# 感知机（Perceptron）

2018年4月20日 / 949次阅读

Today, it's more common to use other models of artificial neurons - in this book, and in much modern work on neural networks, the main neuron model used is one called the sigmoid neuron.

In the example shown the perceptron has three inputs, $$x_1, x_2, x_3$$. In general it could have more or fewer inputs. Rosenblatt proposed a simple rule to compute the output. He introduced weights, $$w_1,w_2,\ldots$$, real numbers expressing the importance of the respective inputs to the output. The neuron's output, 0 or 1, is determined by whether the weighted sum $$\sum_j w_j x_j$$ is less than or greater than some threshold value. Just like the weights, the threshold is a real number which is a parameter of the neuron. To put it in more precise algebraic terms:

$$\begin{eqnarray} \mbox{output} & = & \left\{ \begin{array}{ll} 0 & \mbox{if } \sum_j w_j x_j \leq \mbox{ threshold} \\ 1 & \mbox{if } \sum_j w_j x_j > \mbox{ threshold} \end{array} \right. \end{eqnarray}$$

$$x_1, x_2, x_3$$是输入，0 or 1，输出也是0 or 1，用来模拟人类的神经元，应该就是对应兴奋和抑制的两种状态。感知机的模型中，只有权重是一个实数。

x和w的乘积和，可以写成两个向量的内积形式：$$w \cdot x \equiv \sum_j w_j x_j$$

$$\begin{eqnarray} \mbox{output} = \left\{ \begin{array}{ll} 0 & \mbox{if } w\cdot x + b \leq 0 \\ 1 & \mbox{if } w\cdot x + b > 0 \end{array} \right. \end{eqnarray}$$

You can think of the bias as a measure of how easy it is to get the perceptron to output a 1. Or to put it in more biological terms, the bias is a measure of how easy it is to get the perceptron to fire. For a perceptron with a really big bias, it's extremely easy for the perceptron to output a 1. But if the bias is very negative, then it's difficult for the perceptron to output a 1.

fire这个词很有趣，让一个感知机fire。

### 留言区

《感知机（Perceptron）》有6条留言

• 麦新杰

大脑中的神经元真的是 all or none ？ []

• 麦新杰

The initial idea of the perceptron dates back to the work of Warren McCulloch and Walter Pitts in 1943, who drew an analogy between biological neurons and simple logic gates with binary outputs. 所以，从一开始，就在用biological neuron跟logic gates做类比，因此perceptron的输入输出才是非0即1的。 []

• 麦新杰

思维的过程，难道就是在做决策吗？Perceptron可以看作是一个决策模型，不同条件在不同权重下，产生一个二元结果。思维不应该是做决策，思维更像是在进行不间断的模式匹配。 []

• 麦新杰

Perceptron的输入和输出都是0或1，只有w和b是R。从这个角度看，这是一个简化了输入输出的模型。 []

• 麦新杰

权重和阈值，都是real number []

• 麦新杰

每个感知机有多个输入，但是只有一个输出，上图多层的网络，中间的感知机有多个输出箭头，只是表示其唯一的输出被多个其它感知机使用。 []

Ctrl+D 收藏本页