Week 2 Quiz – Neural Network Basics
Week 2 Quiz – Neural Network Basics
Week 2 Quiz – Neural Network Basics

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: we generally say that the output of a neuron is a = g(Wx + b) where g is the activation function (sigmoid, tanh, ReLU, …).


Which of these is the “Logistic Loss”?
 Check here.
Note: this is the logistic loss you’ve seen in lecture!

Suppose img is a (32,32,3) array, representing a 32×32 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))

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)
. 
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 elementwise multiplication. Elementwise multiplication requires same dimension between two matrices. It’s going to be an error.

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)

Recall that
np.dot(a,b)
performs a matrix multiplication on a and b, whereasa*b
performs an elementwise 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. 
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

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 elementwise product so
c.shape = (3, 3)
. 
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)