吴恩达深度学习学习笔记——C1W2——神经网络基础——练习题

因为文字版排版未优化，带有上下标的公式阅读性较差，先贴出截图。

文字版本在截图之后。

截图版：

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

Note: "*" operator indicates element-wise multiplication. Element-wise multiplication requires same dimension between two matrices. It's going to be an error.

Ans: C（注意：截图所示答案D错误，正确答案为C）

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)

Ans: D

Ans: B

文字版：

1. What does a neuron compute?

A neuron computes an activation function followed by a linear function (z = Wx + b)
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"?

L(i)(y^(i),y(i))=y(i)log(y^(i))+(1−y(i))log(1−y^(i))

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 ∗ is an element-wise product so c.shape = (3, 3).

10. Consider the following computation graph.

What is the output J?

J = u + v - w

  = a * b + a * c - (b + c)

  = a * (b + c) - (b + c)

  = (a - 1) * (b + c)

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