理论知识英文见 ：http://neuralnetworksanddeeplearning.com/chap1.html
第三节 sigmoid neurons
上一节我们聊到了P模，我们学习到了如何运用P模进行人生伴侣的选择。我们学习到了权重(weight)和门槛(threshold)，总之，请凭空设想一个超级大的安检机器，然后接着设想我们把对象放到了机器的运输带上面，再接着设想安检人员就是我们自己、我们的朋友以及我们的长辈，这台安检机器负责接收安检人员的所有指令（权重和门槛），OK，剩下的就是，请耐心等待最终结果。
但是，如果安检进行到一半，某一个安检人员的权重和门槛变了呢？例如，我们会经常听到“其实身高也没有那么重要”；或者“我对长相的要求降低了”等等。
让我们来详细分析一下这个事情，让我们把找对象这个问题抽象到P模的一个识别问题，详情如下（注意bias就是变形了的threshold）：
For example, the inputs to the network might be the raw pixel data from a scanned, handwritten image of a digit. And we'd like the network to learn weights and biases so that the output from the network correctly classifies the digit.
我们再来看看如果让P模完成这个任务会产生怎样的结果：
In fact, a small change in the weights or bias of any single perceptron in the network can sometimes cause the output of that perceptron to completely flip, say from 0 to 1. That flip may then cause the behaviour of the rest of the network to completely change in some very complicated way.
这就好比我们的条件降低了多少，我们就要求对方回头多少，这个这个，在P模这里确实无法实现。
P模的任务处理结果是颠覆性的，“是”变为“不是”，“不是”变为“是”。更为可怕的是，整个系统也变得异常复杂而没有理智了。
困难写尽，只是为了突出它----“sigmoid neuron”。
让我们暂且称“sigmoid neuron”其为“sn”模，s模最厉害的地方就是它能够平衡weights、bias和最终输出结果的变化。原文如下：
We can overcome this problem by introducing a new type of artificial neuron called a sigmoid neuron. Sigmoid neurons are similar to perceptrons, but modified so that small changes in their weights and bias cause only a small change in their output. That's the crucial fact which will allow a network of sigmoid neurons to learn.
如果用数学来解释，我们可以发现一个线性关系如下：
Δoutput is a linear function of the changes Δwj and in the weights and bias.
S模公示
S模还有一个优势，那就是它能够克服p模是就是是不是就是不是的缺点，s模的输入值和输出值都是介于0到1之间的一个数，即S模给出的最终意见仅仅是一个导向意见。
Just like a perceptron, the sigmoid neuron has inputs, x1,x2,…x1,x2,…. But instead of being just 0 or 1, these inputs can also take on any values between 0and 1. So, for instance, 0.638…0.638… is a valid input for a sigmoid neuron. Also just like a perceptron, the sigmoid neuron has weights for each input, w1,w2,…w1,w2,…, and an overall bias, b. But the output is not 0 or 1.
作者提出，对于“导向”我们也可以建立一套规则来使得“导向”服务于我们的工作，举例如下：
But in practice we can set up a convention to deal with this, for example, by deciding to interpret any output of at least 0.5 as indicating a "9", and any output less than 0.5 as indicating "not a 9".
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