深入浅出神经网络与深度学习 (迈克尔·尼尔森（Michael Nielsen）) Chapter1

1.1 感知机perceptron

20 世纪五六十年代，科学家Frank Rosenblatt 发明了感知机，其受到了 Warren McCulloch 和 Walter Pitts 早期研究的影响。

what's weighted sum in perceptron?

In the context of the perceptron algorithm, the weighted sum refers to the linear combination of the input features and their corresponding weights. Specifically, given an input vector x = [x1, x2, ..., xn] and weight vector w = [w1, w2, ..., wn], the weighted sum is computed as:

z = w1*x1 + w2*x2 + ... + wn*xn

This is the linear combination of the input features x with their corresponding weights w. The weighted sum is then passed through an activation function, typically a step function, to produce the output of the perceptron. In other words, the weighted sum determines whether the perceptron should fire (output 1) or not (output 0) based on the input.

The weighted sum can also be expressed in vector notation as the dot product of the input vector x and the weight vector w:

z = w.dot(x)

In this form, the weighted sum is a concise way of representing the linear combination of the input features and their corresponding weights.