【中英】【吳恩達課後測驗】Course 1 - 神經網絡和深度學習 - 第二週測驗

【中英】【吳恩達課後測驗】Course 1 - 神經網絡和深度學習 - 第二週測驗

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上一篇：【課程1 - 第一週測驗】※※※※※ 【回到目錄】※※※※※下一篇：【課程1 - 第二週編程作業】

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第2周測驗 - 神經網絡基礎

1. 神經元節點計算什麼？

   • 【 】神經元節點先計算激活函數，再計算線性函數(z = Wx + b)

   • 【★】神經元節點先計算線性函數（z = Wx + b），再計算激活。

   • 【 】神經元節點計算函數g，函數g計算(Wx + b)。

   • 【 】在 將輸出應用於激活函數之前，神經元節點計算所有特徵的平均值

     請注意：神經元的輸出是a = g（Wx + b），其中g是激活函數（sigmoid，tanh，ReLU，…）。

2. 下面哪一個是Logistic損失？

   • 點擊這裏.

   請注意：我們使用交叉熵損失函數。

3. 假設img是一個（32,32,3）數組，具有3個顏色通道：紅色、綠色和藍色的32x32像素的圖像。 如何將其重新轉換爲列向量？

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

4. 看一下下面的這兩個隨機數組“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

   請問數組c的維度是多少？

   答： B（列向量）複製3次，以便它可以和A的每一列相加，所以：c.shape = (2, 3)

5. 看一下下面的這兩個隨機數組“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

   請問數組“c”的維度是多少？

   答：運算符 “*” 說明了按元素乘法來相乘，但是元素乘法需要兩個矩陣之間的維數相同，所以這將報錯，無法計算。

6. 假設你的每一個實例有n_x個輸入特徵，想一下在X=[x^(1), x^(2)…x^(m)]中，X的維度是多少？

   答： (n_x, m)

   請注意：一個比較笨的方法是當l=1的時候，那麼計算一下Z(l)=W(l)A(l)$Z^{(l)}=W^{(l)}{A}^{(l)}$ ，所以我們就有：

   • A(1)$A^{(1)}$ = X
   • X.shape = (n_x, m)
   • Z(1)$Z^{(1)}$ .shape = (n(1)$n^{(1)}$ , m)
   • W(1)$W^{(1)}$ .shape = (n(1)$n^{(1)}$ , n_x)

7. 回想一下，np.dot（a，b）在a和b上執行矩陣乘法，而`a * b’執行元素方式的乘法。

   看一下下面的這兩個隨機數組“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)

   請問c的維度是多少？

   答： c.shape = (12288, 45), 這是一個簡單的矩陣乘法例子。

8. 看一下下面的這個代碼片段：

   
   # 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]

   請問要怎麼把它們向量化？

   答：c = a + b.T

9. 看一下下面的代碼：

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

   請問c的維度會是多少？
   答：這將會使用廣播機制，b會被複制三次，就會變成(3,3)，再使用元素乘法。所以： c.shape = (3, 3).

10. 看一下下面的計算圖：

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

    答: (a - 1) * (b + c)
    博主注：由於弄不到圖，所以很抱歉。

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上一篇：【第1周測驗-深度學習簡介】※※※※※ 【回到目錄】※※※※※下一篇：【具有神經網絡思維的Logistic迴歸】

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Week 2 Quiz - Neural Network Basics

1. What does a neuron compute?

   • [ ] A neuron computes an activation function followed by a linear function (z = Wx + b)

   • [x] A neuron computes a linear function (z = Wx + b) followed by an activation function

   • [ ] A neuron computes a function g that scales the input x linearly (Wx + b)

   • [ ] A neuron computes the mean of all features before applying the output to an activation function

   Note: The output of a neuron is a = g(Wx + b) where g is the activation function (sigmoid, tanh, ReLU, …).

2. Which of these is the “Logistic Loss”?

   • Check here.

   Note: We are using a cross-entropy loss function.

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?

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

4. Consider the two following random arrays “a” and “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”?

   b (column vector) is copied 3 times so that it can be summed to each column of a. Therefore, c.shape = (2, 3).

5. Consider the two following random arrays “a” and “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”?

   “*” operator indicates element-wise multiplication. Element-wise multiplication requires same dimension between two matrices. It’s going to be an error.

6. Suppose you have n_x input features per example. Recall that X=[x^(1), x^(2)…x^(m)]. What is the dimension of X?

   (n_x, m)

   Note: A stupid way to validate this is use the formula Z^(l) = W^(l)A^(l) when l = 1, then we have

   • A^(1) = X
   • X.shape = (n_x, m)
   • Z^(1).shape = (n^(1), m)
   • W^(1).shape = (n^(1), n_x)

7. 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”:

   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?

   c.shape = (12288, 45), this is a simple matrix multiplication example.

8. Consider the following code snippet:

   
   # 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?

   c = a + b.T

9. Consider the following code:

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

   What will be c?

   This will invoke broadcasting, so b is copied three times to become (3,3), and 鈭� is an element-wise product so c.shape = (3, 3).

10. Consider the following computation graph.

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

    Answer: (a - 1) * (b + c)