## 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)`