{
P
}
(
\textrm
{
'对','with'
}
)
\times
\textrm
{
P
}
(
\textrm
{
'你','you'
}
)
\times
\nonumber
\\
g(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
&
=
&
\textrm
{
P
}
(
\textrm
{
'我','I'
}
)
\times
\textrm
{
P
}
(
\textrm
{
'对','with'
}
)
\times
\textrm
{
P
}
(
\textrm
{
'你','you'
}
)
\times
\nonumber
\\
&
&
\textrm
{
P
}
(
\textrm
{
'感到','am'
}
)
\times
\textrm
{
P
}
(
\textrm
{
'满意','satisfied'
}
)
\nonumber
&
&
\textrm
{
P
}
(
\textrm
{
'感到','am'
}
)
\times
\textrm
{
P
}
(
\textrm
{
'满意','satisfied'
}
)
\nonumber
\end{eqnarray}
\end{eqnarray}
...
@@ -1141,13 +1141,13 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
...
@@ -1141,13 +1141,13 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
\begin{frame}
{
实现一个简单的机器翻译系统：句子级翻译模型(4)
}
\begin{frame}
{
实现一个简单的机器翻译系统：句子级翻译模型(4)
}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
但是
}
，这样设计的
$
g
(
s,t
)
$
没有考虑词序的信息。相同译词出现在不同的位置，得分相同 - 无法选择流畅的译文
\item
\textbf
{
但是
}
，这样设计的
$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
没有考虑词序的信息。相同译词出现在不同的位置，得分相同 - 无法选择流畅的译文
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\begin{tabular}
{
l | l
}
\begin{tabular}
{
l | l
}
&
\footnotesize
{$
\prod\limits
_{
(
j,i
)
\in
\hat
{
A
}}
\textrm
{
P
}
(
s
_
j,t
_
i
)
$}
\visible
<2->
{
\alert
{
\footnotesize
{$
\times\textrm
{
P
}_{
lm
}
(
t
)
$}}}
\\
\hline
&
\footnotesize
{$
\prod\limits
_{
(
j,i
)
\in
\hat
{
A
}}
\textrm
{
P
}
(
s
_
j,t
_
i
)
$}
\visible
<2->
{
\alert
{
\footnotesize
{$
\times\textrm
{
P
}_{
lm
}
(
\mathbf
{
t
}
)
$}}}
\\
\hline
\begin{tikzpicture}
\begin{tikzpicture}
...
@@ -1160,7 +1160,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
...
@@ -1160,7 +1160,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
\node
[anchor=west] (s3) at ([xshift=0.5em]s2.east)
{
你
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (s3) at ([xshift=0.5em]s2.east)
{
你
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (s4) at ([xshift=0.5em]s3.east)
{
感到
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (s4) at ([xshift=0.5em]s3.east)
{
感到
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (s5) at ([xshift=0.5em]s4.east)
{
满意
\footnotesize
{$_
5
$}}
;
\node
[anchor=west] (s5) at ([xshift=0.5em]s4.east)
{
满意
\footnotesize
{$_
5
$}}
;
\node
[anchor=east] (s) at (s1.west)
{$
s
=
$}
;
\node
[anchor=east] (s) at (s1.west)
{$
\mathbf
{
s
}
=
$}
;
\end{scope}
\end{scope}
\begin{scope}
[yshift=-2.6em]
\begin{scope}
[yshift=-2.6em]
...
@@ -1169,7 +1169,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
...
@@ -1169,7 +1169,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
\node
[anchor=west] (t3) at ([xshift=0.3em,yshift=0.1em]t2.east)
{
satisfied
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (t3) at ([xshift=0.3em,yshift=0.1em]t2.east)
{
satisfied
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (t4) at ([xshift=0.3em]t3.east)
{
with
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (t4) at ([xshift=0.3em]t3.east)
{
with
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (t5) at ([xshift=0.3em,yshift=-0.2em]t4.east)
{
you
\footnotesize
{$_
5
$}}
;
\node
[anchor=west] (t5) at ([xshift=0.3em,yshift=-0.2em]t4.east)
{
you
\footnotesize
{$_
5
$}}
;
\node
[anchor=east] (t) at ([xshift=-0.3em]t1.west)
{$
t
'
=
$}
;
\node
[anchor=east] (t) at ([xshift=-0.3em]t1.west)
{$
\mathbf
{
t
}
'
=
$}
;
\end{scope}
\end{scope}
...
@@ -1197,7 +1197,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
...
@@ -1197,7 +1197,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
\node
[anchor=west] (s3) at ([xshift=0.5em]s2.east)
{
你
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (s3) at ([xshift=0.5em]s2.east)
{
你
\footnotesize
{$_
3
$}}
;
\node
[anchor=west] (s4) at ([xshift=0.5em]s3.east)
{
感到
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (s4) at ([xshift=0.5em]s3.east)
{
感到
\footnotesize
{$_
4
$}}
;
\node
[anchor=west] (s5) at ([xshift=0.5em]s4.east)
{
满意
\footnotesize
{$_
5
$}}
;
\node
[anchor=west] (s5) at ([xshift=0.5em]s4.east)
{
满意
\footnotesize
{$_
5
$}}
;
\node
[anchor=east] (s) at (s1.west)
{$
s
=
$}
;
\node
[anchor=east] (s) at (s1.west)
{$
\mathbf
{
s
}
=
$}
;
\end{scope}
\end{scope}
\begin{scope}
[yshift=-2.6em]
\begin{scope}
[yshift=-2.6em]
...
@@ -1206,7 +1206,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
...
@@ -1206,7 +1206,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
\node
[anchor=center] (t3) at ([yshift=-1.7em]s3.south)
{
you
\footnotesize
{$_
3
$}}
;
\node
[anchor=center] (t3) at ([yshift=-1.7em]s3.south)
{
you
\footnotesize
{$_
3
$}}
;
\node
[anchor=center] (t4) at ([yshift=-1.7em]s4.south)
{
am
\footnotesize
{$_
4
$}}
;
\node
[anchor=center] (t4) at ([yshift=-1.7em]s4.south)
{
am
\footnotesize
{$_
4
$}}
;
\node
[anchor=center] (t5) at ([yshift=-1.6em]s5.south)
{
satisfied
\footnotesize
{$_
5
$}}
;
\node
[anchor=center] (t5) at ([yshift=-1.6em]s5.south)
{
satisfied
\footnotesize
{$_
5
$}}
;
\node
[anchor=center] (t) at ([xshift=-1.3em]t1.west)
{$
t
''
=
$}
;
\node
[anchor=center] (t) at ([xshift=-1.3em]t1.west)
{$
\mathbf
{
t
}
''
=
$}
;
\end{scope}
\end{scope}
...
@@ -1225,7 +1225,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
...
@@ -1225,7 +1225,7 @@ g(s,t) & = & \textrm{P}(\textrm{'我','I'}) \times \textrm{P}(\textrm{'对','with'
\end{tabular}
\end{tabular}
\item
<2->
\textbf
{
解决方案
}
：引入语言模型
$
\textrm
{
P
}_{
lm
}
(
t
)
$
来度量译文的流畅度
\item
<2->
\textbf
{
解决方案
}
：引入语言模型
$
\textrm
{
P
}_{
lm
}
(
\mathbf
{
t
}
)
$
来度量译文的流畅度
$
\textrm
{
P
}_{
\textrm
{
2
-
gram
}}
(
w
_
1
...w
_
m
)=
\textrm
{
P
}
(
w
_
1
)
\times
\textrm
{
P
}
(
w
_
2
| w
_
1
)
\times
\textrm
{
P
}
(
w
_
3
| w
_
2
)
...
\times
\textrm
{
P
}
(
w
_
m | w
_{
m
-
1
}
)
$
$
\textrm
{
P
}_{
\textrm
{
2
-
gram
}}
(
w
_
1
...w
_
m
)=
\textrm
{
P
}
(
w
_
1
)
\times
\textrm
{
P
}
(
w
_
2
| w
_
1
)
\times
\textrm
{
P
}
(
w
_
3
| w
_
2
)
...
\times
\textrm
{
P
}
(
w
_
m | w
_{
m
-
1
}
)
$
...
@@ -1234,7 +1234,7 @@ $\textrm{P}_{\textrm{2-gram}}(w_1...w_m)=\textrm{P}(w_1) \times \textrm{P}(w_2 |
...
@@ -1234,7 +1234,7 @@ $\textrm{P}_{\textrm{2-gram}}(w_1...w_m)=\textrm{P}(w_1) \times \textrm{P}(w_2 |
\vspace
{
-1em
}
\vspace
{
-1em
}
\begin{displaymath}
\begin{displaymath}
g(
s,t)=
\prod\nolimits
_{
(j,i)
\in
\hat
{
A
}}
\textrm
{
P
}
(s
_
j,t
_
i)
\times
\textrm
{
P
}_{
lm
}
(t
)
g(
\mathbf
{
s
}
,
\mathbf
{
t
}
)=
\prod\nolimits
_{
(j,i)
\in
\hat
{
A
}}
\textrm
{
P
}
(s
_
j,t
_
i)
\times
\textrm
{
P
}_{
lm
}
(
\mathbf
{
t
}
)
\end{displaymath}
\end{displaymath}
\end{itemize}
\end{itemize}
...
@@ -1260,7 +1260,7 @@ g(s,t)=\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i) \times \textrm{P}_
...
@@ -1260,7 +1260,7 @@ g(s,t)=\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i) \times \textrm{P}_
\end{pgfonlayer}
\end{pgfonlayer}
}
}
\node
[anchor=west,ugreen] (P) at ([xshift=4em,yshift=-0.7em]corpus.east)
{
P(
$
t|s
$
)
}
;
\node
[anchor=west,ugreen] (P) at ([xshift=4em,yshift=-0.7em]corpus.east)
{
P(
$
\mathbf
{
t
}
|
\mathbf
{
s
}
$
)
}
;
\node
[anchor=south] (modellabel) at (P.north)
{{
\color
{
ublue
}
{
\scriptsize
\textbf
{
翻译模型
}}}}
;
\node
[anchor=south] (modellabel) at (P.north)
{{
\color
{
ublue
}
{
\scriptsize
\textbf
{
翻译模型
}}}}
;
\begin{pgfonlayer}
{
background
}
\begin{pgfonlayer}
{
background
}
...
@@ -1287,16 +1287,16 @@ g(s,t)=\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i) \times \textrm{P}_
...
@@ -1287,16 +1287,16 @@ g(s,t)=\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i) \times \textrm{P}_
\end{center}
\end{center}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
步骤3：解码 -
}
对任意的
$
s
$
，找到翻译概率最大的译文
$
\hat
{
t
}$
\item
\textbf
{
步骤3：解码 -
}
对任意的
$
\mathbf
{
s
}$
，找到翻译概率最大的译文
$
\hat
{
\mathbf
{
t
}
}$
\begin{displaymath}
\begin{displaymath}
\hat
{
t
}
=
\argmax
_{
t
}
\textrm
{
P
}
(t|s
)
\hat
{
\mathbf
{
t
}}
=
\argmax
_{
\mathbf
{
t
}}
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
)
\end{displaymath}
\end{displaymath}
这里
$
\argmax
_{
a
}
f
(
a
)
$
表示找到使
$
f
(
a
)
$
达到最大的
$
a
$
输出
这里
$
\argmax
_{
\mathbf
{
a
}}
f
(
\mathbf
{
a
}
)
$
表示找到使
$
f
(
\mathbf
{
a
}
)
$
达到最大的
$
\mathbf
{
a
}
$
输出
\item
<2-> 现在我们可以对任意的
$
(
s,t
)
$
计算
$
\textrm
{
P
}
(
t|s
)
=
\frac
{
g
(
s,t
)
}{
\sum
_{
t'
}
g
(
s,t
'
)
}$
\item
<2-> 现在我们可以对任意的
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
计算
$
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
)
=
\frac
{
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
}{
\sum
_{
\mathbf
{
t
}
'
}
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
'
)
}$
\begin{itemize}
\begin{itemize}
\item
给定
$
s
$
，
$
\sum
_{
t'
}
g
(
s,t'
)
$
是个常数(因为
$
\sum
_{
t'
}
g
(
s,t'
)
$
的变量只有
$
s
$
)
\item
给定
$
\mathbf
{
s
}$
，
$
\sum
_{
\mathbf
{
t
}
'
}
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
'
)
$
是个常数(因为
$
\sum
_{
\mathbf
{
t
}
'
}
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
'
)
$
的变量只有
$
\mathbf
{
s
}
$
)
\item
\textbf
{
这样，我们得到解码步骤的形式化描述为
}
\item
\textbf
{
这样，我们得到解码步骤的形式化描述为
}
\end{itemize}
\end{itemize}
...
@@ -1304,8 +1304,8 @@ g(s,t)=\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i) \times \textrm{P}_
...
@@ -1304,8 +1304,8 @@ g(s,t)=\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i) \times \textrm{P}_
\vspace
{
-1em
}
\vspace
{
-1em
}
\begin{eqnarray}
\begin{eqnarray}
\hat
{
t
}
&
=
&
\argmax
_{
t
}
\frac
{
g(s,t)
}{
\sum
_{
t'
}
g(s,t
')
}
\nonumber
\\
\hat
{
\mathbf
{
t
}}
&
=
&
\argmax
_{
\mathbf
{
t
}}
\frac
{
g(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
}{
\sum
_{
\mathbf
{
t
}
'
}
g(
\mathbf
{
s
}
,
\mathbf
{
t
}
')
}
\nonumber
\\
&
=
&
\argmax
_{
t
}
g(s,t
)
\nonumber
&
=
&
\argmax
_{
\mathbf
{
t
}}
g(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
\nonumber
\end{eqnarray}
\end{eqnarray}
\end{itemize}
\end{itemize}
...
@@ -1317,15 +1317,15 @@ g(s,t)=\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i) \times \textrm{P}_
...
@@ -1317,15 +1317,15 @@ g(s,t)=\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i) \times \textrm{P}_
\begin{frame}
{
实现一个简单的机器翻译系统：解码(2)
}
\begin{frame}
{
实现一个简单的机器翻译系统：解码(2)
}
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
解码的核心问题
}
是在所有可能的翻译结果中找到使
$
g
(
s,t
)
$
达到最大的译文
\\
\item
\textbf
{
解码的核心问题
}
是在所有可能的翻译结果中找到使
$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
达到最大的译文
\\
\vspace
{
-1em
}
\vspace
{
-1em
}
\begin{minipage}
[t]
{
0.58
\linewidth
}
\begin{minipage}
[t]
{
0.58
\linewidth
}
\begin{itemize}
\begin{itemize}
\item
若
$
s
$
有
$
m
$
个词，每个词有
$
n
$
个翻译候选 - 共有
$
n
^
m
$
种组合
\item
若
$
\mathbf
{
s
}
$
有
$
m
$
个词，每个词有
$
n
$
个翻译候选 - 共有
$
n
^
m
$
种组合
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\item
<2-> 词的翻译候选可以任意调序
\item
<2-> 词的翻译候选可以任意调序
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\item
<3->
$
s
$
对应可能的译文至少有
$
n
^
m
\cdot
m
!
$
\item
<3->
$
\mathbf
{
s
}
$
对应可能的译文至少有
$
n
^
m
\cdot
m
!
$
\end{itemize}
\end{itemize}
\end{minipage}
\end{minipage}
\hfill
\hfill
...
@@ -1408,8 +1408,8 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -1408,8 +1408,8 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
{
\scriptsize
{
\scriptsize
\node
[anchor=north west,inner sep=2pt,align=left] (line1) at (0,0)
{
\textrm
{
\textbf
{
Function
}
\textsc
{
WordDecoding
}
(
$
s
$
)
}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line1) at (0,0)
{
\textrm
{
\textbf
{
Function
}
\textsc
{
WordDecoding
}
(
$
\mathbf
{
s
}
$
)
}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line2) at ([yshift=-1pt]line1.south west)
{
\textrm
{
1:
$
\pi
=
$
\textsc
{
GetTransOptions
}
(
$
s
$
)
}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line2) at ([yshift=-1pt]line1.south west)
{
\textrm
{
1:
$
\pi
=
$
\textsc
{
GetTransOptions
}
(
$
\mathbf
{
s
}
$
)
}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line3) at ([yshift=-1pt]line2.south west)
{
\textrm
{
2:
$
best
=
\phi
$}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line3) at ([yshift=-1pt]line2.south west)
{
\textrm
{
2:
$
best
=
\phi
$}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line4) at ([yshift=-1pt]line3.south west)
{
\textrm
{
3:
\textbf
{
for
}
$
i
$
in
$
[
1
,m
]
$
\textbf
{
do
}}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line4) at ([yshift=-1pt]line3.south west)
{
\textrm
{
3:
\textbf
{
for
}
$
i
$
in
$
[
1
,m
]
$
\textbf
{
do
}}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line5) at ([yshift=-1pt]line4.south west)
{
\textrm
{
4:
\hspace
{
1em
}
$
h
=
\phi
$}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line5) at ([yshift=-1pt]line4.south west)
{
\textrm
{
4:
\hspace
{
1em
}
$
h
=
\phi
$}}
;
...
@@ -1421,7 +1421,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -1421,7 +1421,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\node
[anchor=north west,inner sep=2pt,align=left] (line11) at ([yshift=-1pt]line10.south west)
{
\textrm
{
10:
\textbf
{
return
}
$
best.translatoin
$}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line11) at ([yshift=-1pt]line10.south west)
{
\textrm
{
10:
\textbf
{
return
}
$
best.translatoin
$}}
;
\node
[anchor=south west,inner sep=2pt,align=left] (head1) at ([yshift=1pt]line1.north west)
{
输出: 找的最佳译文
}
;
\node
[anchor=south west,inner sep=2pt,align=left] (head1) at ([yshift=1pt]line1.north west)
{
输出: 找的最佳译文
}
;
\node
[anchor=south west,inner sep=2pt,align=left] (head2) at ([yshift=1pt]head1.north west)
{
输入: 源语句子
$
s
=
s
_
1
...s
_
m
$}
;
\node
[anchor=south west,inner sep=2pt,align=left] (head2) at ([yshift=1pt]head1.north west)
{
输入: 源语句子
$
\mathbf
{
s
}
=
s
_
1
...s
_
m
$}
;
}
}
...
@@ -1602,8 +1602,8 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -1602,8 +1602,8 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
{
\tiny
{
\tiny
\node
[anchor=north west,inner sep=2pt,align=left] (line1) at (0,0)
{
\textrm
{
\textbf
{
Function
}
\textsc
{
WordDecoding
}
(
$
s
$
)
}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line1) at (0,0)
{
\textrm
{
\textbf
{
Function
}
\textsc
{
WordDecoding
}
(
$
\mathbf
{
s
}
$
)
}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line2) at ([yshift=-3pt]line1.south west)
{
\textrm
{
1:
$
\pi
=
$
\textsc
{
GetTransOptions
}
(
$
s
$
)
}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line2) at ([yshift=-3pt]line1.south west)
{
\textrm
{
1:
$
\pi
=
$
\textsc
{
GetTransOptions
}
(
$
\mathbf
{
s
}
$
)
}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line3) at ([yshift=-3pt]line2.south west)
{
\textrm
{
2:
$
best
=
\phi
$}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line3) at ([yshift=-3pt]line2.south west)
{
\textrm
{
2:
$
best
=
\phi
$}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line4) at ([yshift=-3pt]line3.south west)
{
\textrm
{
3:
\textbf
{
for
}
$
i
$
in
$
[
1
,m
]
$
\textbf
{
do
}}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line4) at ([yshift=-3pt]line3.south west)
{
\textrm
{
3:
\textbf
{
for
}
$
i
$
in
$
[
1
,m
]
$
\textbf
{
do
}}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line5) at ([yshift=-3pt]line4.south west)
{
\textrm
{
4:
\hspace
{
1em
}
$
h
=
\phi
$}}
;
\node
[anchor=north west,inner sep=2pt,align=left] (line5) at ([yshift=-3pt]line4.south west)
{
\textrm
{
4:
\hspace
{
1em
}
$
h
=
\phi
$}}
;
...
@@ -1620,7 +1620,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -1620,7 +1620,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
}
}
\node
[anchor=south west,inner sep=2pt,align=left] (head1) at ([yshift=3pt]line1.north west)
{
输出: 找的最佳译文
}
;
\node
[anchor=south west,inner sep=2pt,align=left] (head1) at ([yshift=3pt]line1.north west)
{
输出: 找的最佳译文
}
;
\node
[anchor=south west,inner sep=2pt,align=left] (head2) at ([yshift=3pt]head1.north west)
{
输入: 源语句子
$
s
=
s
_
1
...s
_
m
$}
;
\node
[anchor=south west,inner sep=2pt,align=left] (head2) at ([yshift=3pt]head1.north west)
{
输入: 源语句子
$
\mathbf
{
s
}
=
s
_
1
...s
_
m
$}
;
}
}
...
@@ -1900,7 +1900,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -1900,7 +1900,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
}
}
\visible
<6->
{
\visible
<6->
{
\node
[anchor=north west] (glabel) at (hlabel.south west)
{$
g
(
s,t
)
$}
;
\node
[anchor=north west] (glabel) at (hlabel.south west)
{$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$}
;
\node
[anchor=west] (translabel) at (glabel.east)
{
翻译结果
}
;
\node
[anchor=west] (translabel) at (glabel.east)
{
翻译结果
}
;
\draw
[-] (glabel.north east) -- ([yshift=-1.9in]glabel.north east);
\draw
[-] (glabel.north east) -- ([yshift=-1.9in]glabel.north east);
\draw
[-] (glabel.south west) -- ([xshift=3.5in]glabel.south west);
\draw
[-] (glabel.south west) -- ([xshift=3.5in]glabel.south west);
...
@@ -2206,7 +2206,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2206,7 +2206,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\begin{frame}
{
机器翻译的统计建模
}
\begin{frame}
{
机器翻译的统计建模
}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
一个人在做翻译时
}
：对于给定的源语言句子
$
s
$
，可以了翻译为一个（或者若干个）正确的译文
$
\hat
{
t
}$
\item
\textbf
{
一个人在做翻译时
}
：对于给定的源语言句子
$
\mathbf
{
s
}$
，可以了翻译为一个（或者若干个）正确的译文
$
\hat
{
\mathbf
{
t
}
}$
\begin{itemize}
\begin{itemize}
\item
也就是说除了正确的译文，其它的翻译都是不正确的
\item
也就是说除了正确的译文，其它的翻译都是不正确的
\end{itemize}
\end{itemize}
...
