神经网络为什么需要激活函数

激活函数的本质

本身神经网络是线性函数的叠加,但为了能更加的拟合多种函数,必须增加非线性函数。激活函数是来向神经网络中引入非线性因素的,通过激活函数,神经网络就可以拟合各种曲线。

例子

假如我的任务是:将下面的这幅图中的三角形和圆形分开,也就是一个典型的二分类问题。

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

我们用肉眼能很轻松的得出结论:无法用一条直线将这两种图形完全分开,因为数据本身就是线性不可分的。

那么如何才能完美解决这个问题呢?我们试一试多感知器的表现。

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

如果仔细观察,你就会发现,多感知器形成的方程是一条直线,上面已经说了,该问题是线性不可分的,所以多感知器不能解决这个问题。

接下来,就让我们看看激活函数能不能解决。

在每一层叠加完后,我们为输出与输入之间加上一个激活函数,此时的方程就变成了这样:

Untitled

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

此时,我们就引入了非线性因素,这时的函数表达就极为丰富了。让我们再看一看引入激活函数后的多感知器。