July 2018
Intermediate to advanced
310 pages
8h 21m
Chinese
Content preview from 深度学习入门 : 基于Python的理论与实现
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附录 A Softmax-with-Loss层的计算图
270
A.2
反向传播
首先是
Cross Entropy Error
层的反向传播。
Cross Entropy Error
层的
反向传播可以画成图
A-
4 那样。
图A-4 交叉熵误差的反向传播
log
log
log
L
t
1
y
1
t
2
y
2
t
3
y
3
−1
log y
1
log y
2
log y
3
t
1
log y
1
t
2
log y
2
t
3
log y
3
t
1
log y
1
+ t
2
log y
2
+ t
3
log y
3
1−1−1
−1
−1
−t
1
−t
2
−
t
3
t
1
−
y
1
t
2
−
y
2
t
3
−
y
3
求这个计算图的反向传播时，要注意下面几点。
•
反向传播的初始值（图 A-4中最右边的值）是 1（因 为 ）。
•
“
×
”节点的反向传播将正向传播时的输入值翻转，乘以上游传过来的
导数后，再传给下游。
•
“
+
”节点将上游传来的导数原封不动地传给下游。
•
“log”节点的反向传播遵从下式。
A.2 反向传播
271
遵从以上几点，就可以轻松求得
Cross Entropy Error
的反向传播。结
果
是传给
Softmax
层的反向传播的输入。
下面是
Softmax
层的反向传播的步骤。因为
Softmax
层有些复杂，所以
我们来逐一进行确认。
步骤1
exp
exp
exp
S
a
1
a
2
a
3
=
S
1
exp(a
1
)
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