@@ -2214,20 +2214,20 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2214,20 +2214,20 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[draw,red,fill=red!10,thick,anchor=center,circle,inner sep=3.5pt] (s) at (0,0)
{
\black
{$
s
$}}
;
\node
[draw,red,fill=red!10,thick,anchor=center,circle,inner sep=3.5pt] (s) at (0,0)
{
\black
{$
\mathbf
{
s
}
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t) at ([xshift=1in]s.east)
{
\black
{$
\hat
{
t
}$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t) at ([xshift=1in]s.east)
{
\black
{$
\hat
{
\mathbf
{
t
}
}$}}
;
\draw
[->,thick,] (s.north east) .. controls +(north east:1em) and +(north west:1em).. (t.north west) node[pos=0.5,below]
{
\tiny
{
正确翻译
}}
;
\draw
[->,thick,] (s.north east) .. controls +(north east:1em) and +(north west:1em).. (t.north west) node[pos=0.5,below]
{
\tiny
{
正确翻译
}}
;
\end{tikzpicture}
\end{tikzpicture}
\end{center}
\end{center}
\item
<2->
\textbf
{
统计机器翻译的思想是
}
：对于
$
s
$
，所有可能的目标语词串
$
t
$
都是可能的译文。每一对(
$
s
$
,
$
t
$
)都有一个概率值
$
\textrm
{
P
}
(
t|s
)
$
来描述
$
s
$
翻译为
$
t
$
的好与坏
\item
<2->
\textbf
{
统计机器翻译的思想是
}
：对于
$
\mathbf
{
s
}$
，所有可能的目标语词串
$
\mathbf
{
t
}$
都是可能的译文。每一对(
$
\mathbf
{
s
}$
,
$
\mathbf
{
t
}$
)都有一个概率值
$
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
)
$
来描述
$
\mathbf
{
s
}$
翻译为
$
\mathbf
{
t
}
$
的好与坏
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[draw,red,fill=red!10,thick,anchor=center,circle,inner sep=3.5pt] (s) at (0,0)
{
\black
{$
s
$}}
;
\node
[draw,red,fill=red!10,thick,anchor=center,circle,inner sep=3.5pt] (s) at (0,0)
{
\black
{$
\mathbf
{
s
}
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t1) at ([xshift=1in]s.east)
{
\black
{$
t
_
1
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t1) at ([xshift=1in]s.east)
{
\black
{$
t
_
1
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t2) at ([xshift=3em,yshift=2em]t1.north east)
{
\black
{$
t
_
2
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t2) at ([xshift=3em,yshift=2em]t1.north east)
{
\black
{$
t
_
2
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t3) at ([xshift=1em,yshift=4em]t1.north east)
{
\black
{$
t
_
3
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t3) at ([xshift=1em,yshift=4em]t1.north east)
{
\black
{$
t
_
3
$}}
;
...
@@ -2237,10 +2237,10 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2237,10 +2237,10 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\node
[draw,dashed,ublue,fill=blue!10,thick,anchor=center,circle,minimum size=18pt] (t6) at ([xshift=3em]t2.east)
{}
;
\node
[draw,dashed,ublue,fill=blue!10,thick,anchor=center,circle,minimum size=18pt] (t6) at ([xshift=3em]t2.east)
{}
;
\node
[draw,dashed,ublue,fill=blue!10,thick,anchor=center,circle,minimum size=18pt] (t7) at ([xshift=3em]t4.east)
{}
;
\node
[draw,dashed,ublue,fill=blue!10,thick,anchor=center,circle,minimum size=18pt] (t7) at ([xshift=3em]t4.east)
{}
;
\draw
[->,thick,] (s.north east) .. controls +(north east:1em) and +(north west:1em).. (t1.north west) node[pos=0.5,below]
{
\tiny
{
P (
$
t
_
1
|
s
$
)=0.1
}}
;
\draw
[->,thick,] (s.north east) .. controls +(north east:1em) and +(north west:1em).. (t1.north west) node[pos=0.5,below]
{
\tiny
{
P (
$
t
_
1
|
\mathbf
{
s
}
$
)=0.1
}}
;
\draw
[->,thick,] (s.60) .. controls +(50:4em) and +(west:1em).. (t2.west) node[pos=0.5,below]
{
\tiny
{
P(
$
t
_
2
|
s
$
)=0.2
}}
;
\draw
[->,thick,] (s.60) .. controls +(50:4em) and +(west:1em).. (t2.west) node[pos=0.5,below]
{
\tiny
{
P(
$
t
_
2
|
\mathbf
{
s
}
$
)=0.2
}}
;
\draw
[->,thick,] (s.north) .. controls +(70:4em) and +(west:1em).. (t3.west) node[pos=0.5,above,xshift=-1em]
{
\tiny
{
P(
$
t
_
3
|
s
$
)=0.3
}}
;
\draw
[->,thick,] (s.north) .. controls +(70:4em) and +(west:1em).. (t3.west) node[pos=0.5,above,xshift=-1em]
{
\tiny
{
P(
$
t
_
3
|
\mathbf
{
s
}
$
)=0.3
}}
;
\draw
[->,thick,] (s.south east) .. controls +(300:3em) and +(south west:1em).. (t4.south west) node[pos=0.5,below]
{
\tiny
{
P(
$
t
_
4
|
s
$
)=0.1
}}
;
\draw
[->,thick,] (s.south east) .. controls +(300:3em) and +(south west:1em).. (t4.south west) node[pos=0.5,below]
{
\tiny
{
P(
$
t
_
4
|
\mathbf
{
s
}
$
)=0.1
}}
;
\end{tikzpicture}
\end{tikzpicture}
\end{center}
\end{center}
...
@@ -2254,13 +2254,13 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2254,13 +2254,13 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\begin{frame}
{
噪声信道模型
}
\begin{frame}
{
噪声信道模型
}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
噪声信道模型
}
：源语言句子
$
s
$
(信宿)是由目标语句子
$
t
$
(信源)经过一个有噪声的信道得到的。如果知道了
$
s
$
和信道的性质，我们可以通过
$
\textrm
{
P
}
(
t|s
)
$
得到可能的信源的概率。
\\
\item
\textbf
{
噪声信道模型
}
：源语言句子
$
\mathbf
{
s
}$
(信宿)是由目标语句子
$
\mathbf
{
t
}$
(信源)经过一个有噪声的信道得到的。如果知道了
$
\mathbf
{
s
}$
和信道的性质，我们可以通过
$
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
)
$
得到可能的信源的概率。
\\
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[draw,red,fill=red!10,thick,anchor=center,circle,inner sep=3.5pt] (s) at (0,0)
{
\black
{$
s
$}}
;
\node
[draw,red,fill=red!10,thick,anchor=center,circle,inner sep=3.5pt] (s) at (0,0)
{
\black
{$
\mathbf
{
s
}
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=3.3pt] (t) at ([xshift=1.5in]s.east)
{
\black
{$
t
$}}
;
\node
[draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=3.3pt] (t) at ([xshift=1.5in]s.east)
{
\black
{$
\mathbf
{
t
}
$}}
;
\draw
[<->,thick,] (s.east) -- (t.west) node [pos=0.5,draw,fill=white]
{
噪声信道
}
;
\draw
[<->,thick,] (s.east) -- (t.west) node [pos=0.5,draw,fill=white]
{
噪声信道
}
;
\node
[anchor=east] at (s.west)
{
\scriptsize
{
信宿
}}
;
\node
[anchor=east] at (s.west)
{
\scriptsize
{
信宿
}}
;
...
@@ -2272,13 +2272,13 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2272,13 +2272,13 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
而通过上述过程找到最可能的信源的过程被称之为
\alert
{
解码
}
而通过上述过程找到最可能的信源的过程被称之为
\alert
{
解码
}
\begin{displaymath}
\begin{displaymath}
\hat
{
t
}
=
\argmax
_{
t
}
\textrm
{
P
}
(t|s
)
\hat
{
\mathbf
{
t
}}
=
\argmax
_{
\mathbf
{
t
}}
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
)
\end{displaymath}
\end{displaymath}
\item
<2->
\textbf
{
贝叶斯变换
}
\item
<2->
\textbf
{
贝叶斯变换
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
P
}
(
t|s)
&
=
&
\frac
{
\textrm
{
P
}
(s,t)
}{
\textrm
{
P
}
(s
)
}
\nonumber
\\
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
)
&
=
&
\frac
{
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
}{
\textrm
{
P
}
(
\mathbf
{
s
}
)
}
\nonumber
\\
&
=
&
\frac
{
\textrm
{
P
}
(
s|t)
\textrm
{
P
}
(t)
}{
\textrm
{
P
}
(s
)
}
\nonumber
&
=
&
\frac
{
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
\textrm
{
P
}
(
\mathbf
{
t
}
)
}{
\textrm
{
P
}
(
\mathbf
{
s
}
)
}
\nonumber
\end{eqnarray}
\end{eqnarray}
\end{itemize}
\end{itemize}
...
@@ -2291,26 +2291,26 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2291,26 +2291,26 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (p) at (0,0)
{$
\textrm
{
P
}
(
t|s
)
$}
;
\node
[anchor=west] (p) at (0,0)
{$
\textrm
{
P
}
(
\mathbf
{
t
}
|
\mathbf
{
s
}
)
$}
;
\node
[anchor=west] (eqiv) at (p.east)
{
=
}
;
\node
[anchor=west] (eqiv) at (p.east)
{
=
}
;
\node
[anchor=south west,inner sep=2pt] (transmodel) at ([yshift=-2pt]eqiv.north east)
{$
\textrm
{
P
}
(
s|t
)
$}
;
\node
[anchor=south west,inner sep=2pt] (transmodel) at ([yshift=-2pt]eqiv.north east)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west,inner sep=2pt] (lmmodel) at ([xshift=2pt]transmodel.east)
{$
\textrm
{
P
}
(
t
)
$}
;
\node
[anchor=west,inner sep=2pt] (lmmodel) at ([xshift=2pt]transmodel.east)
{$
\textrm
{
P
}
(
\mathbf
{
t
}
)
$}
;
\node
[anchor=north west,inner sep=2pt] (sp) at ([yshift=4pt,xshift=1.5em]eqiv.south east)
{$
\textrm
{
P
}
(
s
)
$}
;
\node
[anchor=north west,inner sep=2pt] (sp) at ([yshift=4pt,xshift=1.5em]eqiv.south east)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
)
$}
;
\visible
<2->
{
\visible
<2->
{
\node
[anchor=south west,fill=red!20,inner sep=2pt] (transmodel) at ([yshift=-2pt]eqiv.north east)
{$
\textrm
{
P
}
(
s|t
)
$}
;
\node
[anchor=south west,fill=red!20,inner sep=2pt] (transmodel) at ([yshift=-2pt]eqiv.north east)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west,fill=blue!20,inner sep=2pt] (lmmodel) at ([xshift=2pt]transmodel.east)
{$
\textrm
{
P
}
(
t
)
$}
;
\node
[anchor=west,fill=blue!20,inner sep=2pt] (lmmodel) at ([xshift=2pt]transmodel.east)
{$
\textrm
{
P
}
(
\mathbf
{
t
}
)
$}
;
\node
[anchor=north west,fill=green!20,inner sep=2pt] (sp) at ([yshift=4pt,xshift=1.5em]eqiv.south east)
{$
\textrm
{
P
}
(
s
)
$}
;
\node
[anchor=north west,fill=green!20,inner sep=2pt] (sp) at ([yshift=4pt,xshift=1.5em]eqiv.south east)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
)
$}
;
}
}
\draw
[-] ([yshift=-4pt]transmodel.south west) -- ([yshift=-4pt]lmmodel.south east);
\draw
[-] ([yshift=-4pt]transmodel.south west) -- ([yshift=-4pt]lmmodel.south east);
\visible
<2->
{
\visible
<2->
{
\node
[anchor=south east,fill=red!20,draw,align=left] (tmmark) at ([xshift=0.5in,yshift=0.4in]p.north)
{
\footnotesize
{
给定信源
$
t
$
，得到信宿
$
s
$
}
\\\footnotesize
{
的概率，称作
\textbf
{
翻译模型
}}}
;
\node
[anchor=south east,fill=red!20,draw,align=left] (tmmark) at ([xshift=0.5in,yshift=0.4in]p.north)
{
\footnotesize
{
给定信源
$
\mathbf
{
t
}$
，得到信宿
$
\mathbf
{
s
}
$
}
\\\footnotesize
{
的概率，称作
\textbf
{
翻译模型
}}}
;
\node
[anchor=west,fill=blue!20,draw,align=left] (lmmark) at ([xshift=0.5in]tmmark.east)
{
\footnotesize
{
信源
$
t
$
出现的概率
}
\\\footnotesize
{
称作
\textbf
{
语言模型
}}}
;
\node
[anchor=west,fill=blue!20,draw,align=left] (lmmark) at ([xshift=0.5in]tmmark.east)
{
\footnotesize
{
信源
$
\mathbf
{
t
}
$
出现的概率
}
\\\footnotesize
{
称作
\textbf
{
语言模型
}}}
;
\node
[anchor=west,fill=green!20,draw,align=left] (smark) at ([xshift=0.2in,yshift=-0.3in]lmmodel.east)
{
\footnotesize
{
信宿
$
s
$
出现的概率
}
\\\footnotesize
{
给定
$
s
$
，
$
\textrm
{
P
}
(
s
)
$
为
\textbf
{
常量
}}}
;
\node
[anchor=west,fill=green!20,draw,align=left] (smark) at ([xshift=0.2in,yshift=-0.3in]lmmodel.east)
{
\footnotesize
{
信宿
$
\mathbf
{
s
}$
出现的概率
}
\\\footnotesize
{
给定
$
\mathbf
{
s
}$
，
$
\textrm
{
P
}
(
\mathbf
{
s
}
)
$
为
\textbf
{
常量
}}}
;
\draw
[->,thick] (transmodel.north) .. controls +(north:1.5em) and + (south:1.5em) .. (tmmark.south);
\draw
[->,thick] (transmodel.north) .. controls +(north:1.5em) and + (south:1.5em) .. (tmmark.south);
\draw
[->,thick] (lmmodel.north) .. controls +(north:1.5em) and + (south:1.3em) .. (lmmark.south);
\draw
[->,thick] (lmmodel.north) .. controls +(north:1.5em) and + (south:1.3em) .. (lmmark.south);
...
@@ -2326,11 +2326,11 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2326,11 +2326,11 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\begin{eqnarray}
\begin{eqnarray}
\hat
{
t
}
&
=
&
\argmax
_{
t
}
\frac
{
\textrm
{
P
}
(s|t)
\textrm
{
P
}
(t)
}{
\textrm
{
P
}
(s
)
}
\nonumber
\\
\hat
{
\mathbf
{
t
}}
&
=
&
\argmax
_{
\mathbf
{
t
}}
\frac
{
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
\textrm
{
P
}
(
\mathbf
{
t
}
)
}{
\textrm
{
P
}
(
\mathbf
{
s
}
)
}
\nonumber
\\
&
=
&
\argmax
_{
t
}
\textrm
{
P
}
(s|t)
\textrm
{
P
}
(t
)
\nonumber
&
=
&
\argmax
_{
\mathbf
{
t
}}
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
\textrm
{
P
}
(
\mathbf
{
t
}
)
\nonumber
\end{eqnarray}
\end{eqnarray}
即，在所有可能的译文中找到使翻译模型
$
\textrm
{
P
}
(
s|t
)
$
和语言模型
$
\textrm
{
P
}
(
t
)
$
乘积最大的译文
即，在所有可能的译文中找到使翻译模型
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
和语言模型
$
\textrm
{
P
}
(
\mathbf
{
t
}
)
$
乘积最大的译文
\end{itemize}
\end{itemize}
\
\
...
@@ -2344,28 +2344,28 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2344,28 +2344,28 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\begin{frame}
{
基本问题
}
\begin{frame}
{
基本问题
}
\begin{displaymath}
\begin{displaymath}
\hat
{
t
}
=
\argmax
_{
t
}
\textrm
{
P
}
(s|t)
\textrm
{
P
}
(t
)
\hat
{
\mathbf
{
t
}}
=
\argmax
_{
\mathbf
{
t
}}
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
\textrm
{
P
}
(
\mathbf
{
t
}
)
\end{displaymath}
\end{displaymath}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
三个基本问题
}
\item
\textbf
{
三个基本问题
}
\begin{enumerate}
\begin{enumerate}
\item
\textbf
{
建模
}
：如何描述计算
$
\textrm
{
P
}
(
s|t
)
$
和
$
\textrm
{
P
}
(
t
)
$
的计算方式
\item
\textbf
{
建模
}
：如何描述计算
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
和
$
\textrm
{
P
}
(
\mathbf
{
t
}
)
$
的计算方式
\item
\textbf
{
训练
}
：如何获得计算
$
\textrm
{
P
}
(
s|t
)
$
和
$
\textrm
{
P
}
(
t
)
$
所需的参数
\item
\textbf
{
训练
}
：如何获得计算
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
和
$
\textrm
{
P
}
(
\mathbf
{
t
}
)
$
所需的参数
\item
\textbf
{
解码
}
：如何完成搜索最优解的过程
$
argmax
$
\item
\textbf
{
解码
}
：如何完成搜索最优解的过程
$
argmax
$
\end{enumerate}
\end{enumerate}
\item
<2-> 回忆一下本章开始的实例，是不是有似曾相识的感觉？
\item
<2-> 回忆一下本章开始的实例，是不是有似曾相识的感觉？
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (e1) at (0,0)
{$
g
(
s,t
)
$}
;
\node
[anchor=west] (e1) at (0,0)
{$
g
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$}
;
\node
[anchor=west] (e2) at (e1.east)
{$
=
$}
;
\node
[anchor=west] (e2) at (e1.east)
{$
=
$}
;
\node
[anchor=west,inner sep=2pt,fill=red!20] (e3) at (e2.east)
{$
\prod\nolimits
_{
(
j,i
)
\in
\hat
{
A
}}
\textrm
{
P
}
(
s
_
j,t
_
i
)
$}
;
\node
[anchor=west,inner sep=2pt,fill=red!20] (e3) at (e2.east)
{$
\prod\nolimits
_{
(
j,i
)
\in
\hat
{
A
}}
\textrm
{
P
}
(
s
_
j,t
_
i
)
$}
;
\node
[anchor=west,inner sep=1pt] (e4) at (e3.east)
{$
\times
$}
;
\node
[anchor=west,inner sep=1pt] (e4) at (e3.east)
{$
\times
$}
;
\node
[anchor=west,inner sep=3pt,fill=blue!20] (e5) at (e4.east)
{$
\textrm
{
P
}_{
lm
}
(
t
)
$}
;
\node
[anchor=west,inner sep=3pt,fill=blue!20] (e5) at (e4.east)
{$
\textrm
{
P
}_{
lm
}
(
\mathbf
{
t
}
)
$}
;
\node
[anchor=north west,inner sep=1pt] (n1) at ([xshift=2.5em,yshift=-1em]e1.south west)
{$
\textrm
{
P
}
(
s|t
)
$}
;
\node
[anchor=north west,inner sep=1pt] (n1) at ([xshift=2.5em,yshift=-1em]e1.south west)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=north] (n1part2) at ([yshift=0.3em]n1.south)
{
\scriptsize
{
\textbf
{
翻译模型
}}}
;
\node
[anchor=north] (n1part2) at ([yshift=0.3em]n1.south)
{
\scriptsize
{
\textbf
{
翻译模型
}}}
;
\node
[anchor=west,inner sep=1pt] (n2) at ([xshift=2em]n1.east)
{$
\textrm
{
P
}
(
t
)
$}
;
\node
[anchor=west,inner sep=1pt] (n2) at ([xshift=2em]n1.east)
{$
\textrm
{
P
}
(
\mathbf
{
t
}
)
$}
;
\node
[anchor=north] (n2part2) at ([yshift=0.3em]n2.south)
{
\scriptsize
{
\textbf
{
语言模型
}}}
;
\node
[anchor=north] (n2part2) at ([yshift=0.3em]n2.south)
{
\scriptsize
{
\textbf
{
语言模型
}}}
;
\draw
[->,thick] (e3.south) .. controls +(south:1em) and +(north:1em) .. (n1.north);
\draw
[->,thick] (e3.south) .. controls +(south:1em) and +(north:1em) .. (n1.north);
\draw
[->,thick] (e5.south) .. controls +(south:1em) and +(70:1em) .. (n2.north);
\draw
[->,thick] (e5.south) .. controls +(south:1em) and +(70:1em) .. (n2.north);
...
@@ -2389,13 +2389,13 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2389,13 +2389,13 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\label
{
ibmmodelingstart
}
\label
{
ibmmodelingstart
}
\begin{itemize}
\begin{itemize}
\item
\textbf
{$
\textrm
{
P
}
(
t
)
$
和解码
}
在前面的内容中有介绍，下面重点求解
$
\textrm
{
P
}
(
s|t
)
$
，即：
\item
\textbf
{$
\textrm
{
P
}
(
\mathbf
{
t
}
)
$
和解码
}
在前面的内容中有介绍，下面重点求解
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
，即：
\begin{itemize}
\begin{itemize}
\item
\textbf
{
翻译模型建模
}
-
$
\textrm
{
P
}
(
s|t
)
$
的计算方法
\item
\textbf
{
翻译模型建模
}
-
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
的计算方法
\item
\textbf
{
翻译模型参数估计
}
- 计算
$
\textrm
{
P
}
(
s|t
)
$
所需的参数
\item
\textbf
{
翻译模型参数估计
}
- 计算
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
所需的参数
\end{itemize}
\end{itemize}
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\item
<2->
\textbf
{
IBM模型的假设
}
：
$
s
=
s
_
1
...s
_
m
$
和
$
t
=
t
_
1
...t
_
n
$
之间有单词一级的对应，称作
\alert
{
单词对齐
}
或者
\alert
{
词对齐
}
。此外：
\item
<2->
\textbf
{
IBM模型的假设
}
：
$
\mathbf
{
s
}
=
s
_
1
...s
_
m
$
和
$
\mathbf
{
t
}
=
t
_
1
...t
_
n
$
之间有单词一级的对应，称作
\alert
{
单词对齐
}
或者
\alert
{
词对齐
}
。此外：
\begin{itemize}
\begin{itemize}
\item
\textbf
{
约束
}
：一个源语言单词只能对应一个目标语单词
\item
\textbf
{
约束
}
：一个源语言单词只能对应一个目标语单词
\vspace
{
0.5em
}
\vspace
{
0.5em
}
...
@@ -2462,10 +2462,10 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2462,10 +2462,10 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% modeling P(s|t)
%%% modeling P(s|t)
\begin{frame}
{
建模 -
$
\textrm
{
P
}
(
s|t
)
$}
\begin{frame}
{
建模 -
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
\begin{itemize}
\begin{itemize}
\item
给定
$
s
$
和
$
t
$
，它们之间的
\alert
{
词对齐
}
被记为
$
a
=
a
_
1
...a
_
m
$
\item
给定
$
\mathbf
{
s
}$
和
$
\mathbf
{
t
}$
，它们之间的
\alert
{
词对齐
}
被记为
$
\mathbf
{
a
}
=
a
_
1
...a
_
m
$
\begin{itemize}
\begin{itemize}
\item
$
a
_
j
$
表示第
$
j
$
个源语单词
$
s
_
j
$
对应的目标语单词的位置
\item
$
a
_
j
$
表示第
$
j
$
个源语单词
$
s
_
j
$
对应的目标语单词的位置
\begin{center}
\begin{center}
...
@@ -2486,15 +2486,15 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2486,15 +2486,15 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\end{tikzpicture}
\end{tikzpicture}
\end{center}
\end{center}
\end{itemize}
\end{itemize}
\item
<2->
\textbf
{
\alert
{
建模!!
}}
:
$
\textrm
{
P
}
(
s|t
)
$
被表示为所有可能的词对齐的生成概率
\\
\item
<2->
\textbf
{
\alert
{
建模!!
