mGalarnyk/Neural NetworksRepresentationStanfordCoursera.md

## Neural NetworksRepresentationStanfordCoursera.md

      
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              Neural NetworksRepresentationStanfordCoursera.md
            
          
    Machine Learning Week 4 Quiz 1 (Neural Networks: Representation) Stanford Coursera

Github repo for the Course: Stanford Machine Learning (Coursera) 

Quiz Needs to be viewed here at the repo (because the image solutions cant be viewed as part of a gist)
Question 1


True or False
Statement
Explanation


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


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


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


True
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).
None Needed


Question 2


Answer
Explanation


AND


Question 3


Answer
Explanation


This correctly uses the first row of Θ⁽²⁾ and includes the "+1" term of a⁽²⁾₀


Question 4


Answer
Explanation


a2 = sigmoid (Theta1 * x);
In the lecture's notation a⁽²⁾ = g(Θ⁽¹⁾x), so this version computes it directly, as the sigmoid function will act element-wise.


Question 5


Answer
Explanation


It will stay the same.
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.
True or False	Statement	Explanation
False	A two layer (one input layer, one output layer; no hidden layer) neural network can represent the XOR function.	We must compose multiple logical operations by using a hidden layer to represent the XOR function.
True	Any logical function over binary-valued (0 or 1) inputs x₁ and x₂ can be (approximately) represented using some neural network.	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.
False	Suppose you have a multi-class classification problem with three classes, trained with a 3 layer network. Let a⁽³⁾₁=(h_Θ(x))₁ be the activation of the first output unit, and similarly a⁽³⁾₂=(h_Θ(x))₂ and a⁽³⁾₃=(h_Θ(x))₃. Then for any input x, it must be the case that a⁽³⁾₁+a⁽³⁾₂+a⁽³⁾₃=1.	The outputs of a neural network are not probabilities, so their sum need not be 1.
True	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).	None Needed