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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第 4章 神经网络的学习
98
>>> numerical_diff(function_1, 5)
0.1999999999990898
>>> numerical_diff(function_1, 10)
0.2999999999986347
这里计算的导数是f
(
x
)
相对于x 的变化量，对应函数的斜率。另外，
f
(
x
) =
0.01x
2
+
0.1x 的解析解是
。因 此，在 x
=
5 和
x
=
10 处，“真的导数”分别为0.2和 0.3。和上面的结果相比，我们发现虽然
严格意义上它们并不一致，但误差非常小。实际上，误差小到基本上可以认
为它们是相等的。
现在，我们用上面的数值微分的值作为斜率，画一条直线。结果如图 4
-
7
所示，可以确认这些直线确实对应函数的切线（源代码在
ch04/gradient_1d.
py
中 ）。
图4-7
x
= 5、
x
= 10 处的切线：直线的斜率使用数值微分的值
f ( x )
f ( x )
4.3.3
偏导数
接下来，我们看一下式
(
4.6
)
表示的函数。虽然它只是一个计算参数的
平方和的简单函数，但是请注意和上例不同的是，这里有两个变量。
（4.6）
这个式子可以用
Python
来实现，如下所示。
def function_2(x):
4.3 数值微分
99
return x[0]**2 + x[1]**2 ...
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