}}
:
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
被表示为所有可能的词对齐的生成概率
\\
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\begin{displaymath}
\begin{displaymath}
\textrm
{
P
}
(
s|t) =
\sum
_{
a
}
\textrm
{
P
}
(s,a|t
)
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
) =
\sum
_{
\mathbf
{
a
}}
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
\end{displaymath}
\\
\end{displaymath}
\\
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\visible
<3->
{
\visible
<3->
{
每一种
$
a
$
对应一个
$
\textrm
{
P
}
(
s,a|t
)
$
每一种
$
\mathbf
{
a
}$
对应一个
$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$
\vspace
{
-0.8em
}
\vspace
{
-0.8em
}
\begin{center}
\begin{center}
...
@@ -2639,7 +2639,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2639,7 +2639,7 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\visible
<4->
{
\visible
<4->
{
\node
[anchor=south east,inner sep=0pt] (p) at (t0.north west)
{
\small
{{
\color
{
ugreen
}
P(
}}}
;
\node
[anchor=south east,inner sep=0pt] (p) at (t0.north west)
{
\small
{{
\color
{
ugreen
}
P(
}}}
;
\node
[anchor=south west,inner sep=0pt] (p2) at ([yshift=0.2em]t2.north east)
{
\small
{{
\color
{
ugreen
}
)
}}}
;
\node
[anchor=south west,inner sep=0pt] (p2) at ([yshift=0.2em]t2.north east)
{
\small
{{
\color
{
ugreen
}
)
}}}
;
\node
[anchor=west] (eq) at (p2.east)
{
\normalsize
{
=
\
P(
$
s|t
$
)
}}
;
\node
[anchor=west] (eq) at (p2.east)
{
\normalsize
{
=
\
P(
$
\mathbf
{
s
}
|
\mathbf
{
t
}
$
)
}}
;
}
}
}
}
\end{scope}
\end{scope}
...
@@ -2652,11 +2652,11 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2652,11 +2652,11 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% modeling P(s,a|t)
%%% modeling P(s,a|t)
\begin{frame}
{
建模 -
$
\textrm
{
P
}
(
s,a|t
)
$}
\begin{frame}
{
建模 -
$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$}
\begin{itemize}
\begin{itemize}
\item
\alert
{
\textbf
{
进一步建模!!
}}
：对于源语句子
$
s
=
s
_
1
...s
_
m
$
(
$
m
$
个词)、目标语译文
$
t
=
t
_
0
...t
_
n
$
(
$
n
$
个词)和词对齐
$
a
=
a
_
1
...a
_
m
$
，按如下方式计算
$
\textrm
{
P
}
(
s,a|t
)
$
\item
\alert
{
\textbf
{
进一步建模!!
}}
：对于源语句子
$
\mathbf
{
s
}
=
s
_
1
...s
_
m
$
(
$
m
$
个词)、目标语译文
$
\mathbf
{
t
}
=
t
_
0
...t
_
n
$
(
$
n
$
个词)和词对齐
$
\mathbf
{
a
}
=
a
_
1
...a
_
m
$
，按如下方式计算
$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$
\begin{itemize}
\begin{itemize}
\item
符号定义：
$
s
_
x
^
y
=
s
_
x...s
_
y
$
,
$
a
_
x
^
y
=
a
_
x...a
_
y
$
\item
符号定义：
$
s
_
x
^
y
=
s
_
x...s
_
y
$
,
$
a
_
x
^
y
=
a
_
x...a
_
y
$
...
@@ -2668,23 +2668,23 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2668,23 +2668,23 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
s,a|t
)=
$}
;
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)=
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em] (eq2) at (eq1.east)
{$
\textrm
{
P
}
(
m|
t
)
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em] (eq2) at (eq1.east)
{$
\textrm
{
P
}
(
m|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em] (eq3) at ([xshift=1pt]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em] (eq3) at ([xshift=1pt]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em] (eq4) at ([xshift=1pt]eq3.east)
{$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
t
)
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em] (eq4) at ([xshift=1pt]eq3.east)
{$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em] (eq5) at ([xshift=1pt]eq4.east)
{$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
t
)
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em] (eq5) at ([xshift=1pt]eq4.east)
{$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$}
;
\visible
<2->
{
\visible
<2->
{
\node
[anchor=west,inner sep=1pt,minimum height=2.64em,fill=red!20] (eq2) at (eq1.east)
{$
\textrm
{
P
}
(
m|
t
)
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em,fill=red!20] (eq2) at (eq1.east)
{$
\textrm
{
P
}
(
m|
\mathbf
{
t
}
)
$}
;
}
}
\visible
<3->
{
\visible
<3->
{
\node
[anchor=west,inner sep=1pt,minimum height=2.64em,fill=blue!20] (eq3) at ([xshift=1pt]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em,fill=blue!20] (eq3) at ([xshift=1pt]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}$}
;
}
}
\visible
<4->
{
\visible
<4->
{
\node
[anchor=west,inner sep=1pt,minimum height=2.64em,fill=green!20] (eq4) at ([xshift=1pt]eq3.east)
{$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
t
)
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em,fill=green!20] (eq4) at ([xshift=1pt]eq3.east)
{$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$}
;
}
}
\visible
<5->
{
\visible
<5->
{
\node
[anchor=west,inner sep=1pt,minimum height=2.64em,fill=purple!20] (eq5) at ([xshift=1pt]eq4.east)
{$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
t
)
$}
;
\node
[anchor=west,inner sep=1pt,minimum height=2.64em,fill=purple!20] (eq5) at ([xshift=1pt]eq4.east)
{$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$}
;
}
}
\visible
<2->
{
\visible
<2->
{
...
@@ -2706,12 +2706,12 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2706,12 +2706,12 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
\vspace
{
-0.0em
}
\vspace
{
-0.0em
}
\begin{itemize}
\begin{itemize}
\item
<2->
\textbf
{
生成模型
}
：给定译文
$
t
$
生成源文
$
s
$
和对齐
$
a
$
\item
<2->
\textbf
{
生成模型
}
：给定译文
$
\mathbf
{
t
}$
生成源文
$
\mathbf
{
s
}$
和对齐
$
\mathbf
{
a
}
$
\begin{enumerate}
\begin{enumerate}
\item
<2-> 根据译文
$
t
$
选择源文的长度
$
m
$
\item
<2-> 根据译文
$
\mathbf
{
t
}
$
选择源文的长度
$
m
$
\item
<3-> 循环源文的每个位置
$
j
$
\item
<3-> 循环源文的每个位置
$
j
$
\item
<4-> 根据译文
$
t
$
、源文长度
$
m
$
、已经生成的源语单词
$
s
_{
1
}^{
j
-
1
}$
和对齐
$
a
_{
1
}^{
j
-
1
}$
，生成第
$
j
$
个位置的对齐结果
$
a
_
j
$
\item
<4-> 根据译文
$
\mathbf
{
t
}
$
、源文长度
$
m
$
、已经生成的源语单词
$
s
_{
1
}^{
j
-
1
}$
和对齐
$
a
_{
1
}^{
j
-
1
}$
，生成第
$
j
$
个位置的对齐结果
$
a
_
j
$
\item
<5-> 根据译文
$
t
$
、源文长度
$
m
$
、已经生成的源语单词
$
s
_{
1
}^{
j
-
1
}$
和对齐
$
a
_{
1
}^{
j
}$
，生成第
$
j
$
个位置的源语言单词
$
s
_
j
$
（注意：这时
$
a
_
j
$
已经生成了）
\item
<5-> 根据译文
$
\mathbf
{
t
}
$
、源文长度
$
m
$
、已经生成的源语单词
$
s
_{
1
}^{
j
-
1
}$
和对齐
$
a
_{
1
}^{
j
}$
，生成第
$
j
$
个位置的源语言单词
$
s
_
j
$
（注意：这时
$
a
_
j
$
已经生成了）
\end{enumerate}
\end{enumerate}
\end{itemize}
\end{itemize}
...
@@ -2721,9 +2721,9 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
...
@@ -2721,9 +2721,9 @@ $m$ & $n$ & $n^m \cdot m!$ \\ \hline
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% generation of s and a given t - a running example
%%% generation of s and a given t - a running example
\begin{frame}
{
实例 -
$
\textrm
{
P
}
(
s,a|t
)
$}
\begin{frame}
{
实例 -
$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$}
$
s
$
= 在 桌子 上
\ \ \ \ \
$
t
$
=
$
t
_
0
$
on the table
\ \ \ \ \
$
a
$
=
\{
1-0,2-3,3-1
\}
$
\mathbf
{
s
}$
= 在 桌子 上
\ \ \ \ \
$
\mathbf
{
t
}$
=
$
t
_
0
$
on the table
\ \ \ \ \
$
\mathbf
{
a
}
$
=
\{
1-0,2-3,3-1
\}
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
...
@@ -2789,7 +2789,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -2789,7 +2789,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
{
\small
{
\small
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
P
}
(
s,a|t)
&
=
&
\textrm
{
P
}
(m|t)
\prod\limits
_{
j=1
}^{
m
}
\textrm
{
P
}
(a
_
j|a
_{
1
}^{
j-1
}
,s
_{
1
}^{
j-1
}
,m,t)
\textrm
{
P
}
(s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j-1
}
,m,t
)
\nonumber
\\
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
&
=
&
\textrm
{
P
}
(m|
\mathbf
{
t
}
)
\prod\limits
_{
j=1
}^{
m
}
\textrm
{
P
}
(a
_
j|a
_{
1
}^{
j-1
}
,s
_{
1
}^{
j-1
}
,m,
\mathbf
{
t
}
)
\textrm
{
P
}
(s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j-1
}
,m,
\mathbf
{
t
}
)
\nonumber
\\
&
\visible
<2->
{
=
}
&
\visible
<2->
{
\textrm
{
P
}
(m=3
\mid
\textrm
{
'
$
t
_
0
$
on the table'
}
)
}
\visible
<3->
{
\times
}
\nonumber
\\
&
\visible
<2->
{
=
}
&
\visible
<2->
{
\textrm
{
P
}
(m=3
\mid
\textrm
{
'
$
t
_
0
$
on the table'
}
)
}
\visible
<3->
{
\times
}
\nonumber
\\
&
&
\visible
<3->
{
\textrm
{
P
}
(a
_
1=0
\mid
\phi
,
\phi
,3,
\textrm
{
'
$
t
_
0
$
on the table'
}
)
}
\visible
<4->
{
\times
}
\nonumber
\\
&
&
\visible
<3->
{
\textrm
{
P
}
(a
_
1=0
\mid
\phi
,
\phi
,3,
\textrm
{
'
$
t
_
0
$
on the table'
}
)
}
\visible
<4->
{
\times
}
\nonumber
\\
&
&
\visible
<4->
{
\textrm
{
P
}
(f
_
1=
\textrm
{
在
}
\mid
\textrm
{
\{
1-0
\}
}
,
\phi
,3,
\textrm
{
'
$
t
_
0
$
on the table'
}
)
}
\visible
<5->
{
\times
}
\nonumber
\\
&
&
\visible
<4->
{
\textrm
{
P
}
(f
_
1=
\textrm
{
在
}
\mid
\textrm
{
\{
1-0
\}
}
,
\phi
,3,
\textrm
{
'
$
t
_
0
$
on the table'
}
)
}
\visible
<5->
{
\times
}
\nonumber
\\
...
@@ -2813,14 +2813,14 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -2813,14 +2813,14 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\vspace
{
-1.0em
}
\vspace
{
-1.0em
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
P
}
(
s|t)
&
=
&
\sum
_{
a
}
\textrm
{
P
}
(s,a|t
)
\nonumber
\\
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
&
=
&
\sum
_{
\mathbf
{
a
}}
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
\nonumber
\\
\textrm
{
P
}
(
s,a|t)
&
=
&
\textrm
{
P
}
(m|t)
\prod\limits
_{
j=1
}^{
m
}
\textrm
{
P
}
(a
_
j|a
_{
1
}^{
j-1
}
,s
_{
1
}^{
j-1
}
,m,t)
\textrm
{
P
}
(s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j-1
}
,m,t
)
\nonumber
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
&
=
&
\textrm
{
P
}
(m|
\mathbf
{
t
}
)
\prod\limits
_{
j=1
}^{
m
}
\textrm
{
P
}
(a
_
j|a
_{
1
}^{
j-1
}
,s
_{
1
}^{
j-1
}
,m,
\mathbf
{
t
}
)
\textrm
{
P
}
(s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j-1
}
,m,
\mathbf
{
t
}
)
\nonumber
\end{eqnarray}
\end{eqnarray}
\item
\textbf
{
两个严重问题
}
\item
\textbf
{
两个严重问题
}
\begin{enumerate}
\begin{enumerate}
\item
第一个公式：如何遍历所有的对齐
$
a
$
\item
第一个公式：如何遍历所有的对齐
$
\mathbf
{
a
}
$
\item
第二个公式：如何计算
$
\textrm
{
P
}
(
m|
t
)
$
、
$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,t
)
$
和
$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,t
)
$
\item
第二个公式：如何计算
$
\textrm
{
P
}
(
m|
\mathbf
{
t
}
)
$
、
$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$
和
$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$
\end{enumerate}
\end{enumerate}
\item
<2-> Brown等人(1993)的解决方法：对问题进行化简
\item
<2-> Brown等人(1993)的解决方法：对问题进行化简
...
@@ -2848,21 +2848,21 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -2848,21 +2848,21 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{enumerate}
\begin{enumerate}
\item
源语长度概率为常数
$
\epsilon
$
\item
源语长度概率为常数
$
\epsilon
$
\begin{displaymath}
\begin{displaymath}
\textrm
{
P
}
(m|
t
)
\equiv
\epsilon
\textrm
{
P
}
(m|
\mathbf
{
t
}
)
\equiv
\epsilon
\end{displaymath}
\end{displaymath}
\item
对齐概率
$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
t
)
$
仅依赖于译文长度
$
l
+
1
$
(均匀分布)
\item
对齐概率
$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$
仅依赖于译文长度
$
l
+
1
$
(均匀分布)
\begin{displaymath}
\begin{displaymath}
\textrm
{
P
}
(a
_
j|a
_{
1
}^{
j-1
}
,s
_{
1
}^{
j-1
}
,m,
t
)
\equiv
\frac
{
1
}{
l+1
}
\textrm
{
P
}
(a
_
j|a
_{
1
}^{
j-1
}
,s
_{
1
}^{
j-1
}
,m,
\mathbf
{
t
}
)
\equiv
\frac
{
1
}{
l+1
}
\end{displaymath}
\end{displaymath}
\item
源语单词
$
s
_
j
$
生成概率
$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
t
)
$
仅依赖与其对齐的译文单词
$
t
_{
a
_
j
}$
，即词汇翻译概率
$
f
(
s
_
j|t
_{
a
_
j
}
)
$
(
$
\sum
_{
s
_
j
}
f
(
s
_
j|t
_{
a
_
j
}
)
=
1
$
)
\item
源语单词
$
s
_
j
$
生成概率
$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$
仅依赖与其对齐的译文单词
$
t
_{
a
_
j
}$
，即词汇翻译概率
$
f
(
s
_
j|t
_{
a
_
j
}
)
$
(
$
\sum
_{
s
_
j
}
f
(
s
_
j|t
_{
a
_
j
}
)
=
1
$
)
\begin{displaymath}
\begin{displaymath}
\textrm
{
P
}
(s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j-1
}
,m,
t
)
\equiv
f(s
_
j|t
_{
a
_
j
}
)
\textrm
{
P
}
(s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j-1
}
,m,
\mathbf
{
t
}
)
\equiv
f(s
_
j|t
_{
a
_
j
}
)
\end{displaymath}
\end{displaymath}
\end{enumerate}
\end{enumerate}
\item
<2->
\textbf
{
核心思想是
}
把复杂参数化简为简单参数
\item
<2->
\textbf
{
核心思想是
}
把复杂参数化简为简单参数
\begin{itemize}
\begin{itemize}
\item
比如：
$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
t
)
\equiv
\frac
{
1
}{
l
-
1
}$
把参数空间
$
(
a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,t
)
$
化简为
$
l
$
\item
比如：
$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
\equiv
\frac
{
1
}{
l
-
1
}$
把参数空间
$
(
a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$
化简为
$
l
$
\item
\alert
{
优点
}
: 模型大大化简；
\alert
{
缺点
}
：化简导致模型不准确
\item
\alert
{
优点
}
: 模型大大化简；
\alert
{
缺点
}
：化简导致模型不准确
\end{itemize}
\end{itemize}
...
@@ -2882,12 +2882,12 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -2882,12 +2882,12 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
s,a|t
)
$}
;
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west] (eq1part2) at (eq1.east)
{$
=
$}
;
\node
[anchor=west] (eq1part2) at (eq1.east)
{$
=
$}
;
\node
[anchor=west,inner sep=1pt] (eq2) at (eq1part2.east)
{$
\textrm
{
P
}
(
m|
t
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq2) at (eq1part2.east)
{$
\textrm
{
P
}
(
m|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq3) at ([xshift=
1
pt]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}$}
;
\node
[anchor=west,inner sep=1pt] (eq3) at ([xshift=
0
pt]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}$}
;
\node
[anchor=west,inner sep=1pt] (eq4) at ([xshift=
1pt]eq3.east)
{$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,t
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq4) at ([xshift=
0pt]eq3.east)
{$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq5) at ([xshift=
1pt]eq4.east)
{$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,t
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq5) at ([xshift=
0pt]eq4.east)
{$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$}
;
\node
[anchor=east,rotate=90] (yes1) at (eq2.south)
{$
\equiv
$}
;
\node
[anchor=east,rotate=90] (yes1) at (eq2.south)
{$
\equiv
$}
;
\node
[anchor=east,rotate=90] (yes2) at (eq4.south)
{$
\equiv
$}
;
\node
[anchor=east,rotate=90] (yes2) at (eq4.south)
{$
\equiv
$}
;
...
@@ -2906,13 +2906,13 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -2906,13 +2906,13 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\end{tikzpicture}
\end{tikzpicture}
\end{center}
\end{center}
\item
<2->
\textbf
{
将上式代入
$
\textrm
{
P
}
(
s|t
)=
\sum
_
a
\textrm
{
P
}
(
s,a|t
)
$}
\item
<2->
\textbf
{
将上式代入
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)=
\sum
_
a
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$}
\vspace
{
-1.0em
}
\vspace
{
-1.0em
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
P
}
(
s|t)
&
=
&
\sum\limits
_{
a
}
\textrm
{
P
}
(s,a|t
)
\nonumber
\\
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
&
=
&
\sum\limits
_{
\mathbf
{
a
}}
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
\nonumber
\\
&
=
&
\sum\limits
_{
a
}
\frac
{
\epsilon
}{
(l+1)
^{
m
}}
\prod\limits
_{
j=1
}^{
m
}
f(s
_
j|t
_{
a
_
j
}
)
\nonumber
&
=
&
\sum\limits
_{
\mathbf
{
a
}
}
\frac
{
\epsilon
}{
(l+1)
^{
m
}}
\prod\limits
_{
j=1
}^{
m
}
f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\end{eqnarray}
\end{eqnarray}
\end{itemize}
\end{itemize}
...
@@ -2925,14 +2925,14 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -2925,14 +2925,14 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{itemize}
\begin{itemize}
\item
$
\textrm
{
P
}
(
s|t
)
=
\sum\limits
_{
a
}
\frac
{
\epsilon
}{
(
l
+
1
)
^{
m
}}
\prod\limits
_{
j
=
1
}^{
m
}
f
(
s
_
j|t
_{
a
_
j
}
)
$
中需要对遍历所有的对齐，即
$
\sum
_{
a
}$
。这个过程可以被重新表示为
\item
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
=
\sum\limits
_{
\mathbf
{
a
}}
\frac
{
\epsilon
}{
(
l
+
1
)
^{
m
}}
\prod\limits
_{
j
=
1
}^{
m
}
f
(
s
_
j|t
_{
a
_
j
}
)
$
中需要对遍历所有的对齐，即
$
\sum
_{
\mathbf
{
a
}
}$
。这个过程可以被重新表示为
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
s|t
)
$}
;
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west] (eq2) at (eq1.east)
{$
=
$}
;
\node
[anchor=west] (eq2) at (eq1.east)
{$
=
$}
;
\node
[anchor=west,inner sep=2pt] (eq3) at (eq2.east)
{$
\sum\limits
_{
a
_
1
=
0
}^{
l
}$}
;
\node
[anchor=west,inner sep=2pt] (eq3) at (eq2.east)
{$
\sum\limits
_{
a
_
1
=
0
}^{
l
}$}
;
\node
[anchor=west,inner sep=0] (eq4) at (eq3.east)
{
...
}
;
\node
[anchor=west,inner sep=0] (eq4) at (eq3.east)
{
...
}
;
...
@@ -2968,7 +2968,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -2968,7 +2968,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\end{center}
\end{center}
\begin{enumerate}
\begin{enumerate}
\item
<2-> 遍历所有的的对齐
$
a
$
。
$
a
$
由
\{
$
a
_
1
$
,...,
$
a
_
m
$
\}
组成，每个
$
a
_
j
\in
\{
a
_
1
,...,a
_
m
\}
$
从第译文开始位置(0)循环到截止位置(
$
l
$
)
\item
<2-> 遍历所有的的对齐
$
\mathbf
{
a
}$
。
$
\mathbf
{
a
}
$
由
\{
$
a
_
1
$
,...,
$
a
_
m
$
\}
组成，每个
$
a
_
j
\in
\{
a
_
1
,...,a
_
m
\}
$
从第译文开始位置(0)循环到截止位置(
$
l
$
)
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\begin{center}
\begin{center}
...
@@ -3003,7 +3003,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3003,7 +3003,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\end{center}
\end{center}
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\item
<5-> 对于每个
$
a
$
累加对齐概率
$
\textrm
{
P
}
(
s,a|t
)
$
\item
<5-> 对于每个
$
\mathbf
{
a
}$
累加对齐概率
$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$
\end{enumerate}
\end{enumerate}
\end{itemize}
\end{itemize}
...
