吴恩达第四周答案 Neural Networks: Representation

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.

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).

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.

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2。

Consider the following neural network which takes two binary-valued inputs x1,x2∈{0,1} and outputs hΘ(x). Which of the following logical functions does it (approximately) compute?

NAND (meaning "NOT AND")

AND

OR

XOR (exclusive OR)

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3。

Consider the neural network given below. Which of the following equations correctly computes the activation a(3)1? Note: g(z) is the sigmoid activation function.

a(3)1=g(Θ(2)1,0a(2)0+Θ(2)1,1a(2)1+Θ(2)1,2a(2)2)

a(3)1=g(Θ(2)1,0a(1)0+Θ(2)1,1a(1)1+Θ(2)1,2a(1)2)

a(3)1=g(Θ(1)1,0a(2)0+Θ(1)1,1a(2)1+Θ(1)1,2a(2)2)

a(3)1=g(Θ(2)2,0a(2)0+Θ(2)2,1a(2)1+Θ(2)2,2a(2)2)

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4。

You have the following neural network:

You'd like to compute the activations of the hidden layer a(2)∈R3. 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.

a2 = sigmoid (Theta1 * x);

a2 = sigmoid (x * Theta1);

a2 = sigmoid (Theta2 * x);

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

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5。

You are using the neural network pictured below and have learned the parameters Θ(1)=[110.51.21.92.7] (used to compute a(2)) and Θ(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 Θ(1)=[111.20.52.71.9] and also swap the output layer so Θ(2)=[1−1.7−0.2]. How will this change the value of the output hΘ(x)?

It will stay the same.

It will increase.

It will decrease

Insufficient information to tell: it may increase or decrease.