C1M2

What does a neuron compute?
Что вычисляет нейрон?

• 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

Which of these is the "Logistic Loss"?

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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, 2))

• • x = img.reshape((32 32 2, 1))

• • x = img.reshape((32 32 3, 1))

• • x = img.reshape((32 33 3, 1))

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).

• b (column vector) is copied 3 times so that it can be summed to each column of a. Therefore, c.shape = (1, 3).

• b (column vector) is copied 3 times so that it can be summed to each column of a. Therefore, c.shape = (0, 4).

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

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"?

• c.shape = (4, 3) because element-wise multiplication is applied.

• c.shape = (4, 2) because NumPy automatically adjusts shapes for multiplication.

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

• c.shape = (3, 2) because broadcasting automatically reshapes a.

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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

• c.shape = (12288, 46), this is a simple matrix multiplication example

• c.shape = (12200, 45), this is a simple matrix multiplication example

• c.shape = (150, 45), this is a simple matrix multiplication example

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 = a2+ 3.T

• c = a + b.T

• c = a + b

• c = a + b3

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

• This will invoke broadcasting, so b is copied three times to become (3,3), and ∗ is an element-wise product so c.shape = (3, 2)

• 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).

• This will invoke broadcasting, so b is copied three times to become (3,3), and ∗ is an element-wise product

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