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

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Neural Networks: Representation

TOTAL POINTS 5

1.

Question 1

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

1 point

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).

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 $a^{(3)}_1 + a^{(3)}_2 + a^{(3)}_3 = 1$.

Any logical function over binary-valued (0 or 1) inputs $x_1$ and $x_2$ can be (approximately) represented using some neural network.

A two layer (one input layer, one output layer; no hidden layer) neural network can represent the XOR function.

EXPLANATION:

A two layer (one input layer, one output layer; no hidden layer) neural network can represent the XOR function. (False)
=>We must compose multiple logical operations by using a hidden layer to represent the XOR function.

Any logical function over binary-valued (0 or 1) inputs x1 and x2 can be (approximately) represented using some neural network.(True)

=>Since we can build the basic AND, OR, and NOT functions with a two layer network, we can (approximately) represent any logical function by composing these basic functions over multiple layers.

Suppose you have a multi-class classification problem with three classes, trained with a 3 layer network. Let a(3)1=(hΘ(x))1 be the activation of the first output unit, and similarly a(3)2=(hΘ(x))2 and a(3)3=(hΘ(x))3. Then for any input x, it must be the case that a(3)1+a(3)2+a(3)3=1. (False)
=>The outputs of a neural network are not probabilities, so their sum need not be 1.

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).(True)

=>fact

2.

Question 2

Consider the following neural network which takes two binary-valued inputs $x_1, x_2 \in \{0, 1\}$ and outputs $h_\Theta(x)$. Which of the following logical functions does it (approximately) compute?

1 point

OR

AND

NAND (meaning "NOT AND")

XOR (exclusive OR)

VARIATION IN 2ND QUESTION:

2.

Question 2

Consider the following neural network which takes two binary-valued inputs $x_1, x_2 \in \{0, 1\}$ and outputs $h_\Theta(x)$. Which of the following logical functions does it (approximately) compute?

1 point

OR

AND

NAND (meaning "NOT AND")

XOR (exclusive OR)

EXPLANATION:

This network outputs approximately 1 when atleast one input is 1.

3.

Question 3

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.

1 point

$a_1^{(3)} = g(\Theta_{1,0}^{(2)}a_0^{(2)} + \Theta_{1,1}^{(2)}a_1^{(2)} + \Theta_{1,2}^{(2)}a_2^{(2)})$

$a_1^{(3)} = g(\Theta_{1,0}^{(1)}a_0^{(1)} + \Theta_{1,1}^{(1)}a_1^{(1)} + \Theta_{1,2}^{(1)}a_2^{(1)})$

$a_1^{(3)} = g(\Theta_{1,0}^{(1)}a_0^{(2)} + \Theta_{1,1}^{(1)}a_1^{(2)} + \Theta_{1,2}^{(1)}a_2^{(2)})$

The activation $a_1^{(3)}$ is not present in this network.

EXPLANATION:

$a_1^{(3)} = g(\Theta_{1,0}^{(2)}a_0^{(2)} + \Theta_{1,1}^{(2)}a_1^{(2)} + \Theta_{1,2}^{(2)}a_2^{(2)})$

This correctly uses the first row of Θ(2) and includes the "+1" term of a0(2)  This correctly uses the first 

row of Θ(2) and includes the "+1" term of   a0(2)

4.

Question 4

You have the following neural network:

You'd like to compute the activations of the hidden layer $a^{(2)} \in \mathbb{R}^3$. 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 $a^{(2)}$? Check all that apply.

1 point

z = Theta1 * x; a2 = sigmoid (z);

a2 = sigmoid (x * Theta1);

a2 = sigmoid (Theta2 * x);

z = sigmoid(x); a2 = sigmoid (Theta1 * z);

EXPLANATION:

a(2) = g(Θ(1)x)=g(z)

5.

Question 5

You are using the neural network pictured below and have learned the parameters $\Theta^{(1)} =$

[11−1.55.13.72.3]

(used to compute $a^{(2)}$) and $\Theta^{(2)} =$

[10.6−0.8]

(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 $\Theta^{(1)} =$

[115.1−1.52.33.7]

and also swap the output layer so $\Theta^{(2)} =$

[1−0.80.6]

. How will this change the value of the output $h_\Theta(x)$?

1 point

It will stay the same.

It will increase.

It will decrease

Insufficient information to tell: it may increase or decrease.

EXPLANATION:

Swapping Θ(1) swaps the hidden layers output a^{(2)}. But the swap of Θ(2) cancels out the change, so the output will remain unchanged.

VARIATION IN 5 TH QUESTION:

5.

Question 5

You are using the neural network pictured below and have learned the parameters $\Theta^{(1)} =$

[110.51.21.92.7]

(used to compute $a^{(2)}$) and $\Theta^{(2)} =$

[1−0.2−1.7]

(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 $\Theta^{(1)} =$

[111.20.52.71.9]

and also swap the output layer so $\Theta^{(2)} =$

[1−1.7−0.2]

. How will this change the value of the output $h_\Theta(x)$?

1 point

It will stay the same.

It will increase.

It will decrease

Insufficient information to tell: it may increase or decrease.

EXPLANATION:

Swapping Θ(1) swaps the hidden layers output a^{(2)}. But the swap of Θ(2) cancels out the change, so the output will remain unchanged.

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reference : coursera