These solutions are for reference only.

try to solve on your own

but if you get stuck in between than you can refer these solutions

there are different set of questions ,

we have provided the variations in particular question at the end.

read questions carefully before marking

-----------------------------------------------------------------------------------------

Neural Networks: Representation

TOTAL POINTS 5

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=(hÎ˜(x))1 be the activation of the first output unit, and similarly a(3)2=(hÎ˜(x))2 and a(3)3=(hÎ˜(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

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?

VARIATION IN 2ND QUESTION:

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

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

EXPLANATION:
a(2) = g(Î˜(1)x)=g(z)

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

VARIATION IN 5 TH QUESTION:

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

---------------------------------------------------------------------------------

reference : coursera

darkmode