导语

本文翻译自deeplearning.ai的深度学习课程测试作业，近期将逐步翻译完毕，一共五门课。

翻译：黄海广

本集翻译Lesson1 Week 2：

Lesson1 Neural Networks and Deep Learning (第一门课 神经网络和深度学习)

Week 2 Quiz - Neural Network Basics（第二周测验 - 神经网络基础）

1.What does a neuron compute?(神经元节点计算什么？)

【 】 A neuron computes an activation function followed by a linear function (z = Wx + b)(神经元节点先计算激活函数，再计算线性函数(z = Wx + b))

【★】 A neuron computes a linear function (z = Wx + b) followed by an activation function(神经元节点先计算线性函数（z = Wx + b），再计算激活。)

【 】 A neuron computes a function g that scales the input x linearly (Wx +b)(神经元节点计算函数g，函数g计算(Wx + b))

【 】 A neuron computes the mean of all features before applying the output to an activation function(在将输出应用于激活函数之前，神经元节点计算所有特征的平均值)

Note: The output of a neuron is a = g(Wx + b) where g is the activation function (sigmoid, tanh, ReLU, …).(注：神经元的输出是a = g(Wx + b)，其中g是激活函数(sigmoid，tanh，ReLU，…))

2. Which of these is the “Logistic Loss”?(下面哪一个是Logistic损失？)

【★】损失函数：

Note: We are using a cross-entropy loss function.(注：我们使用交叉熵损失函数。)

3. 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?(假设img是一个（32,32,3）数组，具有3个颜色通道：红色、绿色和蓝色的32x32像素的图像。如何将其重新转换为列向量？)

Answer（答）:

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

4. Consider the two following random arrays “a” and “b”:(看一下下面的这两个随机数组“a”和“b”：)

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

What will be the shape of “c”?(请问数组c的维度是多少？)

Answer（答）:

c.shape = (2, 3)

b (column vector) is copied 3 times so that it can be summed to each column of a. Therefore, c.shape = (2, 3).( B（列向量）复制3次，以便它可以和A的每一列相加，所以：c.shape = (2, 3))

5. Consider the two following random arrays “a” and “b”:(看一下下面的这两个随机数组“a”和“b”)

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

What will be the shape of “c”?(请问数组“c”的维度是多少？)

Answer（答）:

The computation cannot happen because the sizes don’t match. It’s going to be “error”!(无法进行计算，因为大小不匹配。将会报错！)

Note:“*” operator indicates element-wise multiplication. Element-wise multiplication requires same dimension between two matrices. It’s going to be an error.(注：运算符 “*” 说明了按元素乘法来相乘，但是元素乘法需要两个矩阵之间的维数相同，所以这将报错，无法计算。)

6. Suppose you have  input features per example. Recall that . What is the dimension of X?(假设你的每一个样本有个输入特征，想一下在 中，X的维度是多少？)

Answer（答）:

Note: A stupid way to validate this is use the formula

when, then we have(请注意：一个比较笨的方法是当的时候，那么计算一下，所以我们就有：

7. Recall that np.dot(a,b) performs a matrix multiplication on a and b, whereas a*b performs an element-wise multiplication.(回想一下，np.dot（a，b）在a和b上执行矩阵乘法，而“a * b”执行元素方式的乘法。)Consider the two following random arrays “a” and “b”:(看一下下面的这两个随机数组“a”和“b”：)

• 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)

  What is the shape of c?(请问c的维度是多少？)

Answer（答）:

c.shape = (12288, 45), this is a simple matrix multiplication example.( c.shape = (12288, 45), 这是一个简单的矩阵乘法例子。)

8. Consider the following code snippet:(看一下下面的这个代码片段：)

# 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]

How do you vectorize this?(请问要怎么把它们向量化？)

Answer（答）:

c = a + b.T

9. Consider the following code:(看一下下面的代码：)

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

What will be c?(请问c的维度会是多少？)

Answer（答）:

c.shape = (3, 3)

This will invoke broadcasting, so b is copied three times to become (3,3), and * is an element-wise product so c.shape = (3, 3).(这将会使用广播机制，b会被复制三次，就会变成(3,3)，再使用元素乘法。所以：c.shape = (3, 3).)

10. Consider the following computation graph,What is the output J.(看一下下面的计算图，J输出是什么：)

J = u + v - w
= a * b + a * c - (b + c)
= a * (b + c) - (b + c)
= (a - 1) * (b + c)

Answer（答）:

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

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