@@ -3026,28 +3026,28 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3026,28 +3026,28 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{scope}
\begin{scope}
\node
[anchor=west] (s1) at (0,0)
{$
s
$
= 在
\ \
桌子
\ \
上
}
;
\node
[anchor=west] (s1) at (0,0)
{$
\mathbf
{
s
}
$
= 在
\ \
桌子
\ \
上
}
;
\node
[anchor=west] (t1) at ([yshift=-2em]s1.west)
{$
t
$
= on
\ \
the
\ \
table
}
;
\node
[anchor=west] (t1) at ([yshift=-2em]s1.west)
{$
\mathbf
{
t
}
$
= on
\ \
the
\ \
table
}
;
\draw
[->,double,thick,ublue] ([yshift=0.2em]s1.south) -- ([yshift=-0.8em]s1.south);
\draw
[->,double,thick,ublue] ([yshift=0.2em]s1.south) -- ([yshift=-0.8em]s1.south);
\end{scope}
\end{scope}
\begin{scope}
[xshift=1.5in]
\begin{scope}
[xshift=1.5in]
\node
[anchor=west] (s2) at (0,0)
{$
s
$
= 在
\ \
桌子
\ \
上
}
;
\node
[anchor=west] (s2) at (0,0)
{$
\mathbf
{
s
}
$
= 在
\ \
桌子
\ \
上
}
;
\node
[anchor=west] (t2) at ([yshift=-2em]s2.west)
{$
t
'
$
= table
\
on
\ \
the
}
;
\node
[anchor=west] (t2) at ([yshift=-2em]s2.west)
{$
\mathbf
{
t
}
'
$
= table
\
on
\ \
the
}
;
\draw
[->,double,thick,ublue] ([yshift=0.2em]s2.south) -- ([yshift=-0.8em]s2.south);
\draw
[->,double,thick,ublue] ([yshift=0.2em]s2.south) -- ([yshift=-0.8em]s2.south);
\end{scope}
\end{scope}
\node
[anchor=north] (score11) at ([yshift=-2.0em]s1.south)
{$
\textrm
{
P
}
(
s|t
)
$}
;
\node
[anchor=north] (score11) at ([yshift=-2.0em]s1.south)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=north] (score12) at ([yshift=-2.0em]s2.south)
{$
\textrm
{
P
}
(
s|t
'
)
$}
;
\node
[anchor=north] (score12) at ([yshift=-2.0em]s2.south)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
'
)
$}
;
\node
[anchor=west] (comp1) at ([xshift=2.3em]score11.east)
{
\large
{$
\mathbf
{
=
}$}}
;
\node
[anchor=west] (comp1) at ([xshift=2.3em]score11.east)
{
\large
{$
\mathbf
{
=
}$}}
;
\node
[anchor=east] (label1) at ([xshift=-1em,yshift=0.1em]score11.west)
{
\textbf
{
IBM模型1:
}}
;
\node
[anchor=east] (label1) at ([xshift=-1em,yshift=0.1em]score11.west)
{
\textbf
{
IBM模型1:
}}
;
\visible
<2->
{
\visible
<2->
{
\node
[anchor=north] (score21) at ([yshift=0.2em]score11.south)
{$
\textrm
{
P
}
(
s|t
)
$}
;
\node
[anchor=north] (score21) at ([yshift=0.2em]score11.south)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=north] (score22) at ([yshift=0.2em]score12.south)
{$
\textrm
{
P
}
(
s|t
'
)
$}
;
\node
[anchor=north] (score22) at ([yshift=0.2em]score12.south)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
'
)
$}
;
\node
[anchor=west] (comp2) at ([xshift=2.3em]score21.east)
{
\large
{$
\mathbf
{
>
}$}}
;
\node
[anchor=west] (comp2) at ([xshift=2.3em]score21.east)
{
\large
{$
\mathbf
{
>
}$}}
;
\node
[anchor=east] (label2) at ([xshift=-1em,yshift=0.1em]score21.west)
{
\textbf
{
理想:
}}
;
\node
[anchor=east] (label2) at ([xshift=-1em,yshift=0.1em]score21.west)
{
\textbf
{
理想:
}}
;
}
}
...
@@ -3064,7 +3064,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3064,7 +3064,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\textrm
{
P
}
(a
_
j|a
_{
1
}^{
j-1
}
,s
_{
1
}^{
j-1
}
,m,t)
\equiv
a(a
_
j|j,m,l)
\textrm
{
P
}
(a
_
j|a
_{
1
}^{
j-1
}
,s
_{
1
}^{
j-1
}
,m,t)
\equiv
a(a
_
j|j,m,l)
\end{displaymath}
\end{displaymath}
其它假设与IBM模型1相同，即
$
\textrm
{
P
}
(
m|
t
)
\equiv
\epsilon
$
和
$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,t
)
\equiv
f
(
s
_
j|t
_{
a
_
j
}
)
$
其它假设与IBM模型1相同，即
$
\textrm
{
P
}
(
m|
\mathbf
{
t
}
)
\equiv
\epsilon
$
和
$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
\equiv
f
(
s
_
j|t
_{
a
_
j
}
)
$
\end{itemize}
\end{itemize}
...
@@ -3083,12 +3083,12 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3083,12 +3083,12 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
s,a|t
)
$}
;
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west] (eq1part2) at (eq1.east)
{$
=
$}
;
\node
[anchor=west] (eq1part2) at (eq1.east)
{$
=
$}
;
\node
[anchor=west,inner sep=1pt] (eq2) at (eq1part2.east)
{$
\textrm
{
P
}
(
m|
t
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq2) at (eq1part2.east)
{$
\textrm
{
P
}
(
m|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq3) at ([xshift=
1
pt]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}$}
;
\node
[anchor=west,inner sep=1pt] (eq3) at ([xshift=
0
pt]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}$}
;
\node
[anchor=west,inner sep=1pt] (eq4) at ([xshift=
1pt]eq3.east)
{$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,t
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq4) at ([xshift=
0pt]eq3.east)
{$
\textrm
{
P
}
(
a
_
j|a
_{
1
}^{
j
-
1
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq5) at ([xshift=
1pt]eq4.east)
{$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,t
)
$}
;
\node
[anchor=west,inner sep=1pt] (eq5) at ([xshift=
0pt]eq4.east)
{$
\textrm
{
P
}
(
s
_
j|a
_{
1
}^{
j
}
,s
_{
1
}^{
j
-
1
}
,m,
\mathbf
{
t
}
)
$}
;
\node
[anchor=east,rotate=90] (yes1) at (eq2.south)
{$
\equiv
$}
;
\node
[anchor=east,rotate=90] (yes1) at (eq2.south)
{$
\equiv
$}
;
\node
[anchor=east,rotate=90] (yes2) at (eq4.south)
{$
\equiv
$}
;
\node
[anchor=east,rotate=90] (yes2) at (eq4.south)
{$
\equiv
$}
;
...
@@ -3104,14 +3104,14 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3104,14 +3104,14 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\end{tikzpicture}
\end{tikzpicture}
\end{center}
\end{center}
\item
<2->
\textbf
{
将上式代入
$
\textrm
{
P
}
(
s|t
)=
\sum
_
a
\textrm
{
P
}
(
s,a|t
)
$}
\item
<2->
\textbf
{
将上式代入
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)=
\sum
_
a
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$}
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
s|t
)
$}
;
\node
[anchor=west] (eq1) at (0,0)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=west] (eq2) at (eq1.east)
{$
=
$}
;
\node
[anchor=west] (eq2) at (eq1.east)
{$
=
$}
;
\node
[anchor=west,inner sep=2pt] (eq3) at (eq2.east)
{$
\sum\limits
_{
a
_
1
=
0
}^{
l
}$}
;
\node
[anchor=west,inner sep=2pt] (eq3) at (eq2.east)
{$
\sum\limits
_{
a
_
1
=
0
}^{
l
}$}
;
\node
[anchor=west,inner sep=0] (eq4) at ([xshift=-0.2em]eq3.east)
{
...
}
;
\node
[anchor=west,inner sep=0] (eq4) at ([xshift=-0.2em]eq3.east)
{
...
}
;
...
@@ -3142,8 +3142,8 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3142,8 +3142,8 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\begin{enumerate}
\begin{enumerate}
\item
遍历所有的的对齐
$
a
$
\item
遍历所有的的对齐
$
\mathbf
{
a
}
$
\item
对于每个
$
a
$
累加对齐概率
$
\textrm
{
P
}
(
s,a|t
)
$
，即计算
$
\epsilon
\prod\limits
_{
j
=
1
}^{
m
}
a
(
a
_
j|j,m,l
)
f
(
s
_
j|t
_{
a
_
j
}
)
$
\item
对于每个
$
\mathbf
{
a
}$
累加对齐概率
$
\textrm
{
P
}
(
\mathbf
{
s
}
,
\mathbf
{
a
}
|
\mathbf
{
t
}
)
$
，即计算
$
\epsilon
\prod\limits
_{
j
=
1
}^{
m
}
a
(
a
_
j|j,m,l
)
f
(
s
_
j|t
_{
a
_
j
}
)
$
\end{enumerate}
\end{enumerate}
\end{itemize}
\end{itemize}
...
@@ -3158,8 +3158,8 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3158,8 +3158,8 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\vspace
{
-1.0em
}
\vspace
{
-1.0em
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
\textbf
{
IBM模型1
}}
:
\textrm
{
P
}
(
s|t
)
&
=
&
\frac
{
\epsilon
}{
(l+1)
^{
m
}}
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}
\prod\limits
_{
j=1
}^{
m
}
f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\\
\textrm
{
\textbf
{
IBM模型1
}}
:
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
&
=
&
\frac
{
\epsilon
}{
(l+1)
^{
m
}}
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}
\prod\limits
_{
j=1
}^{
m
}
f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\\
\textrm
{
\textbf
{
IBM模型2
}}
:
\textrm
{
P
}
(
s|t
)
&
=
&
\epsilon
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}
\prod\limits
_{
j=1
}^{
m
}
a(a
_
j|j,m,l) f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\textrm
{
\textbf
{
IBM模型2
}}
:
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
&
=
&
\epsilon
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}
\prod\limits
_{
j=1
}^{
m
}
a(a
_
j|j,m,l) f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\end{eqnarray}
\end{eqnarray}
\begin{itemize}
\begin{itemize}
...
@@ -3227,17 +3227,17 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3227,17 +3227,17 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\vspace
{
-1.0em
}
\vspace
{
-1.0em
}
\begin{eqnarray}
\begin{eqnarray}
\textrm
{
\textbf
{
IBM模型1
}}
:
\textrm
{
P
}
(
s|t
)
&
=
&
\frac
{
\epsilon
}{
(l+1)
^{
m
}}
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}
\prod\limits
_{
j=1
}^{
m
}
f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\\
\textrm
{
\textbf
{
IBM模型1
}}
:
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
&
=
&
\frac
{
\epsilon
}{
(l+1)
^{
m
}}
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}
\prod\limits
_{
j=1
}^{
m
}
f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\\
\textrm
{
\textbf
{
IBM模型2
}}
:
\textrm
{
P
}
(
s|t
)
&
=
&
\epsilon
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}
\prod\limits
_{
j=1
}^{
m
}
a(a
_
j|j,m,l) f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\textrm
{
\textbf
{
IBM模型2
}}
:
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
&
=
&
\epsilon
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}
\prod\limits
_{
j=1
}^{
m
}
a(a
_
j|j,m,l) f(s
_
j|t
_{
a
_
j
}
)
\nonumber
\end{eqnarray}
\end{eqnarray}
\begin{spacing}
{
1.2
}
\begin{spacing}
{
1.2
}
\begin{itemize}
\begin{itemize}
\item
对于翻译模型
$
\textrm
{
P
}
(
s|t
)
$
，再来回顾一下统计机器翻译的三个基本问题
\item
对于翻译模型
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
，再来回顾一下统计机器翻译的三个基本问题
\begin{enumerate}
\begin{enumerate}
\item
\textbf
{
建模
}
：如何描述
$
\textrm
{
P
}
(
s|t
)
$
\visible
<2->
{
\alert
{$
\gets
$
已解！见上面两个公式
}}
\item
\textbf
{
建模
}
：如何描述
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
\visible
<2->
{
\alert
{$
\gets
$
已解！见上面两个公式
}}
\item
\textbf
{
解码
}
：给定模型参数
$
\epsilon
$
、
$
a
(
a
_
j|j,m,l
)
$
和
$
f
(
s
_
j|t
_{
a
_
j
}
)
$
，如何利用上面的公式计算
$
\textrm
{
P
}
(
s|t
)
$
(语言模型计算暂不讨论)，并找到最佳译文
$
\hat
{
t
}$
\visible
<2->
{
\alert
{$
\gets
$
下面讨论
}}
\item
\textbf
{
解码
}
：给定模型参数
$
\epsilon
$
、
$
a
(
a
_
j|j,m,l
)
$
和
$
f
(
s
_
j|t
_{
a
_
j
}
)
$
，如何利用上面的公式计算
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
(语言模型计算暂不讨论)，并找到最佳译文
$
\hat
{
\mathbf
{
t
}
}$
\visible
<2->
{
\alert
{$
\gets
$
下面讨论
}}
\item
\textbf
{
训练
}
；如何从数据中自动学习模型参数
$
\epsilon
$
、
$
a
(
a
_
j|j,m,l
)
$
和
$
f
(
s
_
j|t
_{
a
_
j
}
)
$
\visible
<2->
{
\alert
{$
\gets
$
下面讨论
}}
\item
\textbf
{
训练
}
；如何从数据中自动学习模型参数
$
\epsilon
$
、
$
a
(
a
_
j|j,m,l
)
$
和
$
f
(
s
_
j|t
_{
a
_
j
}
)
$
\visible
<2->
{
\alert
{$
\gets
$
下面讨论
}}
\end{enumerate}
\end{enumerate}
...
@@ -3281,7 +3281,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3281,7 +3281,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (model) at (0,0)
{
\footnotesize
{$
\textrm
{
P
}
(
s|t
)
=
\epsilon
\sum\limits
_{
a
_
1
=
0
}^{
l
}
...
\sum\limits
_{
a
_
m
=
0
}^{
l
}
\prod\limits
_{
j
=
1
}^{
m
}
a
(
a
_
j|j,m,l
)
f
(
s
_
j|t
_{
a
_
j
}
)
$}}
;
\node
[anchor=west] (model) at (0,0)
{
\footnotesize
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
=
\epsilon
\sum\limits
_{
a
_
1
=
0
}^{
l
}
...
\sum\limits
_{
a
_
m
=
0
}^{
l
}
\prod\limits
_{
j
=
1
}^{
m
}
a
(
a
_
j|j,m,l
)
f
(
s
_
j|t
_{
a
_
j
}
)
$}}
;
\node
[anchor=east] (modellabel) at ([yshift=0.1em]model.west)
{
\footnotesize
{
\textbf
{
问题的统计描述:
}}}
;
\node
[anchor=east] (modellabel) at ([yshift=0.1em]model.west)
{
\footnotesize
{
\textbf
{
问题的统计描述:
}}}
;
\node
[anchor=north west] (paras) at (model.south west)
{
\footnotesize
{$
\epsilon
=
?;
\ \ \forall
a
_
j,j,m,l: a
(
a
_
j|j,m,l
)
=
?, f
(
s
_
j|t
_{
a
_
j
}
)
=
?
$}}
;
\node
[anchor=north west] (paras) at (model.south west)
{
\footnotesize
{$
\epsilon
=
?;
\ \ \forall
a
_
j,j,m,l: a
(
a
_
j|j,m,l
)
=
?, f
(
s
_
j|t
_{
a
_
j
}
)
=
?
$}}
;
\node
[anchor=east] (paraslabel) at ([yshift=0.1em]paras.west)
{
\footnotesize
{
\textbf
{
模型的参数:
}}}
;
\node
[anchor=east] (paraslabel) at ([yshift=0.1em]paras.west)
{
\footnotesize
{
\textbf
{
模型的参数:
}}}
;
...
@@ -3300,9 +3300,9 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3300,9 +3300,9 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (scoring) at (0,0)
{
\footnotesize
{
对任意的
$
s
$
和
$
t
$
，(高效地)计算
$
\textrm
{
P
}
(
s|t
)
$
(同时计算
$
\textrm
{
P
}
(
t
)
$
)
}}
;
\node
[anchor=west] (scoring) at (0,0)
{
\footnotesize
{
对任意的
$
\mathbf
{
s
}$
和
$
\mathbf
{
t
}$
，(高效地)计算
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
(同时计算
$
\textrm
{
P
}
(
\mathbf
{
t
}
)
$
)
}}
;
\node
[anchor=east] (scoringlabel) at ([yshift=0.1em]scoring.west)
{
\footnotesize
{
\textbf
{
模型得分计算:
}}}
;
\node
[anchor=east] (scoringlabel) at ([yshift=0.1em]scoring.west)
{
\footnotesize
{
\textbf
{
模型得分计算:
}}}
;
\node
[anchor=north west] (search) at (scoring.south west)
{
\footnotesize
{
对所有可能的
$
t
$
，找到模型得分(
$
\textrm
{
P
}
(
s|t
)
\textrm
{
P
}
(
t
)
$
)最高
}}
;
\node
[anchor=north west] (search) at (scoring.south west)
{
\footnotesize
{
对所有可能的
$
\mathbf
{
t
}$
，找到模型得分(
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
\textrm
{
P
}
(
\mathbf
{
t
}
)
$
)最高
}}
;
\node
[anchor=north west] (searchpart2) at ([yshift=0.3em]search.south west)
{
\footnotesize
{
的译文输出
}}
;
\node
[anchor=north west] (searchpart2) at ([yshift=0.3em]search.south west)
{
\footnotesize
{
的译文输出
}}
;
\node
[anchor=east] (searchlabel) at ([yshift=0.1em]search.west)
{
\footnotesize
{
\textbf
{
搜索:
}}}
;
\node
[anchor=east] (searchlabel) at ([yshift=0.1em]search.west)
{
\footnotesize
{
\textbf
{
搜索:
}}}
;
...
@@ -3317,7 +3317,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3317,7 +3317,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{itemize}
\begin{itemize}
\item
\textbf
{
搜索(解码)问题
}
前面的实例已经描述了一种解法（见
{
\color
{
ublue
}
\hyperref
[simpledecodingalgorithm]
{
第
\hspace
{
-0.2em
}
~
\ref
{
simpledecodingalgorithm
}
页
}}
）：自左向右添加译文单词 + 剪枝技术。这里不再讨论，可以自行学习
\item
\textbf
{
搜索(解码)问题
}
前面的实例已经描述了一种解法（见
{
\color
{
ublue
}
\hyperref
[simpledecodingalgorithm]
{
第
\hspace
{
-0.2em
}
~
\ref
{
simpledecodingalgorithm
}
页
}}
）：自左向右添加译文单词 + 剪枝技术。这里不再讨论，可以自行学习
\item
\textbf
{
剩下的问题是
}
：对于任意的
$
s
$
和
$
t
$
，如何
\alert
{
高效地
}
计算
$
\textrm
{
P
}
(
s|t
)
$
\item
\textbf
{
剩下的问题是
}
：对于任意的
$
\mathbf
{
s
}$
和
$
\mathbf
{
t
}$
，如何
\alert
{
高效地
}
计算
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}
...
@@ -3333,7 +3333,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3333,7 +3333,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\item
$
O
((
l
+
1
)
^
m
\cdot
m
)
$
- IBM模型得分的直接计算几乎不可能！
\item
$
O
((
l
+
1
)
^
m
\cdot
m
)
$
- IBM模型得分的直接计算几乎不可能！
\begin{displaymath}
\begin{displaymath}
\textrm
{
P
}
(
s|t
) =
\frac
{
\epsilon
}{
(l+1)
^{
m
}}
\underbrace
{
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}}_{
(l+1)
^
m
\textrm
{
次循环
}}
\underbrace
{
\prod\limits
_{
j=1
}^{
m
}
f(s
_
j|t
_{
a
_
j
}
)
}_{
m
\textrm
{
次循环
}}
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
) =
\frac
{
\epsilon
}{
(l+1)
^{
m
}}
\underbrace
{
\sum\limits
_{
a
_
1=0
}^{
l
}
...
\sum\limits
_{
a
_
m=0
}^{
l
}}_{
(l+1)
^
m
\textrm
{
次循环
}}
\underbrace
{
\prod\limits
_{
j=1
}^{
m
}
f(s
_
j|t
_{
a
_
j
}
)
}_{
m
\textrm
{
次循环
}}
\end{displaymath}
\end{displaymath}
\item
<2->
$
O
(
l
\cdot
m
)
$
- 实际上我们可以做的更好
\item
<2->
$
O
(
l
\cdot
m
)
$
- 实际上我们可以做的更好
...
@@ -3355,7 +3355,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3355,7 +3355,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
}
}
\visible
<3->
{
\visible
<3->
{
\node
[anchor=west] (eq2) at ([xshift=5em,yshift=-4.5em]eq1.west)
{$
\textrm
{
P
}
(
s|t
)
=
\frac
{
\epsilon
}{
(
l
+
1
)
^{
m
}}
$}
;
\node
[anchor=west] (eq2) at ([xshift=5em,yshift=-4.5em]eq1.west)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
=
\frac
{
\epsilon
}{
(
l
+
1
)
^{
m
}}
$}
;
\node
[anchor=west,inner sep=2pt] (eq2part2) at ([xshift=-0.3em]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}
\sum\limits
_{
i
=
0
}^{
l
}
f
(
s
_
j|t
_
i
)
$}
;
\node
[anchor=west,inner sep=2pt] (eq2part2) at ([xshift=-0.3em]eq2.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}
\sum\limits
_{
i
=
0
}^{
l
}
f
(
s
_
j|t
_
i
)
$}
;
\node
[anchor=east] (eq2label) at ([xshift=-0em,yshift=0.2em]eq2.west)
{
\small
{
IBM模型1:
}}
;
\node
[anchor=east] (eq2label) at ([xshift=-0em,yshift=0.2em]eq2.west)
{
\small
{
IBM模型1:
}}
;
...
@@ -3363,7 +3363,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3363,7 +3363,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
}
}
\visible
<4->
{
\visible
<4->
{
\node
[anchor=west] (eq3) at ([xshift=5em,yshift=-7.5em]eq1.west)
{$
\textrm
{
P
}
(
s|t
)
=
\epsilon
$}
;
\node
[anchor=west] (eq3) at ([xshift=5em,yshift=-7.5em]eq1.west)
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
=
\epsilon
$}
;
\node
[anchor=west,inner sep=2pt] (eq3part2) at ([xshift=-0.3em]eq3.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}
\sum\limits
_{
i
=
0
}^{
l
}
a
(
i|j,m,l
)
f
(
s
_
j|t
_
i
)
$}
;
\node
[anchor=west,inner sep=2pt] (eq3part2) at ([xshift=-0.3em]eq3.east)
{$
\prod\limits
_{
j
=
1
}^{
m
}
\sum\limits
_{
i
=
0
}^{
l
}
a
(
i|j,m,l
)
f
(
s
_
j|t
_
i
)
$}
;
\node
[anchor=east] (eq3label) at ([xshift=-0em,yshift=0.2em]eq3.west)
{
\small
{
类似的，IBM模型2:
}}
;
\node
[anchor=east] (eq3label) at ([xshift=-0em,yshift=0.2em]eq3.west)
{
\small
{
类似的，IBM模型2:
}}
;
}
}
...
@@ -3525,7 +3525,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3525,7 +3525,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{itemize}
\begin{itemize}
\item
<2->
\textbf
{
IBM模型的训练：对于给定的句对
$
(
s,t
)
$
，最大化翻译概率
$
\textrm
{
P
}
(
s|t
)
$}
。这里用符号
$
\textrm
{
P
}_{
\theta
}
(
s|t
)
$
表示概率由参数
$
\theta
$
决定
\item
<2->
\textbf
{
IBM模型的训练：对于给定的句对
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
，最大化翻译概率
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
。这里用符号
$
\textrm
{
P
}_{
\theta
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
表示概率由参数
$
\theta
$
决定
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
...
