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本文翻譯自deeplearning.ai的深度學(xué)習(xí)課程測(cè)試作業(yè)，近期將逐步翻譯完畢，一共五門(mén)課。

翻譯：黃海廣

本集翻譯Lesson1 Week 2：

Lesson1 Neural Networks and Deep Learning (第一門(mén)課 神經(jīng)網(wǎng)絡(luò)和深度學(xué)習(xí))

Week 2 Quiz - Neural Network Basics（第二周測(cè)驗(yàn) - 神經(jīng)網(wǎng)絡(luò)基礎(chǔ)）

1.What does a neuron compute?(神經(jīng)元節(jié)點(diǎn)計(jì)算什么？)

【 】 A neuron computes an activation function followed by a linear function (z = Wx + b)(神經(jīng)元節(jié)點(diǎn)先計(jì)算激活函數(shù)，再計(jì)算線性函數(shù)(z = Wx + b))

【★】 A neuron computes a linear function (z = Wx + b) followed by an activation function(神經(jīng)元節(jié)點(diǎn)先計(jì)算線性函數(shù)（z = Wx + b），再計(jì)算激活。)

【 】 A neuron computes a function g that scales the input x linearly (Wx +b)(神經(jīng)元節(jié)點(diǎn)計(jì)算函數(shù)g，函數(shù)g計(jì)算(Wx + b))

【 】 A neuron computes the mean of all features before applying the output to an activation function(在將輸出應(yīng)用于激活函數(shù)之前，神經(jīng)元節(jié)點(diǎn)計(jì)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：神經(jīng)元的輸出是a = g(Wx + b)，其中g(shù)是激活函數(shù)(sigmoid，tanh，ReLU，…))

2. Which of these is the “Logistic Loss”?(下面哪一個(gè)是Logistic損失？)

【★】損失函數(shù)：

Note: We are using a cross-entropy loss function.(注：我們使用交叉熵?fù)p失函數(shù)。)

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?(假設(shè)img是一個(gè)（32,32,3）數(shù)組，具有3個(gè)顏色通道：紅色、綠色和藍(lán)色的32x32像素的圖像。如何將其重新轉(zhuǎn)換為列向量？)

Answer（答）:

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

4. Consider the two following random arrays “a” and “b”:(看一下下面的這兩個(gè)隨機(jī)數(shù)組“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”?(請(qǐng)問(wèn)數(shù)組c的維度是多少？)

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）復(fù)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”:(看一下下面的這兩個(gè)隨機(jī)數(shù)組“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”?(請(qǐng)問(wèn)數(shù)組“c”的維度是多少？)

Answer（答）:

The computation cannot happen because the sizes don’t match. It’s going to be “error”!(無(wú)法進(jìn)行計(jì)算，因?yàn)榇笮〔黄ヅ洹?huì)報(bào)錯(cuò)！)

Note:“*” operator indicates element-wise multiplication. Element-wise multiplication requires same dimension between two matrices. It’s going to be an error.(注：運(yùn)算符 “*” 說(shuō)明了按元素乘法來(lái)相乘，但是元素乘法需要兩個(gè)矩陣之間的維數(shù)相同，所以這將報(bào)錯(cuò)，無(wú)法計(jì)算。)

6. Suppose you have??input features per example. Recall that?. What is the dimension of X?(假設(shè)你的每一個(gè)樣本有個(gè)輸入特征，想一下在?中，X的維度是多少？)

Answer（答）:

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

when

, then we have(請(qǐng)注意：一個(gè)比較笨的方法是當(dāng)

的時(shí)候，那么計(jì)算一下，所以我們就有：

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上執(zhí)行矩陣乘法，而“a * b”執(zhí)行元素方式的乘法。)Consider the two following random arrays “a” and “b”:(看一下下面的這兩個(gè)隨機(jī)數(shù)組“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?(請(qǐng)問(wèn)c的維度是多少？)

Answer（答）:

c.shape = (12288, 45), this is a simple matrix multiplication example.( c.shape = (12288, 45), 這是一個(gè)簡(jiǎn)單的矩陣乘法例子。)

8. Consider the following code snippet:(看一下下面的這個(gè)代碼片段：)

# 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?(請(qǐng)問(wèn)要怎么把它們向量化？)

Answer（答）:

c = a + b.T

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

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

What will be c?(請(qǐng)問(wèn)c的維度會(huì)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).(這將會(huì)使用廣播機(jī)制，b會(huì)被復(fù)制三次，就會(huì)變成(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.(看一下下面的計(jì)算圖，J輸出是什么：)

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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