# 感知机（Perceptron）

2018年4月20日 / 252次阅读

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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2条留言

• 麦新杰

权重和阈值，都是real number [回复]

• 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。 [回复]

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