@@ -3534,11 +3534,11 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3534,11 +3534,11 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\node
[anchor=west] (eq2) at ([yshift=-0.2em]eq1.east)
{
=
}
;
\node
[anchor=west] (eq2) at ([yshift=-0.2em]eq1.east)
{
=
}
;
\node
[anchor=west,inner sep=2pt] (eq3) at ([yshift=-0.0em]eq2.east)
{$
\argmax
$}
;
\node
[anchor=west,inner sep=2pt] (eq3) at ([yshift=-0.0em]eq2.east)
{$
\argmax
$}
;
\node
[anchor=north,inner sep=1pt] (eq3part2) at ([yshift=-0.2em]eq3.south)
{
\scriptsize
{$
\theta
$}}
;
\node
[anchor=north,inner sep=1pt] (eq3part2) at ([yshift=-0.2em]eq3.south)
{
\scriptsize
{$
\theta
$}}
;
\node
[anchor=west,inner sep=2pt] (eq4) at ([xshift=0.1em]eq3.east)
{$
\textrm
{
P
}_{
\theta
}
(
s|t
)
$}
;
\node
[anchor=west,inner sep=2pt] (eq4) at ([xshift=0.1em]eq3.east)
{$
\textrm
{
P
}_{
\theta
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\visible
<3->
{
\visible
<3->
{
\node
[anchor=west,inner sep=2pt,fill=red!20,minimum height=1.35em] (eq3) at ([yshift=-0.0em]eq2.east)
{$
\argmax
$}
;
\node
[anchor=west,inner sep=2pt,fill=red!20,minimum height=1.35em] (eq3) at ([yshift=-0.0em]eq2.east)
{$
\argmax
$}
;
\node
[anchor=west,inner sep=2pt,fill=green!20] (eq4) at ([xshift=0.1em]eq3.east)
{$
\textrm
{
P
}_{
\theta
}
(
s|t
)
$}
;
\node
[anchor=west,inner sep=2pt,fill=green!20] (eq4) at ([xshift=0.1em]eq3.east)
{$
\textrm
{
P
}_{
\theta
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
;
\node
[anchor=north,draw,inner sep=3pt,fill=red!20] (eq3label) at ([yshift=-1.5em]eq3.south west)
{
\footnotesize
{
\textbf
{
求最优参数
}}}
;
\node
[anchor=north,draw,inner sep=3pt,fill=red!20] (eq3label) at ([yshift=-1.5em]eq3.south west)
{
\footnotesize
{
\textbf
{
求最优参数
}}}
;
\node
[anchor=north,draw,inner sep=3pt,fill=green!20] (eq4label) at ([yshift=-1.5em]eq4.south east)
{
\footnotesize
{
\textbf
{
目标函数
}}}
;
\node
[anchor=north,draw,inner sep=3pt,fill=green!20] (eq4label) at ([yshift=-1.5em]eq4.south east)
{
\footnotesize
{
\textbf
{
目标函数
}}}
;
...
@@ -3561,23 +3561,23 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3561,23 +3561,23 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{itemize}
\begin{itemize}
\item
$
\textrm
{
P
}
(
s|t
)
$
可以被看做是
$
(
s,t
)
$
上的
\alert
{
似然
}
函数(
$
L
(
s,t;
\theta
)
$
)。所谓
\alert
{
极大似然估计
}
，就是要找到使
$
L
(
s,t
;
\theta
)
$
达到最大的
$
\theta
$
：
\item
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
可以被看做是
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
上的
\alert
{
似然
}
函数(
$
L
(
\mathbf
{
s
}
,
\mathbf
{
t
}
;
\theta
)
$
)。所谓
\alert
{
极大似然估计
}
，就是要找到使
$
L
(
\mathbf
{
s
}
,
\mathbf
{
t
}
;
\theta
)
$
达到最大的
$
\theta
$
：
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\begin{displaymath}
\begin{displaymath}
\{\hat
{
\theta
}
\}
\subseteq
\{\argmax
_{
\theta
\in
\Theta
}
L(
s,t
;
\theta
)
\}
\{\hat
{
\theta
}
\}
\subseteq
\{\argmax
_{
\theta
\in
\Theta
}
L(
\mathbf
{
s
}
,
\mathbf
{
t
}
;
\theta
)
\}
\end{displaymath}
\end{displaymath}
\vspace
{
-0.3em
}
\vspace
{
-0.3em
}
$
L
(
s,t
;
\theta
)
$
表示
$
L
(
\cdot
)
$
依赖模型参数
$
\theta
$
（注意分号），
$
\{\hat
{
\theta
}
\}
$
表示可能有多组结果，
$
\Theta
$
表示参数空间
$
L
(
\mathbf
{
s
}
,
\mathbf
{
t
}
;
\theta
)
$
表示
$
L
(
\cdot
)
$
依赖模型参数
$
\theta
$
（注意分号），
$
\{\hat
{
\theta
}
\}
$
表示可能有多组结果，
$
\Theta
$
表示参数空间
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\item
<2-> 先不用考虑上面的公式。我们还是回归到原始问题：如何找到一组
$
\theta
$
使
$
\textrm
{
P
}_{
\theta
}
(
s|t
)
$
达到最大？
\\
\item
<2-> 先不用考虑上面的公式。我们还是回归到原始问题：如何找到一组
$
\theta
$
使
$
\textrm
{
P
}_{
\theta
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
达到最大？
\\
\begin{itemize}
\begin{itemize}
\item
\textbf
{
求函数最大值问题
}
。比如，我们可以对
$
\textrm
{
P
}_{
\theta
}
(
s|t
)
$
求导，令导数为零，得到极值点
\item
\textbf
{
求函数最大值问题
}
。比如，我们可以对
$
\textrm
{
P
}_{
\theta
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
求导，令导数为零，得到极值点
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}
...
@@ -3641,7 +3641,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3641,7 +3641,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% maximizing P(s|t)
%%% maximizing P(s|t)
\begin{frame}
{
最大化
$
\textrm
{
P
}
(
s|t
)
$}
\begin{frame}
{
最大化
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}
\begin{itemize}
\begin{itemize}
...
@@ -3710,7 +3710,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3710,7 +3710,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{itemize}
\begin{itemize}
\item
\textbf
{
含有约束的优化问题
}
: 不好解
\\
\item
\textbf
{
含有约束的优化问题
}
: 不好解
\\
\textbf
{
目标:
}
$
\max
(
\textrm
{
P
}_{
\theta
}
(
s|t
))
$
+
\textbf
{
约束:
}
$
\forall
t
_
y:
\sum
_{
s
_
x
}
\textrm
{
P
}
(
s
_
x|t
_
y
)=
1
$
\textbf
{
目标:
}
$
\max
(
\textrm
{
P
}_{
\theta
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
))
$
+
\textbf
{
约束:
}
$
\forall
t
_
y:
\sum
_{
s
_
x
}
\textrm
{
P
}
(
s
_
x|t
_
y
)=
1
$
\vspace
{
0.3em
}
\vspace
{
0.3em
}
\item
<2->
\textbf
{
解决方法
}
: 含有约束优化
$
\Rightarrow
$
不含约束优化
\\
\item
<2->
\textbf
{
解决方法
}
: 含有约束优化
$
\Rightarrow
$
不含约束优化
\\
...
@@ -3746,7 +3746,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
...
@@ -3746,7 +3746,7 @@ $s$ = 在 桌子 上 \ \ \ \ \ $t$ = $t_0$ on the table \ \ \ \ \ $a$ = \{1-0,2-3,3-
\begin{center}
\begin{center}
\begin{tabular}
{
c | c
}
\begin{tabular}
{
c | c
}
\makebox
[0.35\textwidth][c]
{
\textbf
{
原始问题
}}
&
\makebox
[0.35\textwidth][c]
{
\textbf
{
转化后的问题
}}
\\
\hline
\makebox
[0.35\textwidth][c]
{
\textbf
{
原始问题
}}
&
\makebox
[0.35\textwidth][c]
{
\textbf
{
转化后的问题
}}
\\
\hline
$
\max
(
\textrm
{
P
}
(
s|t
))
$
&
$
\max
(
L
(
f,
\lambda
))
$
\\
$
\max
(
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
))
$
&
$
\max
(
L
(
f,
\lambda
))
$
\\
s.t.
$
\forall
t
_
y:
\sum
_{
s
_
x
}
f
(
s
_
x|t
_
y
)
=
1
$
&
\\
s.t.
$
\forall
t
_
y:
\sum
_{
s
_
x
}
f
(
s
_
x|t
_
y
)
=
1
$
&
\\
\end{tabular}
\end{tabular}
\end{center}
\end{center}
...
@@ -4022,11 +4022,11 @@ f(s_u|t_v) = \frac{\lambda_{t_v}^{-1} \epsilon}{(l+1)^{m}} \cdot \frac{\sum\limi
...
@@ -4022,11 +4022,11 @@ f(s_u|t_v) = \frac{\lambda_{t_v}^{-1} \epsilon}{(l+1)^{m}} \cdot \frac{\sum\limi
}
}
\visible
<2->
{
\visible
<2->
{
\node
[anchor=south west,inner sep=2pt] (label1) at (eq4.north west)
{
\textbf
{
\scriptsize
{
翻译概率
$
\textrm
{
P
}
(
s|t
)
$}}}
;
\node
[anchor=south west,inner sep=2pt] (label1) at (eq4.north west)
{
\textbf
{
\scriptsize
{
翻译概率
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}}}
;
}
}
\visible
<3->
{
\visible
<3->
{
\node
[anchor=south west,inner sep=2pt] (label2) at (eq5.north west)
{
\textbf
{
\scriptsize
{
配对的总次数
}}}
;
\node
[anchor=south west,inner sep=2pt] (label2) at (eq5.north west)
{
\textbf
{
\scriptsize
{
配对的总次数
}}}
;
\node
[anchor=south west,inner sep=2pt] (label2part2) at ([yshift=-3pt]label2.north west)
{
\textbf
{
\scriptsize
{$
(
s
_
u,t
_
v
)
$
在句对
$
(
s,t
)
$
中
}}}
;
\node
[anchor=south west,inner sep=2pt] (label2part2) at ([yshift=-3pt]label2.north west)
{
\textbf
{
\scriptsize
{$
(
s
_
u,t
_
v
)
$
在句对
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
中
}}}
;
}
}
\visible
<4->
{
\visible
<4->
{
\node
[anchor=south west,inner sep=2pt] (label3) at (eq6.north west)
{
\textbf
{
\scriptsize
{
有的
$
t
_
i
$
的相对值
}}}
;
\node
[anchor=south west,inner sep=2pt] (label3) at (eq6.north west)
{
\textbf
{
\scriptsize
{
有的
$
t
_
i
$
的相对值
}}}
;
...
@@ -4035,7 +4035,7 @@ f(s_u|t_v) = \frac{\lambda_{t_v}^{-1} \epsilon}{(l+1)^{m}} \cdot \frac{\sum\limi
...
@@ -4035,7 +4035,7 @@ f(s_u|t_v) = \frac{\lambda_{t_v}^{-1} \epsilon}{(l+1)^{m}} \cdot \frac{\sum\limi
\visible
<2->
{
\visible
<2->
{
\node
[anchor=east,rotate=90] (neweq1) at ([yshift=-0em]eq4.south)
{
=
}
;
\node
[anchor=east,rotate=90] (neweq1) at ([yshift=-0em]eq4.south)
{
=
}
;
\node
[anchor=north,inner sep=1pt] (neweq1full) at (neweq1.west)
{
\large
{$
\textrm
{
P
}
(
s|t
)
$}}
;
\node
[anchor=north,inner sep=1pt] (neweq1full) at (neweq1.west)
{
\large
{$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$}}
;
}
}
\visible
<5->
{
\visible
<5->
{
...
@@ -4123,16 +4123,16 @@ $x_3$ & 5 & 0.2 & 1.0 \\ \hline
...
@@ -4123,16 +4123,16 @@ $x_3$ & 5 & 0.2 & 1.0 \\ \hline
\end{center}
\end{center}
\begin{itemize}
\begin{itemize}
\item
<5->
\textbf
{
定义
}
：在
$
\textrm
{
P
}
(
s|t
)
$
中，
$
t
_
v
$
翻译(连接)到
$
s
_
u
$
的期望频次为
\item
<5->
\textbf
{
定义
}
：在
$
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
$
中，
$
t
_
v
$
翻译(连接)到
$
s
_
u
$
的期望频次为
\vspace
{
-0.5em
}
\vspace
{
-0.5em
}
\begin{displaymath}
\begin{displaymath}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
s,t
)
\equiv
\sum\limits
_{
j=1
}^{
m
}
\delta
(s
_
j,s
_
u)
\sum\limits
_{
i=0
}^{
l
}
\delta
(t
_
i,t
_
v)
\cdot
\frac
{
f(s
_
u|t
_
v)
}{
\sum
_{
i=0
}^{
l
}
f(s
_
u|t
_
i)
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
\equiv
\sum\limits
_{
j=1
}^{
m
}
\delta
(s
_
j,s
_
u)
\sum\limits
_{
i=0
}^{
l
}
\delta
(t
_
i,t
_
v)
\cdot
\frac
{
f(s
_
u|t
_
v)
}{
\sum
_{
i=0
}^{
l
}
f(s
_
u|t
_
i)
}
\end{displaymath}
\end{displaymath}
\vspace
{
-0.8em
}
\vspace
{
-0.8em
}
\item
<6->
\textbf
{
重写
$
f
(
s
_
u|t
_
v
)
$}
!!!
\item
<6->
\textbf
{
重写
$
f
(
s
_
u|t
_
v
)
$}
!!!
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west,draw,red,thick,inner sep=5pt] (p) at (0,0)
{
\black
{$
f
(
s
_
u|t
_
v
)
=
\lambda
_{
t
_
v
}^{
-
1
}
\cdot
\textrm
{
P
}
(
s|t
)
\cdot
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;s,t
)
$}}
;
\node
[anchor=west,draw,red,thick,inner sep=5pt] (p) at (0,0)
{
\black
{$
f
(
s
_
u|t
_
v
)
=
\lambda
_{
t
_
v
}^{
-
1
}
\cdot
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
\cdot
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$}}
;
\end{tikzpicture}
\end{tikzpicture}
\end{center}
\end{center}
\end{itemize}
\end{itemize}
...
@@ -4144,13 +4144,13 @@ $x_3$ & 5 & 0.2 & 1.0 \\ \hline
...
@@ -4144,13 +4144,13 @@ $x_3$ & 5 & 0.2 & 1.0 \\ \hline
\begin{frame}
{
通过期望频次计算
$
f
(
s
_
u|t
_
v
)
$}
\begin{frame}
{
通过期望频次计算
$
f
(
s
_
u|t
_
v
)
$}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
一个小trick
}
: 令
$
\lambda
_{
t
_
v
}^{
'
}
=
\frac
{
\lambda
_{
t
_
v
}}{
\textrm
{
P
}
(
s|t
)
}$
\item
\textbf
{
一个小trick
}
: 令
$
\lambda
_{
t
_
v
}^{
'
}
=
\frac
{
\lambda
_{
t
_
v
}}{
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
}$
\vspace
{
-1.0em
}
\vspace
{
-1.0em
}
\begin{eqnarray}
\begin{eqnarray}
f(s
_
u|t
_
v)
&
=
&
\lambda
_{
t
_
v
}^{
-1
}
\cdot
\textrm
{
P
}
(
s|t)
\cdot
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;s,t
)
\nonumber
\\
f(s
_
u|t
_
v)
&
=
&
\lambda
_{
t
_
v
}^{
-1
}
\cdot
\textrm
{
P
}
(
\mathbf
{
s
}
|
\mathbf
{
t
}
)
\cdot
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
\nonumber
\\
&
=
&
(
\lambda
_{
t
_
v
}^{
'
}
)
^{
-1
}
\cdot
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
s,t
)
\nonumber
&
=
&
(
\lambda
_{
t
_
v
}^{
'
}
)
^{
-1
}
\cdot
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
\nonumber
\end{eqnarray}
\end{eqnarray}
\item
<2->
\textbf
{$
\lambda
_{
t
_
v
}^{
'
}$
究竟是什么？
}
- 回忆一下IBM模型对
$
f
(
\cdot
|
\cdot
)
$
的约束
\item
<2->
\textbf
{$
\lambda
_{
t
_
v
}^{
'
}$
究竟是什么？
}
- 回忆一下IBM模型对
$
f
(
\cdot
|
\cdot
)
$
的约束
...
@@ -4163,7 +4163,7 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
...
@@ -4163,7 +4163,7 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
\vspace
{
-0.3em
}
\vspace
{
-0.3em
}
\begin{displaymath}
\begin{displaymath}
\lambda
_{
t
_
v
}^{
'
}
=
\sum
_{
s
_
u
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
s,t
)
\lambda
_{
t
_
v
}^{
'
}
=
\sum
_{
s
_
u
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
\end{displaymath}
\end{displaymath}
\vspace
{
-0.6em
}
\vspace
{
-0.6em
}
...
@@ -4173,8 +4173,8 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
...
@@ -4173,8 +4173,8 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
\begin{tikzpicture}
\begin{tikzpicture}
\node
[anchor=west] (eq1) at (0,0)
{$
f
(
s
_
u|t
_
v
)
=
$}
;
\node
[anchor=west] (eq1) at (0,0)
{$
f
(
s
_
u|t
_
v
)
=
$}
;
\draw
[-] (eq1.east) -- ([xshift=8em]eq1.east);
\draw
[-] (eq1.east) -- ([xshift=8em]eq1.east);
\node
[anchor=south west] (eq2) at ([xshift=1em]eq1.east)
{$
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
s,t
)
$}
;
\node
[anchor=south west] (eq2) at ([xshift=1em]eq1.east)
{$
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$}
;
\node
[anchor=north west] (eq3) at (eq1.east)
{$
\sum
_{
s
_
u
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
s,t
)
$}
;
\node
[anchor=north west] (eq3) at (eq1.east)
{$
\sum
_{
s
_
u
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$}
;
\begin{pgfonlayer}
{
background
}
\begin{pgfonlayer}
{
background
}
\node
[rectangle,draw,red,thick,inner sep=0]
[fit = (eq1) (eq2) (eq3)]
{}
;
\node
[rectangle,draw,red,thick,inner sep=0]
[fit = (eq1) (eq2) (eq3)]
{}
;
...
@@ -4190,9 +4190,9 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
...
@@ -4190,9 +4190,9 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
%%% scale it up to the full corpus
%%% scale it up to the full corpus
\begin{frame}
{
在整个数据集上计算
}
\begin{frame}
{
在整个数据集上计算
}
\begin{itemize}
\begin{itemize}
\item
\textbf
{
更真实的情况
}
：我们拥有一系列互译的句对（称作
\alert
{
平行语料
}
），记为
$
\{
(
s
^{
[
1
]
}
,t
^{
[
1
]
}
)
,
(
s
^{
[
2
]
}
,t
^{
[
2
]
}
)
,...,
(
s
^{
[
N
]
}
,t
^{
[
N
]
}
)
\}
$
。对于这
$
N
$
个训练用句对，定义
$
f
(
s
_
u|t
_
v
)
$
的期望频次为
\item
\textbf
{
更真实的情况
}
：我们拥有一系列互译的句对（称作
\alert
{
平行语料
}
），记为
$
\{
(
\mathbf
{
s
}^{
[
1
]
}
,
\mathbf
{
t
}^{
[
1
]
}
)
,
(
\mathbf
{
s
}^{
[
2
]
}
,
\mathbf
{
t
}^{
[
2
]
}
)
,...,
(
\mathbf
{
s
}^{
[
N
]
}
,
\mathbf
{
t
}
^{
[
N
]
}
)
\}
$
。对于这
$
N
$
个训练用句对，定义
$
f
(
s
_
u|t
_
v
)
$
的期望频次为
\begin{displaymath}
\begin{displaymath}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v) =
\sum
_{
i=1
}^{
N
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
s
^{
[i]
}
,t
^{
[i]
}
)
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v) =
\sum
_{
i=1
}^{
N
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
\mathbf
{
s
}^{
[i]
}
,
\mathbf
{
t
}
^{
[i]
}
)
\end{displaymath}
\end{displaymath}
\item
<2->
\textbf
{
于是
}
\item
<2->
\textbf
{
于是
}
\begin{center}
\begin{center}
...
@@ -4200,8 +4200,8 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
...
@@ -4200,8 +4200,8 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
\node
[anchor=west,inner sep=2pt] (eq1) at (0,0)
{$
f
(
s
_
u|t
_
v
)
$}
;
\node
[anchor=west,inner sep=2pt] (eq1) at (0,0)
{$
f
(
s
_
u|t
_
v
)
$}
;
\node
[anchor=west] (eq2) at (eq1.east)
{$
=
$
\
}
;
\node
[anchor=west] (eq2) at (eq1.east)
{$
=
$
\
}
;
\draw
[-] ([xshift=0.3em]eq2.east) -- ([xshift=11.6em]eq2.east);
\draw
[-] ([xshift=0.3em]eq2.east) -- ([xshift=11.6em]eq2.east);
\node
[anchor=south west] (eq3) at ([xshift=1em]eq2.east)
{$
\sum
_{
i
=
1
}^{
N
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
s
^{
[
i
]
}
,t
^{
[
i
]
}
)
$}
;
\node
[anchor=south west] (eq3) at ([xshift=1em]eq2.east)
{$
\sum
_{
i
=
1
}^{
N
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
\mathbf
{
s
}^{
[
i
]
}
,
\mathbf
{
t
}
^{
[
i
]
}
)
$}
;
\node
[anchor=north west] (eq4) at (eq2.east)
{$
\sum
_{
s
_
u
}
\sum
_{
i
=
1
}^{
N
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
s
^{
[
i
]
}
,t
^{
[
i
]
}
)
$}
;
\node
[anchor=north west] (eq4) at (eq2.east)
{$
\sum
_{
s
_
u
}
\sum
_{
i
=
1
}^{
N
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
\mathbf
{
s
}^{
[
i
]
}
,
\mathbf
{
t
}
^{
[
i
]
}
)
$}
;
\visible
<4->
{
\visible
<4->
{
\node
[anchor=south] (label1) at ([yshift=-6em,xshift=3em]eq1.north west)
{
利用这个公式计算
}
;
\node
[anchor=south] (label1) at ([yshift=-6em,xshift=3em]eq1.north west)
{
利用这个公式计算
}
;
...
@@ -4250,17 +4250,17 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
...
