# ▸ Neural Networks - Representation :

1. 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 be the activation of the first output unit, and similarly and . Then for any input x, it must be the case that .

• 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).

1. Consider the following neural network which takes two binary-valued inputs
and outputs . 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)

1. Consider the following neural network which takes two binary-valued inputs
and outputs . 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)

1. Consider the neural network given below. Which of the following equations correctly computes the activation ? Note: is the sigmoid activation
function. • Thiscorrectly uses the first row of and includes the “+1” term of .

1. You have the following neural network: You’d like to compute the activations of the hidden layer . 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 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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1. You are using the neural network pictured below and have learned the parameters (used to compute ) and (used to compute as a function of ). Suppose you swap the parameters for the first hidden layer between its two units so and also swap the output layer so . How will this change the value of the output ? • It will stay the same.
Swapping swaps the hidden layers output . But the swap of 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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