## 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: we generally say that 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](https://en.wikipedia.org/wiki/Cross_entropy#Cross-entropy_error_function_and_logistic_regression).
Note: this is the logistic loss you've seen in lecture!
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)`
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.
```
J = u + v - w
= a * b + a * c - (b + c)
= a * (b + c) - (b + c)
= (a - 1) * (b + c)
```
Answer: `(a - 1) * (b + c)`