@@ -4250,17 +4250,17 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
\label
{
ibmtraining
}
\label
{
ibmtraining
}
\begin{beamerboxesrounded}
[upper=uppercolblue,lower=lowercolblue,shadow=true]
{
IBM模型1的训练（EM算法）
}
\begin{beamerboxesrounded}
[upper=uppercolblue,lower=lowercolblue,shadow=true]
{
IBM模型1的训练（EM算法）
}
输入: 平行语料
$
\{
(
s
^{
[
1
]
}
,t
^{
[
1
]
}
)
,...,
(
s
^{
[
N
]
}
,t
^{
[
N
]
}
)
\}
$
\\
输入: 平行语料
$
\{
(
\mathbf
{
s
}^{
[
1
]
}
,
\mathbf
{
t
}^{
[
1
]
}
)
,...,
(
\mathbf
{
s
}^{
[
N
]
}
,
\mathbf
{
t
}
^{
[
N
]
}
)
\}
$
\\
输出：参数
$
f
(
\cdot
|
\cdot
)
$
的最优值
\\
输出：参数
$
f
(
\cdot
|
\cdot
)
$
的最优值
\\
1:
\textbf
{
Function
}
\textsc
{
TrainItWithEM
}
(
$
\{
(
s
^{
[
1
]
}
,t
^{
[
1
]
}
)
,...,
(
s
^{
[
N
]
}
,t
^{
[
N
]
}
)
\}
$
)
\\
1:
\textbf
{
Function
}
\textsc
{
TrainItWithEM
}
(
$
\{
(
\mathbf
{
s
}^{
[
1
]
}
,
\mathbf
{
t
}^{
[
1
]
}
)
,...,
(
\mathbf
{
s
}^{
[
N
]
}
,
\mathbf
{
t
}
^{
[
N
]
}
)
\}
$
)
\\
2:
\ \
Initialize
$
f
(
\cdot
|
\cdot
)
$
\hspace
{
5em
}
$
\rhd
$
比如给
$
f
(
\cdot
|
\cdot
)
$
一个均匀分布
\\
2:
\ \
Initialize
$
f
(
\cdot
|
\cdot
)
$
\hspace
{
5em
}
$
\rhd
$
比如给
$
f
(
\cdot
|
\cdot
)
$
一个均匀分布
\\
3:
\ \
Loop until
$
f
(
\cdot
|
\cdot
)
$
converges
\\
3:
\ \
Loop until
$
f
(
\cdot
|
\cdot
)
$
converges
\\
4:
\ \ \ \ \textbf
{
foreach
}
$
k
=
1
$
to
$
N
$
\textbf
{
do
}
\\
4:
\ \ \ \ \textbf
{
foreach
}
$
k
=
1
$
to
$
N
$
\textbf
{
do
}
\\
5:
\ \ \ \ \ \ \ \footnotesize
{$
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
s
^{
[
k
]
}
,t
^{
[
k
]
}
)
=
\sum\limits
_{
j
=
1
}^{
|s
^{
[
k
]
}
|
}
\delta
(
s
_
j,s
_
u
)
\sum\limits
_{
i
=
0
}^{
|t
^{
[
k
]
}
|
}
\delta
(
t
_
i,t
_
v
)
\cdot
\frac
{
f
(
s
_
u|t
_
v
)
}{
\sum
_{
i
=
0
}^{
l
}
f
(
s
_
u|t
_
i
)
}$}
\normalsize
{}
\\
5:
\ \ \ \ \ \ \ \footnotesize
{$
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
\mathbf
{
s
}^{
[
k
]
}
,
\mathbf
{
t
}^{
[
k
]
}
)
=
\sum\limits
_{
j
=
1
}^{
|
\mathbf
{
s
}^{
[
k
]
}
|
}
\delta
(
s
_
j,s
_
u
)
\sum\limits
_{
i
=
0
}^{
|
\mathbf
{
t
}
^{
[
k
]
}
|
}
\delta
(
t
_
i,t
_
v
)
\cdot
\frac
{
f
(
s
_
u|t
_
v
)
}{
\sum
_{
i
=
0
}^{
l
}
f
(
s
_
u|t
_
i
)
}$}
\normalsize
{}
\\
6:
\ \ \ \ \textbf
{
foreach
}
$
t
_
v
$
appears at least one of
$
\{
t
^{
[
1
]
}
,...,t
^{
[
N
]
}
\}
$
\textbf
{
do
}
\\
6:
\ \ \ \ \textbf
{
foreach
}
$
t
_
v
$
appears at least one of
$
\{
\mathbf
{
t
}^{
[
1
]
}
,...,
\mathbf
{
t
}
^{
[
N
]
}
\}
$
\textbf
{
do
}
\\
7:
\ \ \ \ \ \ \
$
\lambda
_{
t
_
v
}^{
'
}
=
\sum
_{
s
_
u
}
\sum
_{
k
=
1
}^{
N
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
s
^{
[
k
]
}
,t
^{
[
k
]
}
)
$
\\
7:
\ \ \ \ \ \ \
$
\lambda
_{
t
_
v
}^{
'
}
=
\sum
_{
s
_
u
}
\sum
_{
k
=
1
}^{
N
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
\mathbf
{
s
}^{
[
k
]
}
,
\mathbf
{
t
}
^{
[
k
]
}
)
$
\\
8:
\ \ \ \ \ \ \ \textbf
{
foreach
}
$
s
_
u
$
appears at least one of
$
\{
s
^{
[
1
]
}
,...,s
^{
[
N
]
}
\}
$
\textbf
{
do
}
\\
8:
\ \ \ \ \ \ \ \textbf
{
foreach
}
$
s
_
u
$
appears at least one of
$
\{
\mathbf
{
s
}^{
[
1
]
}
,...,
\mathbf
{
s
}
^{
[
N
]
}
\}
$
\textbf
{
do
}
\\
9:
\ \ \ \ \ \ \ \ \
$
f
(
s
_
u|t
_
v
)
=
\sum
_{
k
=
1
}^{
N
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
s
^{
[
k
]
}
,t
^{
[
k
]
}
)
\cdot
(
\lambda
_{
t
_
v
}^{
'
}
)
^{
-
1
}$
\\
9:
\ \ \ \ \ \ \ \ \
$
f
(
s
_
u|t
_
v
)
=
\sum
_{
k
=
1
}^{
N
}
c
_{
\mathbb
{
E
}}
(
s
_
u|t
_
v;
\mathbf
{
s
}^{
[
k
]
}
,
\mathbf
{
t
}
^{
[
k
]
}
)
\cdot
(
\lambda
_{
t
_
v
}^{
'
}
)
^{
-
1
}$
\\
10:
\ \textbf
{
return
}
$
f
(
\cdot
|
\cdot
)
$
10:
\ \textbf
{
return
}
$
f
(
\cdot
|
\cdot
)
$
\end{beamerboxesrounded}
\end{beamerboxesrounded}
\vspace
{
-0.3em
}
\vspace
{
-0.3em
}
...
@@ -4280,15 +4280,15 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
...
@@ -4280,15 +4280,15 @@ f(s_u|t_v) & = & \lambda_{t_v}^{-1} \cdot \textrm{P}(s|t) \cdot c_{\mathbb{E}}(s
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}
\begin{enumerate}
\begin{enumerate}
\item
\textbf
{
E-Step
}
(对于句对
$
(
s,t
)
$
，
$
m
=
|s|,l
=
|t
|
$
)
\item
\textbf
{
E-Step
}
(对于句对
$
(
\mathbf
{
s
}
,
\mathbf
{
t
}
)
$
，
$
m
=
|
\mathbf
{
s
}
|,l
=
|
\mathbf
{
t
}
|
$
)
\begin{eqnarray}
\begin{eqnarray}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
s,t
)
&
=
&
\sum
_{
j=1
}^{
m
}
\sum
_{
i=0
}^{
l
}
\frac
{
f(s
_
u|t
_
v)a(i|j,m,l)
\delta
(s
_
j,s
_
u)
\delta
(t
_
i,t
_
v)
}{
\sum
_{
k=0
}^{
l
}
f(s
_
u|t
_
k)a(k|j,m,l)
}
\nonumber
\\
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
&
=
&
\sum
_{
j=1
}^{
m
}
\sum
_{
i=0
}^{
l
}
\frac
{
f(s
_
u|t
_
v)a(i|j,m,l)
\delta
(s
_
j,s
_
u)
\delta
(t
_
i,t
_
v)
}{
\sum
_{
k=0
}^{
l
}
f(s
_
u|t
_
k)a(k|j,m,l)
}
\nonumber
\\
c
_{
\mathbb
{
E
}}
(i|j,m,l;
s,t
)
&
=
&
\frac
{
f(s
_
j|t
_
i)a(i|j,m,l)
}{
\sum
_{
k=0
}^{
l
}
f(s
_
j|t
_
k)a(k|j,m,l)
}
\nonumber
c
_{
\mathbb
{
E
}}
(i|j,m,l;
\mathbf
{
s
}
,
\mathbf
{
t
}
)
&
=
&
\frac
{
f(s
_
j|t
_
i)a(i|j,m,l)
}{
\sum
_{
k=0
}^{
l
}
f(s
_
j|t
_
k)a(k|j,m,l)
}
\nonumber
\end{eqnarray}
\end{eqnarray}
\item
\textbf
{
M-Step
}
\item
\textbf
{
M-Step
}
\begin{eqnarray}
\begin{eqnarray}
f(s
_
u|t
_
v)
&
=
&
\frac
{
\sum
_{
k=0
}^{
K
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
s
^{
[k]
}
,t
^{
[k]
}
)
}{
\sum
_{
s
_
u
}
\sum
_{
k=0
}^{
K
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;s
^{
[k]
}
,t
^{
[k]
}
)
}
\nonumber
\\
f(s
_
u|t
_
v)
&
=
&
\frac
{
\sum
_{
k=0
}^{
K
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
\mathbf
{
s
}^{
[k]
}
,
\mathbf
{
t
}^{
[k]
}
)
}{
\sum
_{
s
_
u
}
\sum
_{
k=0
}^{
K
}
c
_{
\mathbb
{
E
}}
(s
_
u|t
_
v;
\mathbf
{
s
}^{
[k]
}
,
\mathbf
{
t
}
^{
[k]
}
)
}
\nonumber
\\
a(i|j,m,l)
&
=
&
\frac
{
\sum
_{
k=0
}^{
K
}
c
_{
\mathbb
{
E
}}
(i|j;
s
^{
[k]
}
,t
^{
[k]
}
)
}{
\sum
_{
i
}
\sum
_{
k=0
}^{
K
}
c
_{
\mathbb
{
E
}}
(i|j;s
^{
[k]
}
,t
^{
[k]
}
)
}
\nonumber
a(i|j,m,l)
&
=
&
\frac
{
\sum
_{
k=0
}^{
K
}
c
_{
\mathbb
{
E
}}
(i|j;
\mathbf
{
s
}^{
[k]
}
,
\mathbf
{
t
}^{
[k]
}
)
}{
\sum
_{
i
}
\sum
_{
k=0
}^{
K
}
c
_{
\mathbb
{
E
}}
(i|j;
\mathbf
{
s
}^{
[k]
}
,
\mathbf
{
t
}
^{
[k]
}
)
}
\nonumber
\end{eqnarray}
\end{eqnarray}
\end{enumerate}
\end{enumerate}
\end{frame}
\end{frame}
...
...
Section04-Phrasal-and-Syntactic-Models/section04.tex
查看文件 @
e10537de
...
@@ -3706,8 +3706,8 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
...
@@ -3706,8 +3706,8 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
\subsection
{
基于chart的解码
}
\subsection
{
基于chart的解码
}
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% C
YK
解码
%%% C
KY
解码
\begin{frame}
{
C
YK
解码
}
\begin{frame}
{
C
KY
解码
}
% 看NiuTrans Manual
% 看NiuTrans Manual
\begin{itemize}
\begin{itemize}
\item
基于层次短语的翻译解码与基于短语的模型类似，都是要找到使
$
\textrm
{
score
}
(
d
)
$
达到最大的翻译推导
$
d
$
\item
基于层次短语的翻译解码与基于短语的模型类似，都是要找到使
$
\textrm
{
score
}
(
d
)
$
达到最大的翻译推导
$
d
$
...
@@ -3717,8 +3717,8 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
...
@@ -3717,8 +3717,8 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
\end{displaymath}
\end{displaymath}
\vspace
{
-0.8em
}
\vspace
{
-0.8em
}
\begin{itemize}
\begin{itemize}
\item
由于翻译推导由SCFG构成，使用C
YK
算法进行解码
\item
由于翻译推导由SCFG构成，使用C
KY
算法进行解码
\item
C
YK
算法解码是一个用来判定任意给定的字符串 是否属于一个上下文无关文法的算法，具体流程如下
\item
C
KY
算法解码是一个用来判定任意给定的字符串 是否属于一个上下文无关文法的算法，具体流程如下
\end{itemize}
\end{itemize}
\vspace
{
0.5em
}
\vspace
{
0.5em
}
\begin{center}
\begin{center}
...
@@ -3740,16 +3740,16 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
...
@@ -3740,16 +3740,16 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
\end{tikzpicture}
\end{tikzpicture}
\end{center}
\end{center}
\vspace
{
0.3em
}
\vspace
{
0.3em
}
%\item 由于对文法中的非终结符进行了限制，可以直接使用C
YK
算法进行解码，无需转换成乔姆斯基范式
%\item 由于对文法中的非终结符进行了限制，可以直接使用C
KY
算法进行解码，无需转换成乔姆斯基范式
\end{itemize}
\end{itemize}
\end{frame}
\end{frame}
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% C
YK
解码
%%% C
KY
解码
\begin{frame}
{
C
YK
算法
}
\begin{frame}
{
C
KY
算法
}
% 看NiuTrans Manual
% 看NiuTrans Manual
\begin{itemize}
\begin{itemize}
\item
C
YK
算法通过遍历不同
\alert
{
span
}
来判断字符串是否符合文法
\item
C
KY
算法通过遍历不同
\alert
{
span
}
来判断字符串是否符合文法
\begin{itemize}
\begin{itemize}
\item
输入：源语串
\textbf
{
s =
}
$
s
_
1
... s
_
J
$
，以及CNF文法
$
G
$
\item
输入：源语串
\textbf
{
s =
}
$
s
_
1
... s
_
J
$
，以及CNF文法
$
G
$
\item
输出：判断字符串是否符合G
\item
输出：判断字符串是否符合G
...
@@ -3762,7 +3762,7 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
...
@@ -3762,7 +3762,7 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
\tikzstyle
{
srcnode
}
= [anchor=south west]
\tikzstyle
{
srcnode
}
= [anchor=south west]
\begin{scope}
[scale=0.85]
\begin{scope}
[scale=0.85]
\node
[srcnode]
(c1) at (0,0)
{
\small
{
\textbf
{
Function
}
C
YK
-Algorithm(
$
\textbf
{
s
}
,G
$
)
}}
;
\node
[srcnode]
(c1) at (0,0)
{
\small
{
\textbf
{
Function
}
C
KY
-Algorithm(
$
\textbf
{
s
}
,G
$
)
}}
;
\node
[srcnode,anchor=north west]
(c21) at ([xshift=1.5em,yshift=0.4em]c1.south west)
{
\small
{
\textbf
{
fore
}
$
j
=
0
$
to
$
J
-
1
$}}
;
\node
[srcnode,anchor=north west]
(c21) at ([xshift=1.5em,yshift=0.4em]c1.south west)
{
\small
{
\textbf
{
fore
}
$
j
=
0
$
to
$
J
-
1
$}}
;
\node
[srcnode,anchor=north west]
(c22) at ([xshift=1.5em,yshift=0.4em]c21.south west)
{
\small
{$
span
[
j,j
+
1
]
$
.Add(
$
A
\to
a
\in
G
$
)
}}
;
\node
[srcnode,anchor=north west]
(c22) at ([xshift=1.5em,yshift=0.4em]c21.south west)
{
\small
{$
span
[
j,j
+
1
]
$
.Add(
$
A
\to
a
\in
G
$
)
}}
;
\node
[srcnode,anchor=north west]
(c3) at ([xshift=-1.5em,yshift=0.4em]c22.south west)
{
\small
{
\textbf
{
for
}
$
l
$
= 1 to
$
J
$}}
;
\node
[srcnode,anchor=north west]
(c3) at ([xshift=-1.5em,yshift=0.4em]c22.south west)
{
\small
{
\textbf
{
for
}
$
l
$
= 1 to
$
J
$}}
;
...
@@ -3810,11 +3810,11 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
...
@@ -3810,11 +3810,11 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
\end{frame}
\end{frame}
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% C
YK
解码
%%% C
KY
解码
\begin{frame}
{
C
YK
算法
}
\begin{frame}
{
C
KY
算法
}
% 看NiuTrans Manual
% 看NiuTrans Manual
\begin{itemize}
\begin{itemize}
\item
我们来看一个C
YK
算法的具体例子，给定一个上下无关文法以及一个单词
\alert
{
aabbc
}
，来判断该单词是否属于此文法，解析流程如下
\item
我们来看一个C
KY
算法的具体例子，给定一个上下无关文法以及一个单词
\alert
{
aabbc
}
，来判断该单词是否属于此文法，解析流程如下
\vspace
{
-0.3em
}
\vspace
{
-0.3em
}
\begin{center}
\begin{center}
\begin{tikzpicture}
\begin{tikzpicture}
...
@@ -3946,11 +3946,11 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
...
@@ -3946,11 +3946,11 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
\end{frame}
\end{frame}
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% C
YK
解码
%%% C
KY
解码
\begin{frame}
{
C
YK
解码（续）
}
\begin{frame}
{
C
KY
解码（续）
}
% 看NiuTrans Manual
% 看NiuTrans Manual
\begin{itemize}
\begin{itemize}
\item
实际上，在层次短语解码的时候，不能直接使用C
YK
算法，需要先转化为乔姆斯基范式，才能进行解码
\item
实际上，在层次短语解码的时候，不能直接使用C
KY
算法，需要先转化为乔姆斯基范式，才能进行解码
\begin{itemize}
\begin{itemize}
\item
<2-> 对于每个源语句子，使用短语规则表初始化它的span
\item
<2-> 对于每个源语句子，使用短语规则表初始化它的span
\item
<3-> 自底向上对span中的每个子span进行重新组合（正、反向）
\item
<3-> 自底向上对span中的每个子span进行重新组合（正、反向）
...
@@ -4166,7 +4166,7 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
...
@@ -4166,7 +4166,7 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
% 实验结果
% 实验结果
\begin{itemize}
\begin{itemize}
\item
从实验结果中可以看出，基于层次短语的翻译模型性能要优于基于短语的翻译模型
\item
从实验结果中可以看出，基于层次短语的翻译模型性能要优于基于短语的翻译模型
\item
选择使用层次短语信息实际上增加了模型的复杂度，但是可以通过借鉴基于短语的翻译模型模型以及C
YK
解码和立方剪枝等技术来解决
\item
选择使用层次短语信息实际上增加了模型的复杂度，但是可以通过借鉴基于短语的翻译模型模型以及C
KY
解码和立方剪枝等技术来解决
\item
可以考虑加入更多句法信息来进一步提升模型性能
\item
可以考虑加入更多句法信息来进一步提升模型性能
\end{itemize}
\end{itemize}
%\vspace{-1em}
%\vspace{-1em}
...
@@ -6785,7 +6785,7 @@ NP-BAR(NN$_1$ NP-BAR$_2$) $\to$ NN$_1$ NP-BAR$_2$
...
@@ -6785,7 +6785,7 @@ NP-BAR(NN$_1$ NP-BAR$_2$) $\to$ NN$_1$ NP-BAR$_2$
搜索空间
&
与输入的源语句法树
&
所有推导
$
D
$
\\
搜索空间
&
与输入的源语句法树
&
所有推导
$
D
$
\\
&
兼容的推导
$
D
_{
\textrm
{
tree
}}$
&
\\
\hline
&
兼容的推导
$
D
_{
\textrm
{
tree
}}$
&
\\
\hline
适用模型
&
树到串、树到树
&
所有句法模型
\\
\hline
适用模型
&
树到串、树到树
&
所有句法模型
\\
\hline
解码算法
&
chart解码
&
C
YK
+
规则二叉化
\\
\hline
解码算法
&
chart解码
&
C
KY
+
规则二叉化
\\
\hline
速度
&
快
&
一般较慢
速度
&
快
&
一般较慢
\end
{
tabular
}
\end
{
tabular
}
...
@@ -7358,7 +7358,7 @@ NP-BAR(NN$_1$ NP-BAR$_2$) $\to$ NN$_1$ NP-BAR$_2$
...
@@ -7358,7 +7358,7 @@ NP-BAR(NN$_1$ NP-BAR$_2$) $\to$ NN$_1$ NP-BAR$_2$
\end
{
frame
}
\end
{
frame
}
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% 基于串的解码 - C
YK
+ 规则二叉化
%%% 基于串的解码 - C
KY
+ 规则二叉化
\begin
{
frame
}{
基于串的解码
-
CKY
+
规则二叉化
}
\begin
{
frame
}{
基于串的解码
-
CKY
+
规则二叉化
}
\begin
{
itemize
}
\begin
{
itemize
}
...
...
Section05-Neural-Networks-and-Language-Modeling/section05.tex
查看文件 @
e10537de
...
@@ -5031,6 +5031,10 @@ GPT-2 (Transformer) & Radford et al. & 2019 & 35.7
...
@@ -5031,6 +5031,10 @@ GPT-2 (Transformer) & Radford et al. & 2019 & 35.7
\node
[anchor=west,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e2) at ([xshift=1em]e1.east)
{
\scriptsize
{$
\textbf
{
e
}_
2
$}}
;
\node
[anchor=west,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e2) at ([xshift=1em]e1.east)
{
\scriptsize
{$
\textbf
{
e
}_
2
$}}
;
\node
[anchor=west,inner sep=4pt] (sep5) at ([xshift=1em]e2.east)
{
\scriptsize
{
...
}}
;
\node
[anchor=west,inner sep=4pt] (sep5) at ([xshift=1em]e2.east)
{
\scriptsize
{
...
}}
;
\node
[anchor=west,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e3) at ([xshift=1em]sep5.east)
{
\scriptsize
{$
\textbf
{
e
}_
m
$}}
;
\node
[anchor=west,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e3) at ([xshift=1em]sep5.east)
{
\scriptsize
{$
\textbf
{
e
}_
m
$}}
;
\node
[anchor=south] (word1) at ([yshift=-1.5em]e1.south)
{
\footnotesize
{
Once
}}
;
\node
[anchor=south] (word2) at ([yshift=-1.6em]e2.south)
{
\footnotesize
{
upon
}}
;
\node
[anchor=south] (wordseq) at ([yshift=-1.5em]sep5.south)
{
\footnotesize
{
...
}}
;
\node
[anchor=south] (word3) at ([yshift=-1.5em]e3.south)
{
\footnotesize
{
island
}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t1) at ([xshift=-2em,yshift=1em]Lstm5.north)
{
\scriptsize
{$
\textbf
{
h
}_
1
$}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t1) at ([xshift=-2em,yshift=1em]Lstm5.north)
{
\scriptsize
{$
\textbf
{
h
}_
1
$}}
;
\node
[anchor=west,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t2) at ([xshift=1em]t1.east)
{
\scriptsize
{$
\textbf
{
h
}_
2
$}}
;
\node
[anchor=west,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t2) at ([xshift=1em]t1.east)
{
\scriptsize
{$
\textbf
{
h
}_
2
$}}
;
...
@@ -5130,6 +5134,12 @@ GPT-2 (Transformer) & Radford et al. & 2019 & 35.7
...
@@ -5130,6 +5134,12 @@ GPT-2 (Transformer) & Radford et al. & 2019 & 35.7
\node
[anchor=north,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e4) at ([yshift=-1em]Trm3.south)
{
\scriptsize
{$
\textbf
{
e
}_
4
$}}
;
\node
[anchor=north,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e4) at ([yshift=-1em]Trm3.south)
{
\scriptsize
{$
\textbf
{
e
}_
4
$}}
;
\node
[anchor=north,inner sep=4pt] (sep5) at ([yshift=-1em]sep.south)
{
\scriptsize
{
...
}}
;
\node
[anchor=north,inner sep=4pt] (sep5) at ([yshift=-1em]sep.south)
{
\scriptsize
{
...
