Neural Networks and Deep Learning 学习笔记(一)

1. 为什么假设w⋅x≡∑jwjxj后，w与x就变成向量了？

The first change is to write ∑jwjxj as a dot product, w⋅x≡∑jwjxj, where w and x are vectors whose components are the weights and inputs, respectively.

向量的点积为标量，两个同样维度的向量的点积恰好是每个维度积的累加，以上变换可用公式表示为

(w1,w2,w3,...,wj)⋅(x1,x2,x3,...,xj)=w1x1+w2x2+w3x3+...+wjxj=∑jwjxj

2. 用perceptron实现‘与非’、‘与’、‘或’门。

we have a perceptron with two inputs, each with weight −2, and an overall bias of 3. Then we see that input 00 produces output 1, since (−2)∗0+(−2)∗0+3=3 is positive. Here, I’ve introduced the ∗ symbol to make the multiplications explicit. Similar calculations show that the inputs 01 and 10 produce output 1. But the input 11 produces output 0, since (−2)∗1+(−2)∗1+3=−1 is negative. And so our perceptron implements a NAND gate!

以上是电子书中实现的与非门。以此类推实现与门的方式可以为bias设置为-3，x1与x2的权重设置为2，则输入00，计算为 2×0+2×0+(−3)=−3，为负。输入01，计算为 2×0 +2×1+(−3)=−1 为负。输入11，2×1+2×1+(−3)=1 为正。实现与门。

实现或门的bias设置为-1，权重设置为2。则输入00，输出为负，输入01，输出为正，输入11，输出为正。

3. exp是啥？

exp是以e为底的自然对数，特点是对ex求导还是ex。

4. 这个偏导数是怎么得到的（未解决）?

Δoutput≈∑j∂output∂wjΔwj+∂output∂bΔb