吴恩达 Machine Learning week4--quiz4--Neural Networks: Representation课后习题

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

• Suppose you have a multi-class classification problem with three classes, trained with a 3 layer network. Let a^{(3)}1 = (h\Theta(x))1a1(3)=(hΘ(x))1 be the activation of the first output unit, and similarly a^{(3)}_2 = (h\Theta(x))2a2(3)=(hΘ(x))2 and a^{(3)}_3 = (h\Theta(x))_3a3(3)=(hΘ(x))3. Then for any input xx, it must be the case that a^{(3)}_1 + a^{(3)}_2 + a^{(3)}_3 = 1a1(3)+a2(3)+a3(3)=1.
• two layer (one input layer, one output layer; no hidden layer) neural network can represent the XOR function.
• Any logical function over binary-valued (0 or 1) inputs x_1x1 and x_2x2 can be (approximately) represented using some neural network.
• 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).
  答案：CD
  解析：
  A选项：每一层的节点都是通过前一层计算而来，同层节点互不影响，加上softmax才会影响。
  B选项：XOR异或，需要通过叠加产生。

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? -30 ，20，20

• AND
• NAND (meaning “NOT AND”)
• OR
• XOR (exclusive OR）
  答案A
  解析：
  将-30，20，20，带入sigmoid函数，得到只有x1=1，x2=1时输出为g(10)=1，即表示逻辑AND.

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.
答案：A

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;
  答案：A
  解析：（Theta1是个3×的矩阵，x是个列向量）

答案：A