}}
;
\node
[anchor=north,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e5) at ([yshift=-1em]Trm4.south)
{
\scriptsize
{$
\textbf
{
e
}_
m
$}}
;
\node
[anchor=north,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e5) at ([yshift=-1em]Trm4.south)
{
\scriptsize
{$
\textbf
{
e
}_
m
$}}
;
\node
[anchor=south] (word1) at ([yshift=-1.5em]e1.south)
{
\footnotesize
{
Once
}}
;
\node
[anchor=south] (word2) at ([yshift=-1.6em]e2.south)
{
\footnotesize
{
upon
}}
;
\node
[anchor=south] (word3) at ([yshift=-1.5em]e3.south)
{
\footnotesize
{
a
}}
;
\node
[anchor=south] (word4) at ([yshift=-1.5em]e4.south)
{
\footnotesize
{
time
}}
;
\node
[anchor=south] (wordseq) at ([yshift=-2.0em]sep5.south)
{
\footnotesize
{
...
}}
;
\node
[anchor=south] (word4) at ([yshift=-1.5em]e5.south)
{
\footnotesize
{
island
}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t1) at ([yshift=1em]Trm5.north)
{
\scriptsize
{$
\textbf
{
h
}_
1
$}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t1) at ([yshift=1em]Trm5.north)
{
\scriptsize
{$
\textbf
{
h
}_
1
$}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t2) at ([yshift=1em]Trm6.north)
{
\scriptsize
{$
\textbf
{
h
}_
2
$}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t2) at ([yshift=1em]Trm6.north)
{
\scriptsize
{$
\textbf
{
h
}_
2
$}}
;
...
@@ -5214,6 +5224,12 @@ GPT-2 (Transformer) & Radford et al. & 2019 & 35.7
...
@@ -5214,6 +5224,12 @@ GPT-2 (Transformer) & Radford et al. & 2019 & 35.7
\node
[anchor=north,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e4) at ([yshift=-1em]Trm3.south)
{
\scriptsize
{$
\textbf
{
e
}_
4
$}}
;
\node
[anchor=north,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e4) at ([yshift=-1em]Trm3.south)
{
\scriptsize
{$
\textbf
{
e
}_
4
$}}
;
\node
[anchor=north,inner sep=4pt] (sep5) at ([yshift=-1em]sep.south)
{
\scriptsize
{
...
}}
;
\node
[anchor=north,inner sep=4pt] (sep5) at ([yshift=-1em]sep.south)
{
\scriptsize
{
...
}}
;
\node
[anchor=north,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e5) at ([yshift=-1em]Trm4.south)
{
\scriptsize
{$
\textbf
{
e
}_
m
$}}
;
\node
[anchor=north,draw,inner sep=4pt,fill=ugreen!20!white,minimum width=2em] (e5) at ([yshift=-1em]Trm4.south)
{
\scriptsize
{$
\textbf
{
e
}_
m
$}}
;
\node
[anchor=south] (word1) at ([yshift=-1.5em]e1.south)
{
\footnotesize
{
Once
}}
;
\node
[anchor=south] (word2) at ([yshift=-1.7em]e2.south)
{
\footnotesize
{
[MASK]
}}
;
\node
[anchor=south] (word3) at ([yshift=-1.5em]e3.south)
{
\footnotesize
{
a
}}
;
\node
[anchor=south] (word4) at ([yshift=-1.5em]e4.south)
{
\footnotesize
{
time
}}
;
\node
[anchor=south] (wordseq) at ([yshift=-2.0em]sep5.south)
{
\footnotesize
{
...
}}
;
\node
[anchor=south] (word4) at ([yshift=-1.5em]e5.south)
{
\footnotesize
{
island
}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t1) at ([yshift=1em]Trm5.north)
{
\scriptsize
{$
\textbf
{
h
}_
1
$}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t1) at ([yshift=1em]Trm5.north)
{
\scriptsize
{$
\textbf
{
h
}_
1
$}}
;
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[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t2) at ([yshift=1em]Trm6.north)
{
\scriptsize
{$
\textbf
{
h
}_
2
$}}
;
\node
[anchor=south,draw,inner sep=4pt,fill=yellow!30,minimum width=2em] (t2) at ([yshift=1em]Trm6.north)
{
\scriptsize
{$
\textbf
{
h
}_
2
$}}
;
...
...
Section06-Neural-Machine-Translation/section06.tex
查看文件 @
e10537de
...
@@ -520,12 +520,12 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -520,12 +520,12 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\node
[rnnnode,fill=blue!30!white,right=\base of rnn3]
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{}
;
\node
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(rnn4)
{}
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(emb4)
{}
;
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(emb4)
{}
;
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(word4)
{
EOS
}
;
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[wordnode,below=0pt of emb4]
(word4)
{
$
\langle
$
eos
$
\rangle
$
}
;
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[-latex']
(emb4.north) to (rnn4.south);
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[-latex']
(emb4.north) to (rnn4.south);
\draw
[-latex']
(rnn3.east) to (rnn4.west);
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[-latex']
(rnn3.east) to (rnn4.west);
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\visible
<4->
{
\visible
<4->
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\draw
[decoration={mirror,brace},decorate]
(word1.south west) to node [auto,anchor=north,align=center]
{
编码器
}
([yshift=-0.2em]word4.south east);
\draw
[decoration={mirror,brace},decorate]
(
[yshift=-0.2em]
word1.south west) to node [auto,anchor=north,align=center]
{
编码器
}
([yshift=-0.2em]word4.south east);
}
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\visible
<5->
{
\visible
<5->
{
\node
[rnnnode,fill=purple]
(repr) at (rnn4)
{}
;
\node
[rnnnode,fill=purple]
(repr) at (rnn4)
{}
;
...
@@ -535,7 +535,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -535,7 +535,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\visible
<6->
{
\visible
<6->
{
\node
[rnnnode,fill=blue!30!white,right=\base of rnn4]
(rnn5)
{}
;
\node
[rnnnode,fill=blue!30!white,right=\base of rnn4]
(rnn5)
{}
;
\node
[rnnnode,fill=green!30!white,below=\base of rnn5]
(emb5)
{}
;
\node
[rnnnode,fill=green!30!white,below=\base of rnn5]
(emb5)
{}
;
\node
[wordnode,below=0pt of emb5]
(word5)
{
SOS
}
;
\node
[wordnode,below=0pt of emb5]
(word5)
{
$
\langle
$
sos
$
\rangle
$
}
;
\draw
[-latex']
(emb5.north) to (rnn5.south);
\draw
[-latex']
(emb5.north) to (rnn5.south);
\draw
[-latex']
(rnn4.east) to (rnn5.west);
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[-latex']
(rnn4.east) to (rnn5.west);
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[rnnnode,fill=red!30!white,above=\base of rnn5]
(softmax1)
{}
;
\node
[rnnnode,fill=red!30!white,above=\base of rnn5]
(softmax1)
{}
;
...
@@ -578,7 +578,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -578,7 +578,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\node
[wordnode,anchor=base]
(word8) at (
\XCoord
,
\YCoord
)
{
fine
}
;
\node
[wordnode,anchor=base]
(word8) at (
\XCoord
,
\YCoord
)
{
fine
}
;
\ExtractX
{$
(
emb
8
)
$}
\ExtractX
{$
(
emb
8
)
$}
\ExtractY
{$
(
out
1
.base
)
$}
\ExtractY
{$
(
out
1
.base
)
$}
\node
[wordnode,anchor=base]
(out4) at (
\XCoord
,
\YCoord
)
{
EOS
}
;
\node
[wordnode,anchor=base]
(out4) at (
\XCoord
,
\YCoord
)
{
$
\langle
$
eos
$
\rangle
$
}
;
\draw
[-latex']
(emb8.north) to (rnn8.south);
\draw
[-latex']
(emb8.north) to (rnn8.south);
\draw
[-latex']
(rnn7.east) to (rnn8.west);
\draw
[-latex']
(rnn7.east) to (rnn8.west);
\draw
[-latex']
(rnn8.north) to (softmax4.south);
\draw
[-latex']
(rnn8.north) to (softmax4.south);
...
@@ -720,7 +720,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -720,7 +720,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
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[anchor=north,rnnnode,fill=blue!30!white] (e2) at ([yshift=-1em]node12.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e2) at ([yshift=-1em]node12.south)
{
\tiny
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;
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{
\tiny
{}}
;
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[anchor=north,rnnnode,fill=blue!30!white] (e3) at ([yshift=-1em]node13.south)
{
\tiny
{}}
;
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[anchor=north,rnnnode,fill=blue!30!white] (e4) at ([yshift=-1em]node14.south)
{
\tiny
{}}
;
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[anchor=north,rnnnode,fill=blue!30!white] (e4) at ([yshift=-1em]node14.south)
{
\tiny
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;
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[anchor=north,inner sep=2pt] (w1) at ([yshift=-1em]e1.south)
{
\tiny
{$
<
$
s
$
>
$}}
;
\node
[anchor=north,inner sep=2pt] (w1) at ([yshift=-1em]e1.south)
{
\tiny
{$
<
$
s
os
$
>
$}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-1em]e2.south)
{
\tiny
{
让
}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-1em]e2.south)
{
\tiny
{
让
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-1em]e3.south)
{
\tiny
{
我们
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-1em]e3.south)
{
\tiny
{
我们
}}
;
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\tiny
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开始
}}
;
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{
\tiny
{
开始
}}
;
...
@@ -1072,10 +1072,10 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -1072,10 +1072,10 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\draw
[-latex']
(enc3.north) .. controls +(north:0.3
\base
) and +(east:
\base
) .. (bridge) .. controls +(west:2.7
\base
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\base
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[-latex']
(enc3.north) .. controls +(north:0.3
\base
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\base
) .. (bridge) .. controls +(west:2.7
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\visible
<2->
{
\visible
<2->
{
\node
[anchor=east] (line1) at ([xshift=-3em,yshift=0.5em]softmax1.west)
{
\scriptsize
{
基于RNN的隐层状态
$
\textbf
{
s
}_
i
$}}
;
\node
[anchor=east] (line1) at ([xshift=-3em,yshift=0.5em]softmax1.west)
{
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{
基于RNN的隐层状态
$
\textbf
{
s
}_
j
$}}
;
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[anchor=north west] (line2) at ([yshift=0.3em]line1.south west)
{
\scriptsize
{
预测目标词的概率
}}
;
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[anchor=north west] (line2) at ([yshift=0.3em]line1.south west)
{
\scriptsize
{
预测目标词的概率
}}
;
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[anchor=north west] (line3) at ([yshift=0.3em]line2.south west)
{
\scriptsize
{
通常，用Softmax函数
}}
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{
\scriptsize
{
通常，用Softmax函数
}}
;
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{
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实现
$
\textrm
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P
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(
y
_
i
|...
)
$}}
;
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{
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{
实现
$
\textrm
{
P
}
(
y
_
j
|...
)
$}}
;
}
}
\visible
<3->
{
\visible
<3->
{
...
@@ -1833,7 +1833,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -1833,7 +1833,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\node
[rnnnode,minimum height=0.5\base,fill=red!30!white,anchor=south]
(softmax
\x
) at ([yshift=0.5
\base
]dec
\x
.north)
{}
;
\node
[rnnnode,minimum height=0.5\base,fill=red!30!white,anchor=south]
(softmax
\x
) at ([yshift=0.5
\base
]dec
\x
.north)
{}
;
% Decoder input words
% Decoder input words
\node
[wordnode,below=0pt of demb1]
(decwordin)
{
EOS
}
;
\node
[wordnode,below=0pt of demb1]
(decwordin)
{
$
\langle
$
sos
$
\rangle
$
}
;
\ExtractX
{$
(
demb
2
.south
)
$}
\ExtractX
{$
(
demb
2
.south
)
$}
\ExtractY
{$
(
decwordin.base
)
$}
\ExtractY
{$
(
decwordin.base
)
$}
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
Do
}
;
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
Do
}
;
...
@@ -1890,7 +1890,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -1890,7 +1890,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
Station
}
;
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
Station
}
;
\ExtractX
{$
(
softmax
10
.north
)
$}
\ExtractX
{$
(
softmax
10
.north
)
$}
\ExtractY
{$
(
decwordout.base
)
$}
\ExtractY
{$
(
decwordout.base
)
$}
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
EOS
}
;
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
$
\langle
$
eos
$
\rangle
$
}
;
% Connections
% Connections
\draw
[-latex']
(init.east) to (enc1.west);
\draw
[-latex']
(init.east) to (enc1.west);
...
@@ -1971,7 +1971,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -1971,7 +1971,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\node
[wordnode,below=0pt of eemb7]
()
{
怎么
}
;
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[wordnode,below=0pt of eemb7]
()
{
怎么
}
;
\node
[wordnode,below=0pt of eemb8]
()
{
走
}
;
\node
[wordnode,below=0pt of eemb8]
()
{
走
}
;
\node
[wordnode,below=0pt of eemb9]
()
{
吗
}
;
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[wordnode,below=0pt of eemb9]
()
{
吗
}
;
\node
[wordnode,below=0pt of eemb10]
()
{
EOS
}
;
\node
[wordnode,below=0pt of eemb10]
()
{
$
\langle
$
eos
$
\rangle
$
}
;
% RNN Decoder
% RNN Decoder
\foreach
\x
in
{
1,2,...,10
}
\foreach
\x
in
{
1,2,...,10
}
...
@@ -2041,7 +2041,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -2041,7 +2041,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
Station
}
;
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
Station
}
;
\ExtractX
{$
(
softmax
10
.north
)
$}
\ExtractX
{$
(
softmax
10
.north
)
$}
\ExtractY
{$
(
decwordout.base
)
$}
\ExtractY
{$
(
decwordout.base
)
$}
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[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
EOS
}
;
\node
[wordnode,anchor=base]
() at (
\XCoord
,
\YCoord
)
{
$
\langle
$
eos
$
\rangle
$
}
;
% Connections
% Connections
\draw
[-latex']
(init1.east) to (enc11.west);
\draw
[-latex']
(init1.east) to (enc11.west);
...
@@ -2187,7 +2187,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -2187,7 +2187,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
\begin{itemize}
\begin{itemize}
\item
在注意力机制中，每个目标语单词的生成会使用一个动态的源语表示，而非一个统一的固定表示
\item
在注意力机制中，每个目标语单词的生成会使用一个动态的源语表示，而非一个统一的固定表示
\begin{itemize}
\begin{itemize}
\item
这里
$
\textbf
{
C
}_
i
$
表示第
$
i
$
个目标语单词所使用的源语表示
\item
这里
$
\textbf
{
C
}_
j
$
表示第
$
j
$
个目标语单词所使用的源语表示
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}
...
@@ -2286,15 +2286,15 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -2286,15 +2286,15 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
%%%------------------------------------------------------------------------------------------------------------
%%%------------------------------------------------------------------------------------------------------------
%%% C_i的定义
%%% C_i的定义
\begin{frame}
{
上下文向量
$
\textbf
{
C
}_
i
$}
\begin{frame}
{
上下文向量
$
\textbf
{
C
}_
j
$}
\begin{itemize}
\begin{itemize}
\item
对于目标语位置
$
i
$
，
$
\textbf
{
C
}_
i
$
是目标语
$
i
$
使用的上下文向量
\item
对于目标语位置
$
j
$
，
$
\textbf
{
C
}_
j
$
是目标语
$
j
$
使用的上下文向量
\begin{itemize}
\begin{itemize}
\item
$
\textbf
{
h
}_
j
$
表示编码器第
$
j
$
个位置的隐层状态
\item
$
\textbf
{
h
}_
i
$
表示编码器第
$
i
$
个位置的隐层状态
\item
$
\textbf
{
s
}_
i
$
表示解码器第
$
i
$
个位置的隐层状态
\item
$
\textbf
{
s
}_
j
$
表示解码器第
$
j
$
个位置的隐层状态
\item
<2->
$
\alpha
_{
i,j
}$
表示注意力权重，表示目标语第
$
i
$
个位置与源语第
$
j
$
个位置之间的相关性大小
\item
<2->
$
\alpha
_{
i,j
}$
表示注意力权重，表示目标语第
$
j
$
个位置与源语第
$
i
$
个位置之间的相关性大小
\item
<2->
$
a
(
\cdot
)
$
表示注意力函数，计算
$
\textbf
{
s
}_{
i
-
1
}$
和
$
\textbf
{
h
}_
j
$
之间的相关性
\item
<2->
$
a
(
\cdot
)
$
表示注意力函数，计算
$
\textbf
{
s
}_{
j
-
1
}$
和
$
\textbf
{
h
}_
i
$
之间的相关性
\item
<3->
$
\textbf
{
C
}_
i
$
是所有源语编码表示
$
\{\textbf
{
h
}_
j
\}
$
的加权求和，权重为
$
\{\alpha
_{
i,j
}
\}
$
\item
<3->
$
\textbf
{
C
}_
j
$
是所有源语编码表示
$
\{\textbf
{
h
}_
i
\}
$
的加权求和，权重为
$
\{\alpha
_{
i,j
}
\}
$
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}
...
@@ -2306,23 +2306,23 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -2306,23 +2306,23 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
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h
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1
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;
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{
h
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n
$}}
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\textbf
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h
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{}
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{}
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\alpha
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{
\scriptsize
{$
\textbf
{
C
}_{
i
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;
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[->] (sum.north) .. controls +(north:0.8) and +(west:0.2) .. ([yshift=-0.4em,xshift=-0.1em]th2.west) node [pos=0.2,right] (ci)
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{$
\textbf
{
C
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j
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输出层
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输出层
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\draw
[->] ([yshift=0.1em]th2.north) -- ([yshift=-0.1em]output.south);
...
@@ -2334,11 +2334,11 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -2334,11 +2334,11 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
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[anchor=north] (enc42) at ([yshift=0.5em]enc4.south)
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(位置
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{
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[anchor=west] (math1) at ([xshift=5em,yshift=1em]th2.east)
{$
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{
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i
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j
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\alpha
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\textbf
{
h
}_
j
\ \
$}
;
\node
[anchor=west] (math1) at ([xshift=5em,yshift=1em]th2.east)
{$
\textbf
{
C
}_
j
=
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_{
i
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\alpha
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i,j
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\textbf
{
h
}_
i
\ \
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{
\node
[anchor=north west] (math2) at ([yshift=-2em]math1.south west)
{$
\alpha
_{
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}
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{
\exp
(
\beta
_{
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;
\node
[anchor=north west] (math2) at ([yshift=-2em]math1.south west)
{$
\alpha
_{
i,j
}
=
\frac
{
\exp
(
\beta
_{
i,j
}
)
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\sum
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i'
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\exp
(
\beta
_{
i',j
}
)
}$}
;
\node
[anchor=north west] (math3) at ([yshift=-0em]math2.south west)
{$
\beta
_{
i,j
}
=
a
(
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{
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h
}_
j
)
$}
;
\node
[anchor=north west] (math3) at ([yshift=-0em]math2.south west)
{$
\beta
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i,j
}
=
a
(
\textbf
{
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}_
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;
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background
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\begin{pgfonlayer}
{
background
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...
@@ -2418,7 +2418,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -2418,7 +2418,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
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(src3) at ([xshift=0.5
\hnode
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learned
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learned
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{
nothing
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;
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(src4) at ([xshift=0.5
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\scriptsize
{
nothing
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(src5) at ([xshift=0.5
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{
\scriptsize
{
?
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(src5) at ([xshift=0.5
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{
\scriptsize
{
?
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(src6) at ([xshift=0.5
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\scriptsize
{
EOS
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(src6) at ([xshift=0.5
\hnode
]src5.south west)
{
\scriptsize
{
$
\langle
$
eos
$
\rangle
$
}}
;
% target
% target
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[tgtnode]
(tgt1) at (-6.0*0.5*
\hnode
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\hnode
+7.5*0.5*
\hnode
)
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\scriptsize
{
你
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\hnode
+7.5*0.5*
\hnode
)
{
\scriptsize
{
你
}}
;
...
@@ -2428,7 +2428,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -2428,7 +2428,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
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学
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到
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到
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{
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...
@@ -2464,7 +2464,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
...
@@ -2464,7 +2464,7 @@ NLP问题的隐含结构假设 & 无隐含结构假设，端到端学习 \\
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<3->
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\visible
<3->
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% coverage score formula node
% coverage score formula node
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[anchor=north west] (formula) at ([xshift=-0.3
\hnode
,yshift=-1.5
\hnode
]attn11.south)
{
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{
不同
$
\textbf
{
C
}_
i
$
所对应的源语言词的权重是不同的
}}
;
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[anchor=north west] (formula) at ([xshift=-0.3
\hnode
,yshift=-1.5
\hnode
]attn11.south)
{
\small
{
不同
$
\textbf
{
C
}_
j
$
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{
\footnotesize
{$
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{
C
}_
2
=
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.
4
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{
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.
4
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{
h
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(
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+
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{
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{$
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{
C
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4
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(
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``你''
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0
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4
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\textbf
{
h
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(
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{
``什么''
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{$
\ \ \ \ \ \ \ \
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\textbf
{
h
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(
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+
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.
1
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{
h
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(
\textrm
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...
@@ -2526,7 +2526,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -2526,7 +2526,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\item
再来看一下注意力权重的定义。这个过程实际上是对
$
a
(
\cdot
,
\cdot
)
$
做指数归一化：
\\
\item
再来看一下注意力权重的定义。这个过程实际上是对
$
a
(
\cdot
,
\cdot
)
$
做指数归一化：
\\
\vspace
{
-0.3em
}
\vspace
{
-0.3em
}
\begin{displaymath}
\begin{displaymath}
\alpha
_{
i,j
}
=
\frac
{
\exp
(a(
\textbf
{
s
}_{
i-1
}
,
\textbf
{
h
}_
j))
}{
\sum
_{
j'
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\exp
(a(
\textbf
{
s
}_{
i-1
}
,
\textbf
{
h
}_{
j
'
}
))
}
\alpha
_{
i,j
}
=
\frac
{
\exp
(a(
\textbf
{
s
}_{
j-1
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,
\textbf
{
h
}_
i))
}{
\sum
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i'
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{
s
}_{
j-1
}
,
\textbf
{
h
}_{
i
'
}
))
}
\end{displaymath}
\end{displaymath}
\item
<2-> 注意力函数
$
a
(
\textbf
{
s
}
,
\textbf
{
h
}
)
$
的目的是捕捉
$
\textbf
{
s
}$
和
$
\textbf
{
h
}$
之间的
\alert
{
相似性
}
，这也可以被看作是目标语表示和源语言表示的一种``统一化''，即把源语言和目标语表示在同一个语义空间，进而语义相近的内容有更大的相似性。
\visible
<3->
{
定义
$
a
(
\textbf
{
s
}
,
\textbf
{
h
}
)
$
的方式：
}
\item
<2-> 注意力函数
$
a
(
\textbf
{
s
}
,
\textbf
{
h
}
)
$
的目的是捕捉
$
\textbf
{
s
}$
和
$
\textbf
{
h
}$
之间的
\alert
{
相似性
}
，这也可以被看作是目标语表示和源语言表示的一种``统一化''，即把源语言和目标语表示在同一个语义空间，进而语义相近的内容有更大的相似性。
\visible
<3->
{
定义
$
a
(
\textbf
{
s
}
,
\textbf
{
h
}
)
$
的方式：
}
...
