Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place. Commercial Alternative to JupyterHub.

Week 4 Quiz - Deep Neural Networks

1. We use the "cache" in our implementation of forward and backward propagation to pass useful values to the next layer in the forwar propergation. True/False?

• True

• False

📌 The "cache" is used in our implementation to store values computed during forward propagation to be used in backward propagation.

2. Which of the following are "parameters" of a neural network? (Check all that apply.)

• $W^{[l]}$ the weight matrices

• $b^{[l]}$ the bias vector.

📌 The weight matrices and the bias vectors are the parameters of the network.

• $L$ the number of layers of the neural network.

• $g^{[l]}$ the activation functions.

3. Which of the following statements is true?

• The deeper layers of a neural network are typically computing more complex features of the input than the earlier layers.

• The earlier layers of a neural network are typically computing more complex features of the input than the deeper layers.

4. We can not use vectorization to calculate $da^{[l]}$ in backpropagation, we must use a for loop over all the examples.

• True

• False

�� We can use vectorization in backpropagation to calculate $dA^{[l]}$ for each layer.
This computation is done over all the training examples.

5. Assume we store the values for $n^{[l]}$ in an array called layer_dims, as follows: layer_dims = [$n_xn$,4,3,2,1]. So layer 1 has four hidden units, layer 2 has 3 hidden units, and so on. Which of the following for-loop will allow you to initialize the parameters for the model?

• for i range(len(layer_dims)-1:
  parameter['W' + str(i+1)] = np.random.randn(layer_dims[i], layer_dims[i+1]) * 0.01
  parameter['b' + str(i+1)] = np.random.randn(layer_dims[i+1], 1) * 0.01

• ...

📌 This iterates over 0, 1, 2, 3 and assigns to $W^{[l]}$ the shape ($n^{[l]}, n^{[l-1]}$).

6. Consider the following neural network:

What are all the values of $n^{[0]},n^{[1]},n^{[2]},n^{[3]}$ and $n^{[4]}$?

• 4, 4, 3, 2, 1

• ...

📌 The $n^{[l]}$ are the number of units in each layer, notice that $n^{[0]} = n_x$.

7. If L is the number of layers of a neural network then $dZ^{[L]} = A^{[L]} - Y$. True/False?

• True, The gradient of the output layer depends on the difference between the value computed during the forward propagation process and the target values.

• False, The gradient of the output layer depends on the difference between the value computed during the forward propagation process and the target values.

8. There are certain functions with the following properties:

(i) to compute the function using a shallow network circuit, you will need a large network
(where we measure size by the number of logic gates in the network),
but (ii) To compute it using a deep network circuit,
you need only an exponentially smaller network. True/False?

• True

• False

9. Consider the following 2 hidden layers neural network:

Which of the following statements are true? (Check all the apply).

• $W^{[2]}$ will have shape (4,3)

• $W^{[2]}$ will have shape (3,1)

• $W^{[1]}$ will have shape (4,3)

• $W^{[1]}$ will have shape (3,4)

📌 More generally, the shape of $W^{[l]}$ is ($n^{[l]}, n^{[l-1]}$).

• $W^{[2]}$ will have shape (3,4)

• $W^{[2]}$ will have shape (1,3)

• $b^{[1]}$ will have shape (1,3)

• $b^{[1]}$ will have shape (3,1)

📌 More generally, the shape of $b^{[l]}$ is ($n^{[l]}, 1$).

• $b^{[1]}$ will have shape (4,1)

10. Whereas the previous question used a specific network, in the general case what is the dimension of $W^{[l]}$, the weight matrix associated with layer $l$?

• $W^{[l]}$ has shape ($n^{[l-1]}, n^{[l]}$)

• ...