吴恩达《深度学习》-课后测验-第一门课 (Neural Networks and Deep Learning)-Week 2 - Neural Network Basics（第二周测验 - 神经网络基础）

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)

答案

【【★】 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。)

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：\(L(\hat{y}^{(i)},y^{(i)})=-y^{(i)}log\hat{y}^{(i)}-(1-y^{(i)})log(1-\hat{y}^{(i)})\)

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？)

答案

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？)

答案

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？)

答案

The computation cannot happen because the sizes don’t match. It’s going to be “error”! 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 𝒏𝒙 input features per example. Recall that \(𝑿 = [𝒙^{(𝟏)} , 𝒙^{(𝟐)} … 𝒙^{(𝒎)} ]\). What is the dimension of X?(假设你的每一个样本有𝒏𝒙个输入特征，想一下在\(𝑿 = [𝒙^{(𝟏)} , 𝒙^{(𝟐)} … 𝒙^{(𝒎)} ]\)中，X 的维度是多少？)

答案

(𝑛𝑥, 𝑚)

\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？)

答案

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？)

答案

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？ )

答案

c.shape = (3, 3)

This will invoke broadcasting, so b is copied three times to become (3,3), and * is an elementwise 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：)