Coursera: Machine Learning (Week 4) Quiz - Neural Networks: Representation| Andrew NG

byAkshay Daga (APDaga) -يونيو 06, 2021

11

▸ Neural Networks - Representation :

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Which of the following statements are true? Check all that apply.
- Any logical function over binary-valued (0 or 1) inputs x1 and x2 can be (approximately) represented using some neural network.
- Suppose you have a multi-class classification problem with three classes, trained with a 3 layer network. Let $a^{(3)}_1 = (h_\theta(x))_1$ be the activation of the first output unit, and similarly $a^{(3)}_2 = (h_\theta(x))_2$ and $a^{(3)}_3 = (h_\theta(x))_3$ . Then for any input x, it must be the case that $a^{(3)}_1 + a^{(3)}_2 + a^{(3)}_3 = 1$ .
- A two layer (one input layer, one output layer; no hidden layer) neural network can represent the XOR function.
- The activation values of the hidden units in a neural network, with the sigmoid activation function applied at every layer, are always in the range (0, 1).

Consider the following neural network which takes two binary-valued inputs
$x_1,x_2 \ \epsilon \ \{0,1\}$ and outputs $h_\theta(x)$ . Which of the following logical functions does it (approximately) compute?
- AND
  This network outputs approximately 1 only when both inputs are 1.
- NAND (meaning “NOT AND”)
- OR
- XOR (exclusive OR)

Consider the following neural network which takes two binary-valued inputs
$x_1,x_2 \ \epsilon \ \{0,1\}$ and outputs $h_\theta(x)$ . Which of the following logical functions does it (approximately) compute?
- AND
- NAND (meaning “NOT AND”)
- OR
  This network outputs approximately 1 when atleast one input is 1.
- XOR (exclusive OR)

Consider the neural network given below. Which of the following equations correctly computes the activation $a_1^{(3)}$ ? Note: $g(z)$ is the sigmoid activation
function.
- $a_1^{(3)} = g(\theta_{1,0}^{(2)}a_0^{(2)}+\theta_{1,1}^{(2)}a_1^{(2)}+\theta_{1,2}^{(2)}a_2^{(2)})$
  Thiscorrectly uses the first row of $\theta^{(2)}$ and includes the “+1” term of $a_0^{(2)}$ .
- $a_1^{(3)} = g(\theta_{1,0}^{(2)}a_0^{(1)}+\theta_{1,1}^{(2)}a_1^{(1)}+\theta_{1,2}^{(2)}a_2^{(1)})$
- $a_1^{(3)} = g(\theta_{1,0}^{(1)}a_0^{(2)}+\theta_{1,1}^{(1)}a_1^{(2)}+\theta_{1,2}^{(1)}a_2^{(2)})$
- $a_1^{(3)} = g(\theta_{2,0}^{(2)}a_0^{(2)}+\theta_{2,1}^{(2)}a_1^{(2)}+\theta_{2,2}^{(2)}a_2^{(2)})$

You have the following neural network:

You’d like to compute the activations of the hidden layer $a^{(2)} \ \epsilon \ R^3$ . One way to do
so is the following Octave code:

You want to have a vectorized implementation of this (i.e., one that does not use for loops). Which of the following implementations correctly compute ? Check all
that apply.
- z = Theta1 * x; a2 = sigmoid (z);
  This version computes $a^{(2)} = g(\theta^{(1)}x)$ correctly in two steps , first the multiplication and then the sigmoid activation.
- a2 = sigmoid (x * Theta1);
- a2 = sigmoid (Theta2 * x);
- z = sigmoid(x); a2 = sigmoid (Theta1 * z);

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You are using the neural network pictured below and have learned the parameters $\theta^{(1)} = \begin{bmatrix} 1 & 1 & 2.4\\ 1 & 1.7 & 3.2 \end{bmatrix}$ (used to compute $a^{(2)}$ ) and $\theta^{(2)} = \begin{bmatrix} 1 & 0.3 & -1.2 \end{bmatrix}$ (used to compute $a^{(3)}$ as a function of $a^{(2)}$ ). Suppose you swap the parameters for the first hidden layer between its two units so $\theta^{(1)} = \begin{bmatrix} 1 & 1.7 & 3.2 \\ 1 & 1 & 2.4 \end{bmatrix}$ and also swap the output layer so $\theta^{(2)} = \begin{bmatrix} 1 & -1.2 & 0.3 \end{bmatrix}$ . How will this change the value of the output $h_\theta(x)$ ?
- It will stay the same.
  Swapping $\theta^{(1)}$ swaps the hidden layers output $a^{(2)}$ . But the swap of $\theta^{(2)}$ cancels out the change, so the output will remain unchanged.
- It will increase.
- It will decrease
- Insufficient information to tell: it may increase or decrease.

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Feel free to ask doubts in the comment section. I will try my best to answer it.
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- APDaga DumpBox

11 تعليقات

Juan Bomfim30 يوليو 2020 في 8:52 م
Why I can't represent XOR function without hidden layers? If I have a case like question 2 but with the weights: -10, 20, -20 I would get:

x1 | x2 | xor
0 | 0 | 0
0 | 1 | 1
1 | 0 | 1
1 | 1 | 0

wouldn't I?
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sun light2 أغسطس 2020 في 9:58 ص
please explain 2 one some clearly'i did not undertand what is the target of output.
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sun light3 أغسطس 2020 في 7:29 م
in 2nd question they ask Which of the following logical functions does it (approximately) compute?
out put answer what shoud come to satisfy the truth table. In 2 nd one first bit you answered This network outputs approximately 1 only when both inputs are 1.In bit 2 also same.out put howmuch should come to satisfy the truth table.(that means -30,20,10)
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Bye12 سبتمبر 2020 في 1:26 ص
Why question 1 option 2 is incorrect?
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Unknown23 سبتمبر 2020 في 11:24 ص
I didn't get the question numbers 4 and 5 can you please explain in detail?
I mean how did writing the vectorized implementation here work in place of for loop? and similarly in question 5 how do I calculate whether output changes or remains same?
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Unknown6 ديسمبر 2020 في 12:14 م
consider to the mnn with sigmoidal functions and the training data set x1:0.6,0.2 x2:0.1,0.3 t1:1,0 t2:0,1
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Coursera: Machine Learning (Week 4) Quiz - Neural Networks: Representation| Andrew NG

▸ Neural Networks - Representation :

Check-out our free tutorials on IOT (Internet of Things):

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