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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4.2 损失函数
87
4.2.2
交叉熵误差
除了均方误差之外，交叉熵误差（
cross entropy error
）也经常被用作损
失函数。交叉熵误差如下式所示。
（4.2）
这里，
log
表示以
e
为底数的自然对数（
log
e
）。 y
k
是神经网络的输出，t
k
是
正确解标签。并且，t
k
中只有正确解标签的索引为 1，其他均为 0（
one-hot
表 示 ）。
因此，式（4.2）实际上只计算对应正确解标签的输出的自然对数。比如，假设
正确解标签的索引是“2”，与之对应的神经网络的输出是0.6，则交叉熵误差
是
−log
0.6
=
0.51； 若“ 2”对应的输出是 0.1，则交叉熵误差为
−log
0.1
=
2.30。
也就是说，交叉熵误差的值是由正确解标签所对应的输出结果决定的。
自然对数的图像如图4
-
3 所示。
图4-3 自然对数
y = log x
的图像
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