CS 5541 Study Questions and Homework 4

Homework (15 points) due Wednesday, November 19, 2003.

Homework assignment

For this Homework, turn in your answers for the following study questions:

Q7 (2 pts)
Q9 (3 pts)
Q12 (2 pts)
Q14 (3 pts)
Q32 (2 pts)
Q34 (3 pts)

Study questions

  1. Is the SAIL robotic system an example of supervised or unsupervised learning? Explain your answer.
  2. What kinds of generalization might you expect from the SAIL system?
  3. Give a diagram of a biological neuron, naming the following neuron parts: soma, axon, dendritic tree, synapses.
  4. Do ANN's model 'a' brain or 'the' brain? Explain your answer.
  5. Give two aspects of biological neuron that an ANN models.
  6. Give two aspects of a biological neuron that an ANN does not model.
  7. Excitatory synapses work by increasing the potential of a downstream neuron to fire. Inhibitory synapses work by decreasing the potential of a downstream neuron to fire. Explain how excitatation and inhibition such as this might be modeled using an ANN unit.
  8. Draw a fully connected feedforward ANN with three input units, one hidden unit, and two output units.
  9. Using the sigmodal activation function with sigma=1, for the following neural net:

    give the outputs of the network with the following weights and inputs.
    weights:

    x1-y1

    x1-y2

    x2-y1

    x2-y2

    y1-z

    y2-z

    -4.6151

    4.4739

    4.5015

    -4.573

    6.0281

    6.0176

     

    b1

    b2

    Bias wts

    -2.6033

    -2.5628

     

     

     

     

    b3

     

    Bias wt

    -3.0466

     

    x1 x2
    0 0
    0 1
    1 0
    1 1
    What problem does the network (approximately) solve?
  10. We call neural networks such as that above function approximators. Explain this.
  11. For the ANN in problem 9, how might this neural net exhibit generalization?
  12. What is a step activation function? Give an example.
  13. Use a spreadsheet to generate sigmoidal curves for sigma=5, 15, 25
  14. Let A2 = f(W1 * A1), and let A3 = f(W2 * A2), where f(X) is an activation function operating individually on elements of matrices. If W1 is a 5x3 matrix, and A1 is a 3x1 matrix, and W2 is a 4x5 matrix, give a diagram of the feedforward network represented by these operations. What is another name for A1? What is another name for A2? For A3? How many outputs does the ANN have? How many inputs does it have? How many hidden units?
  15. Is a self-organizing map (a) supervised, or (b) unsupervised? Explain.
  16. Draw a diagram in terms of neural units, and connection weights for the general self-organizing map (SOM) architecture.
  17. A given SOM has 3 inputs and two outputs. Draw the architecture of the SOM.
  18. How many categories can the SOM in question #17 represent?
  19. How do we test for generalization in a SOM?
  20. In the algorithm for training (establishing) the weights in a SOM, before the weight update rule can be applied, what is done?
  21. Give the weight update rule for the SOM algorithm. Make sure to explain your notation.
  22. For a SOM with three inputs and two outputs, one input data sample is: (1, 1, 0). Assuming the weight vectors are (.5 .2 .3) for unit 1 in the output, and (.8 .9 0) for unit 2 in the output, compute the weight update for that data sample.
  23. For a SOM with four inputs and two outputs, and weight vector (0 0 .5 1.0) for output unit 1, and (1.0 .5 0 0) for output unit 2, what category does the input vector: (0 1 0 0) fall into?
  24. On what basis do SOMs achieve categorization?
  25. Give a Scheme language expression that will return the first element of a list, given the list.
  26. What does (cdr '(1 2 3)) evaluate to in Scheme?
  27. What does 'abc evaluate to in Scheme?
  28. What does (equal? (+ 1 2) (+ 2 1)) evaluate to in Scheme?
  29. What does (equal? '(+ 1 2) '(+ 2 1)) evaluate to in Scheme?
  30. What does (member 'b '(a b c)) evaluate to in Scheme?
  31. What is the difference between the list function and the append function in Scheme?
  32. Define a Scheme function (using define and lambda), named last, that returns the last element of a list, given the list as the parameter of the function.If you find iteration is necessary, use only recursion as your means of iteration. Don't use global variables.
  33. Define a Scheme function (using define and lambda), named reverse, that reverses the elements of a list, given the list as the parameter of the function. Don't use the built-in Scheme function that reverses lists. An example of calling this function is: (reverse '(a b c)) ==> (c b a). Use only recursion as your means of iteration. Don't use global variables.
  34. In Scheme, write a recursive function for set union. Your function should take two parameters, S1 and S2, both sets, and return the union of the sets. Remember that sets don't contain duplicates, and that sets are unordered. Don't use global variables.
  35. In Scheme, write a recursive function for set intersection. Again, your function should take two parameters, S1 and S2, both sets, this time returning the intersection of the sets. Don't use global variables.