Neural Networks and Deep Learning week2 Neural Network Basics

看别人见解违法coursera荣誉，看懂和做对是两码事
What does a neuron compute?

A neuron computes a linear function (z = Wx + b) followed by an activation function
A neuron computes the mean of all features before applying the output to an activation function
A neuron computes an activation function followed by a linear function (z = Wx + b)
A neuron computes a function g that scales the input x linearly (Wx + b)

神经元做什么，前半部分线性回归，后半部分非线性化变换（**函数）

Which of these is the "Logistic Loss"?

希望你还记得熵， Y=-ylogy-(1-y)log(1-y)

Suppose img is a (32,32,3) array, representing a 32x32 image with 3 color channels red, green and blue. How do you reshape this into a column vector?

x = img.reshape((32*32*3,1))
x = img.reshape((3,32*32))
x = img.reshape((1,32*32,*3))
x = img.reshape((32*32,3))

图片如何变换，我们经常用的是列向量，所以 32*32*3，1，默认列向量各领域通用

Consider the two following random arrays "a" and "b":What will be the shape of "c"？

a = np.random.randn(2, 3) # a.shape = (2, 3)
b = np.random.randn(2, 1) # b.shape = (2, 1)
c = a + b

c.shape = (3, 2)
c.shape = (2, 3)
The computation cannot happen because the sizes don't match. It's going to be "Error"!
c.shape = (2, 1)

python有广播的性质，（2，3）广播性质就是方便矩阵加常数

Consider the two following random arrays "a" and "b":What will be the shape of "c"?

a = np.random.randn(4, 3) # a.shape = (4, 3)
b = np.random.randn(3, 2) # b.shape = (3, 2)
c = a*b

c.shape = (3, 3)
The computation cannot happen because the sizes don't match. It's going to be "Error"!
c.shape = (4, 3)
c.shape = (4,2)

np.dot和 * 是有区别的，一个是矩阵乘法，一个是数乘，这两个大小不匹配，没法点对点乘法

Suppose you have n_xnx input features per example. Recall that Neural Networks and Deep Learning week2 Neural Network Basics What is the dimension of X?

(m,1)

(1,m)

Neural Networks and Deep Learning week2 Neural Network Basics

x是列向量，X写成这样，那就只能是nx（x向量的特征数），m（x向量的个数）

Recall that "np.dot(a,b)" performs a matrix multiplication on a and b, whereas "a*b" performs an element-wise multiplication.

Consider the two following random arrays "a" and "b":What is the shape of c?

a = np.random.randn(12288, 150) # a.shape = (12288, 150)
b = np.random.randn(150, 45) # b.shape = (150, 45)
c = np.dot(a,b)

c.shape = (12288, 150)
The computation cannot happen because the sizes don't match. It's going to be "Error"!
c.shape = (150,150)
c.shape = (12288, 45)

矩阵乘法前行*后列，前面的列数=后面的行数，大小前行数*后列数

Consider the following code snippet:How do you vectorize this?

# a.shape = (3,4)
# b.shape = (4,1)

for i in range(3):
for j in range(4):
c[i][j] = a[i][j] + b[j]

c = a.T + b.T
c = a.T + b
c = a + b.T
c = a + b

有问题建议画图，画图是一个好习惯，可以捋清自己的思路

Consider the following code:What will be c? (If you’re not sure, feel free to run this in python to find out).

a = np.random.randn(3, 3)
b = np.random.randn(3, 1)
c = a*b

This will invoke broadcasting, so b is copied three times to become (3,3), and *∗ is an element-wise product so c.shape will be (3, 3)
This will invoke broadcasting, so b is copied three times to become (3, 3), and *∗ invokes a matrix multiplication operation of two 3x3 matrices so c.shape will be (3, 3)
This will multiply a 3x3 matrix a with a 3x1 vector, thus resulting in a 3x1 vector. That is, c.shape = (3,1).
It will lead to an error since you cannot use “*” to operate on these two matrices. You need to instead use np.dot(a,b)

python 的广播性质

Consider the following computation graph.

第 10 个问题

Consider the following computation graph. What is the output J?

Neural Networks and Deep Learning week2 Neural Network Basics

J = (c - 1)*(b + a)
J = (a - 1) * (b + c)
J = a*b + b*c + a*c
J = (b - 1) * (c + a)

基础计算，都不需要看书的，毕竟都没涉及到偏导的重要公式

Neural Networks and Deep Learning week2 Neural Network Basics

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