@@ -2572,7 +2572,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -2572,7 +2572,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
ymin=-0.5,ymax=5.5,
ymin=-0.5,ymax=5.5,
xmin=-0.5,xmax=2.5,
xmin=-0.5,xmax=2.5,
ytick=
{
0,1,...,5
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,
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0,1,...,5
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,
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The,New,York,Times,comments,
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The,New,York,Times,comments,
$
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$
eos
$
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{
font=
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}
,
yticklabel style=
{
font=
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,
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0,1,2
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纽约时报,发表,评论
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,
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纽约时报,发表,评论
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,
...
@@ -2593,7 +2593,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -2593,7 +2593,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
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{
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,
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{
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,
xtick=
{
0,1,2,3
}
,
xtick=
{
0,1,2,3
}
,
xticklabels=
{
我,来到,这个,世界
}
,
xticklabels=
{
我,来到,这个,世界
}
,
...
@@ -2715,7 +2715,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -2715,7 +2715,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
%%% 如何进一步理解注意力机制 - 回到机器翻译任务
%%% 如何进一步理解注意力机制 - 回到机器翻译任务
\begin{frame}
{
重新解释注意力机制(续)
}
\begin{frame}
{
重新解释注意力机制(续)
}
\begin{itemize}
\begin{itemize}
\item
回到机器翻译，如果把目标语状态
$
\textbf
{
s
}_{
i
-
1
}$
看做query，而把源语言所有位置的最上层RNN表示
$
\textbf
{
h
}_{
j
}$
看做
{
\color
{
ugreen
}
\textbf
{
key
}}
和
{
\color
{
red
}
\textbf
{
value
}}
\item
回到机器翻译，如果把目标语状态
$
\textbf
{
s
}_{
j
-
1
}$
看做query，而把源语言所有位置的最上层RNN表示
$
\textbf
{
h
}_{
i
}$
看做
{
\color
{
ugreen
}
\textbf
{
key
}}
和
{
\color
{
red
}
\textbf
{
value
}}
\end{itemize}
\end{itemize}
\vspace
{
-1.5em
}
\vspace
{
-1.5em
}
...
@@ -3084,7 +3084,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3084,7 +3084,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
% step 6
% step 6
\visible
<6->
{
\visible
<6->
{
\node
[rnnnode]
(rnn34) at ([xshift=2
\base
]rnn33)
{}
;
\node
[rnnnode]
(rnn34) at ([xshift=2
\base
]rnn33)
{}
;
\node
[wordnode,anchor=south]
(o4) at ([yshift=
\base
]rnn34.north)
{
EOS
}
;
\node
[wordnode,anchor=south]
(o4) at ([yshift=
\base
]rnn34.north)
{
$
\langle
$
eos
$
\rangle
$
}
;
\draw
[-latex']
(rnn33) to (rnn34);
\draw
[-latex']
(rnn33) to (rnn34);
\draw
[-latex']
(rnn24) to (rnn34);
\draw
[-latex']
(rnn24) to (rnn34);
\draw
[-latex']
(rnn34) to (o4);
\draw
[-latex']
(rnn34) to (o4);
...
@@ -3136,7 +3136,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3136,7 +3136,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\hat
{
\textbf
{
y
}}
=
\argmax
_{
\textbf
{
y
}}
\log\textrm
{
P
}
(
\textbf
{
y
}
|
\textbf
{
x
}
) =
\argmax
_{
\textbf
{
y
}}
\sum
_{
j=1
}^{
n
}
\log\textrm
{
P
}
(y
_
j|
\textbf
{
y
}_{
<j
}
,
\textbf
{
x
}
)
\hat
{
\textbf
{
y
}}
=
\argmax
_{
\textbf
{
y
}}
\log\textrm
{
P
}
(
\textbf
{
y
}
|
\textbf
{
x
}
) =
\argmax
_{
\textbf
{
y
}}
\sum
_{
j=1
}^{
n
}
\log\textrm
{
P
}
(y
_
j|
\textbf
{
y
}_{
<j
}
,
\textbf
{
x
}
)
\end{displaymath}
\end{displaymath}
\item
<2-> 由于
$
y
_
i
$
的生成需要依赖
$
y
_{
i
-
1
}$
，因此无法同时生成
$
\{
y
_
1
,...,y
_
n
\}
$
。常用的方法是自左向右逐个单词生成
\item
<2-> 由于
$
y
_
j
$
的生成需要依赖
$
y
_{
j
-
1
}$
，因此无法同时生成
$
\{
y
_
1
,...,y
_
n
\}
$
。常用的方法是自左向右逐个单词生成
\end{itemize}
\end{itemize}
...
@@ -3156,7 +3156,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3156,7 +3156,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[rnnnode,anchor=west,fill=green!20] (e3) at ([xshift=1em]e2.east)
{
\tiny
{$
e
_
x
()
$}}
;
\node
[rnnnode,anchor=west,fill=green!20] (e3) at ([xshift=1em]e2.east)
{
\tiny
{$
e
_
x
()
$}}
;
\node
[anchor=north,inner sep=2pt] (w1) at ([yshift=-0.6em]e1.south)
{
\tiny
{
你
}}
;
\node
[anchor=north,inner sep=2pt] (w1) at ([yshift=-0.6em]e1.south)
{
\tiny
{
你
}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-0.8em]e2.south)
{
\tiny
{
...
}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-0.8em]e2.south)
{
\tiny
{
...
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-0.6em]e3.south)
{
\tiny
{
EOS
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-0.6em]e3.south)
{
\tiny
{
$
\langle
$
eos
$
\rangle
$
}}
;
\draw
[->] (w1.north) -- ([yshift=-0.1em]e1.south);
\draw
[->] (w1.north) -- ([yshift=-0.1em]e1.south);
\draw
[->] (w3.north) -- ([yshift=-0.1em]e3.south);
\draw
[->] (w3.north) -- ([yshift=-0.1em]e3.south);
...
@@ -3202,7 +3202,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3202,7 +3202,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[anchor=west,inner sep=2pt] (o5) at ([xshift=0.3em]o4.east)
{
\tiny
{
...
}}
;
\node
[anchor=west,inner sep=2pt] (o5) at ([xshift=0.3em]o4.east)
{
\tiny
{
...
}}
;
}
}
\visible
<4->
{
\visible
<4->
{
\node
[anchor=north,inner sep=2pt] (wt1) at ([yshift=-0.6em]t1.south)
{
\tiny
{
EOS
}}
;
\node
[anchor=north,inner sep=2pt] (wt1) at ([yshift=-0.6em]t1.south)
{
\tiny
{
$
\langle
$
sos
$
\rangle
$
}}
;
}
}
\visible
<7->
{
\visible
<7->
{
\node
[anchor=north,inner sep=2pt] (wt2) at ([yshift=-0.6em]t2.south)
{
\tiny
{
Have
}}
;
\node
[anchor=north,inner sep=2pt] (wt2) at ([yshift=-0.6em]t2.south)
{
\tiny
{
Have
}}
;
...
@@ -3355,7 +3355,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3355,7 +3355,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[anchor=west,inner sep=2pt] (o4) at ([xshift=0.3em]o3.east)
{
\tiny
{
...
}}
;
\node
[anchor=west,inner sep=2pt] (o4) at ([xshift=0.3em]o3.east)
{
\tiny
{
...
}}
;
}
}
\node
[wnode,anchor=north] (wt1) at ([yshift=-0.8em]t1.south)
{
\tiny
{
EOS
}}
;
\node
[wnode,anchor=north] (wt1) at ([yshift=-0.8em]t1.south)
{
\tiny
{
$
\langle
$
sos
$
\rangle
$
}}
;
\visible
<6->
{
\visible
<6->
{
\node
[wnode,anchor=north] (wt2) at ([yshift=-0.8em]t2.south)
{
\tiny
{
Have
}}
;
\node
[wnode,anchor=north] (wt2) at ([yshift=-0.8em]t2.south)
{
\tiny
{
Have
}}
;
...
@@ -3546,7 +3546,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3546,7 +3546,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
% words
% words
\node
[wnode,below=0pt of encemb1]
(encword1)
{
你
}
;
\node
[wnode,below=0pt of encemb1]
(encword1)
{
你
}
;
\node
[wnode,below=0pt of encemb2]
(encword2)
{
什么
}
;
\node
[wnode,below=0pt of encemb2]
(encword2)
{
什么
}
;
\node
[wnode,below=0pt of encemb4]
(encword4)
{
EOS
}
;
\node
[wnode,below=0pt of encemb4]
(encword4)
{
$
\langle
$
eos
$
\rangle
$
}
;
% connections
% connections
\draw
[-latex']
(enc11) to (enc12);
\draw
[-latex']
(enc11) to (enc12);
...
@@ -3645,7 +3645,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3645,7 +3645,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[rnnnode,fill=blue!20,above=\base of dec54]
(softmax4)
{}
;
\node
[rnnnode,fill=blue!20,above=\base of dec54]
(softmax4)
{}
;
% words
% words
\node
[wnode,below=0pt of decemb1]
(decinword1)
{
SOS
}
;
\node
[wnode,below=0pt of decemb1]
(decinword1)
{
$
\langle
$
sos
$
\rangle
$
}
;
\node
[wnode,below=0pt of decemb2]
(decinword2)
{
Have
}
;
\node
[wnode,below=0pt of decemb2]
(decinword2)
{
Have
}
;
\node
[wnode,below=0pt of decemb4]
(decinword4)
{
?
}
;
\node
[wnode,below=0pt of decemb4]
(decinword4)
{
?
}
;
...
@@ -3655,7 +3655,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3655,7 +3655,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[wnode,anchor=base]
(decoutword2) at (
\XCoord
,
\YCoord
)
{
you
}
;
\node
[wnode,anchor=base]
(decoutword2) at (
\XCoord
,
\YCoord
)
{
you
}
;
\ExtractX
{$
(
softmax
4
.north
)
$}
\ExtractX
{$
(
softmax
4
.north
)
$}
\ExtractY
{$
(
decoutword
1
.base
)
$}
\ExtractY
{$
(
decoutword
1
.base
)
$}
\node
[wnode,anchor=base]
(decoutword4) at (
\XCoord
,
\YCoord
)
{
EOS
}
;
\node
[wnode,anchor=base]
(decoutword4) at (
\XCoord
,
\YCoord
)
{
$
\langle
$
eos
$
\rangle
$
}
;
% connections
% connections
\draw
[-latex']
(dec11) to (dec12);
\draw
[-latex']
(dec11) to (dec12);
...
@@ -3810,7 +3810,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -3810,7 +3810,7 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[anchor=north,rnnnode,fill=blue!30!white] (e2) at ([yshift=-2em]node12.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e2) at ([yshift=-2em]node12.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e3) at ([yshift=-2em]node13.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e3) at ([yshift=-2em]node13.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e4) at ([yshift=-2em]node14.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e4) at ([yshift=-2em]node14.south)
{
\tiny
{}}
;
\node
[anchor=north,inner sep=2pt] (w1) at ([yshift=-1em]e1.south)
{
\tiny
{$
<
$
s
$
>
$}}
;
\node
[anchor=north,inner sep=2pt] (w1) at ([yshift=-1em]e1.south)
{
\tiny
{$
\langle
$
sos
$
\rangle
$}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-1em]e2.south)
{
\tiny
{
让
}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-1em]e2.south)
{
\tiny
{
让
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-1em]e3.south)
{
\tiny
{
我们
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-1em]e3.south)
{
\tiny
{
我们
}}
;
\node
[anchor=north,inner sep=2pt] (w4) at ([yshift=-1em]e4.south)
{
\tiny
{
开始
}}
;
\node
[anchor=north,inner sep=2pt] (w4) at ([yshift=-1em]e4.south)
{
\tiny
{
开始
}}
;
...
@@ -4100,9 +4100,9 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -4100,9 +4100,9 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[outputnode,anchor=south] (o1) at ([yshift=1em]res5.north)
{
\tiny
{$
\textbf
{
Output layer
}$}}
;
\node
[outputnode,anchor=south] (o1) at ([yshift=1em]res5.north)
{
\tiny
{$
\textbf
{
Output layer
}$}}
;
\node
[inputnode,anchor=north west] (input2) at ([yshift=-1em]sa2.south west)
{
\tiny
{$
\textbf
{
Embedding
}$}}
;
\node
[inputnode,anchor=north west] (input2) at ([yshift=-1em]sa2.south west)
{
\tiny
{$
\textbf
{
Embedding
}$}}
;
\node
[posnode,anchor=north east] (pos2) at ([yshift=-1em]sa2.south east)
{
\tiny
{$
\textbf
{
Postion
}$}}
;
\node
[posnode,anchor=north east] (pos2) at ([yshift=-1em]sa2.south east)
{
\tiny
{$
\textbf
{
Postion
}$}}
;
\node
[anchor=north] (outputs) at ([yshift=-3em]sa2.south)
{
\tiny
{$
\textbf
{
解码器输入:
$
<
$
SOS
$
>
$
I am fine
}$}}
;
\node
[anchor=north] (outputs) at ([yshift=-3em]sa2.south)
{
\tiny
{$
\textbf
{
解码器输入:
$
<
$
sos
$
>
$
I am fine
}$}}
;
\node
[anchor=east] (decoder) at ([xshift=-1em,yshift=-1.5em]o1.west)
{
\scriptsize
{
\textbf
{
解码器
}}}
;
\node
[anchor=east] (decoder) at ([xshift=-1em,yshift=-1.5em]o1.west)
{
\scriptsize
{
\textbf
{
解码器
}}}
;
\node
[anchor=north] (decoutputs) at ([yshift=1.5em]o1.north)
{
\tiny
{$
\textbf
{
解码器输出: I am fine
$
<
$
EOS
$
>
$
}$}}
;
\node
[anchor=north] (decoutputs) at ([yshift=1.5em]o1.north)
{
\tiny
{$
\textbf
{
解码器输出: I am fine
$
<
$
eos
$
>
$
}$}}
;
\draw
[->] (sa2.north) -- (res3.south);
\draw
[->] (sa2.north) -- (res3.south);
\draw
[->] (res3.north) -- (ed1.south);
\draw
[->] (res3.north) -- (ed1.south);
...
@@ -4127,6 +4127,9 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -4127,6 +4127,9 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[rectangle,inner sep=0.7em,rounded corners=1pt,very thick,dotted,draw=ugreen!70] [fit = (sa1) (res1) (ffn1) (res2)] (box0)
{}
;
\node
[rectangle,inner sep=0.7em,rounded corners=1pt,very thick,dotted,draw=ugreen!70] [fit = (sa1) (res1) (ffn1) (res2)] (box0)
{}
;
\node
[rectangle,inner sep=0.7em,rounded corners=1pt,very thick,dotted,draw=red!60] [fit = (sa2) (res3) (res5)] (box1)
{}
;
\node
[rectangle,inner sep=0.7em,rounded corners=1pt,very thick,dotted,draw=red!60] [fit = (sa2) (res3) (res5)] (box1)
{}
;
\node
[ugreen,font=
\scriptsize
] (count) at ([xshift=-1.5em,yshift=-1em]encoder.south)
{$
6
\times
$}
;
\node
[red,font=
\scriptsize
] (count) at ([xshift=10.8em,yshift=0em]decoder.south)
{$
\times
6
$}
;
\end{scope}
\end{scope}
\end{tikzpicture}
\end{tikzpicture}
\end{center}
\end{center}
...
@@ -4180,9 +4183,9 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
...
@@ -4180,9 +4183,9 @@ $\textrm{``you''} = \argmax_{y_2} \textrm{P}(y_2|\textbf{s}_1, y_1)$ & $\textrm{
\node
[outputnode,anchor=south] (o1) at ([yshift=1em]res5.north)
{
\tiny
{$
\textbf
{
Output layer
}$}}
;
\node
[outputnode,anchor=south] (o1) at ([yshift=1em]res5.north)
{
\tiny
{$
\textbf
{
Output layer
}$}}
;
\node
[inputnode,anchor=north west] (input2) at ([yshift=-1em]sa2.south west)
{
\tiny
{$
\textbf
{
Embedding
}$}}
;
\node
[inputnode,anchor=north west] (input2) at ([yshift=-1em]sa2.south west)
{
\tiny
{$
\textbf
{
Embedding
}$}}
;
\node
[posnode,anchor=north east] (pos2) at ([yshift=-1em]sa2.south east)
{
\tiny
{$
\textbf
{
Postion
}$}}
;
\node
[posnode,anchor=north east] (pos2) at ([yshift=-1em]sa2.south east)
{
\tiny
{$
\textbf
{
Postion
}$}}
;
\node
[anchor=north] (outputs) at ([yshift=-3em]sa2.south)
{
\tiny
{$
\textbf
{
解码器输入:
$
<
$
SOS
$
>
$
I am fine
}$}}
;
\node
[anchor=north] (outputs) at ([yshift=-3em]sa2.south)
{
\tiny
{$
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sos
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...
@@ -4414,9 +4417,9 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
...
@@ -4414,9 +4417,9 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
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...
@@ -4591,7 +4594,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
...
@@ -4591,7 +4594,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
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...
@@ -4599,7 +4602,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
...
@@ -4599,7 +4602,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
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...
@@ -4630,7 +4633,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
...
@@ -4630,7 +4633,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
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...
@@ -4638,7 +4641,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
...
@@ -4638,7 +4641,7 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
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...
@@ -4800,9 +4803,9 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
...
@@ -4800,9 +4803,9 @@ PE_{(pos,2i+1)} = cos(pos/10000^{2i/d_{model}})
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...
@@ -5030,9 +5033,9 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
...
@@ -5030,9 +5033,9 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
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...
@@ -5170,7 +5173,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
...
@@ -5170,7 +5173,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
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...
@@ -5212,7 +5215,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
...
@@ -5212,7 +5215,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
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...
@@ -5413,7 +5416,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
...
@@ -5413,7 +5416,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
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{$
e
_
x
()
$}}
;
\node
[rnnnode,anchor=west,fill=green!20] (e3) at ([xshift=1em]e2.east)
{
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{$
e
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x
()
$}}
;
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[anchor=north,inner sep=2pt] (w1) at ([yshift=-0.6em]e1.south)
{
\tiny
{
你
}}
;
\node
[anchor=north,inner sep=2pt] (w1) at ([yshift=-0.6em]e1.south)
{
\tiny
{
你
}}
;
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[anchor=north,inner sep=2pt] (w2) at ([yshift=-0.6em]e2.south)
{
\tiny
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}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-0.6em]e2.south)
{
\tiny
{
好
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-0.6em]e3.south)
{
\tiny
{
EOS
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-0.6em]e3.south)
{
\tiny
{
$
\langle
$
eos
$
\rangle
$
}}
;
%\node [anchor=south] (dot1) at ([xshift=0.4em,yshift=-0.7em]h1.south) {\tiny{...}};
%\node [anchor=south] (dot1) at ([xshift=0.4em,yshift=-0.7em]h1.south) {\tiny{...}};
%\node [anchor=south] (dot2) at ([xshift=-0.4em,yshift=-0.7em]h3.south) {\tiny{...}};
%\node [anchor=south] (dot2) at ([xshift=-0.4em,yshift=-0.7em]h3.south) {\tiny{...}};
...
@@ -5473,7 +5476,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
...
@@ -5473,7 +5476,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
%\node [anchor=west,inner sep=2pt] (o5) at ([xshift=0.3em]o4.east) {\tiny{...}};
%\node [anchor=west,inner sep=2pt] (o5) at ([xshift=0.3em]o4.east) {\tiny{...}};
}
}
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<4->
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\visible
<4->
{
\node
[anchor=north,inner sep=2pt] (wt1) at ([yshift=-0.6em]t1.south)
{
\tiny
{
EOS
}}
;
\node
[anchor=north,inner sep=2pt] (wt1) at ([yshift=-0.6em]t1.south)
{
\tiny
{
$
\langle
$
sos
$
\rangle
$
}}
;
}
}
\visible
<6->
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<6->
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\node
[anchor=north,inner sep=2pt] (wt2) at ([yshift=-0.6em]t2.south)
{
\tiny
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How
}}
;
\node
[anchor=north,inner sep=2pt] (wt2) at ([yshift=-0.6em]t2.south)
{
\tiny
{
How
}}
;
...
@@ -5497,7 +5500,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
...
@@ -5497,7 +5500,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
\visible
<8->
{
\visible
<8->
{
\node
[anchor=center,inner sep=2pt] (wo3) at ([yshift=1.2em]o3.north)
{
\tiny
{
you
}}
;
\node
[anchor=center,inner sep=2pt] (wo3) at ([yshift=1.2em]o3.north)
{
\tiny
{
you
}}
;
\node
[anchor=south,inner sep=2pt] (wos3) at (wo3.north)
{
\tiny
{
\textbf
{
[step 3]
}}}
;
\node
[anchor=south,inner sep=2pt] (wos3) at (wo3.north)
{
\tiny
{
\textbf
{
[step 3]
}}}
;
\node
[anchor=center,inner sep=2pt] (wo4) at ([yshift=1.2em]o4.north)
{
\tiny
{
EOS
}}
;
\node
[anchor=center,inner sep=2pt] (wo4) at ([yshift=1.2em]o4.north)
{
\tiny
{
$
\langle
$
eos
$
\rangle
$
}}
;
\node
[anchor=south,inner sep=2pt] (wos4) at (wo4.north)
{
\tiny
{
\textbf
{
[step 4]
}}}
;
\node
[anchor=south,inner sep=2pt] (wos4) at (wo4.north)
{
\tiny
{
\textbf
{
[step 4]
}}}
;
}
}
...
@@ -5606,7 +5609,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
...
@@ -5606,7 +5609,7 @@ x_{l+1} = x_l+\mathcal{F}(x_l)
\node
[anchor=north,rnnnode,fill=blue!30!white] (e2) at ([yshift=-2em]node12.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e2) at ([yshift=-2em]node12.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e3) at ([yshift=-2em]node13.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e3) at ([yshift=-2em]node13.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e4) at ([yshift=-2em]node14.south)
{
\tiny
{}}
;
\node
[anchor=north,rnnnode,fill=blue!30!white] (e4) at ([yshift=-2em]node14.south)
{
\tiny
{}}
;
\node
[anchor=north,inner sep=2pt] (w1) at ([yshift=-1em]e1.south)
{
\tiny
{$
<
$
s
$
>
$}}
;
\node
[anchor=north,inner sep=2pt] (w1) at ([yshift=-1em]e1.south)
{
\tiny
{$
<
$
s
os
$
>
$}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-1em]e2.south)
{
\tiny
{
让
}}
;
\node
[anchor=north,inner sep=2pt] (w2) at ([yshift=-1em]e2.south)
{
\tiny
{
让
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-1em]e3.south)
{
\tiny
{
我们
}}
;
\node
[anchor=north,inner sep=2pt] (w3) at ([yshift=-1em]e3.south)
{
\tiny
{
我们
}}
;
\node
[anchor=north,inner sep=2pt] (w4) at ([yshift=-1em]e4.south)
{
\tiny
{
开始
}}
;
\node
[anchor=north,inner sep=2pt] (w4) at ([yshift=-1em]e4.south)
{
\tiny
{
开始
}}
;
...
...
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