1. 為什麼假設w⋅x≡∑jwjxj後，w與x就變成向量了？

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.

向量的點積為標量，兩個同樣維度的向量的點積恰好是每個維度積的累加，以上變換可用公式表示為

2. 用perceptron實現‘與非’、‘與’、‘或’門。

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!

以上是電子書中實現的與非門。以此類推實現與門的方式可以為bias設定為-3，x1與x2的權重設定為2，則輸入00，計算為 2×0+2×0+(−3)=−3，為負。輸入01，計算為 2×0+2×1+(−3)=−1 為負。輸入11，2×1+2×1+(−3)=1 為正。實現與門。

實現或門的bias設定為-1，權重設定為2。則輸入00，輸出為負，輸入01，輸出為正，輸入11，輸出為正。

3. exp是啥？

exp是以e為底的自然對數，特點是對ex求導還是e

4. 這個偏導數是怎麼得到的（未解決）?

Δoutput≈∑j∂output∂wjΔwj+∂output∂bΔb