Name: ___________________

Student No: ___________________

Faculty: ___________________

Signature: ___________________

THE UNIVERSITY OF QUEENSLAND

FINAL EXAMINATION, SEMESTER II, NOVEMBER 2002

COGS2010

LABORATORY INTRODUCTION TO MODELS IN COGNITIVE SCIENCE

Time: Two (2) hours for working

Ten (10) minutes for perusal before examination begins

General Directions to Candidates

There are twelve questions on the paper. You should attempt all questions. Each one is worth 10 marks (Total marks 120).

The examination has been set to take the full two hours, so answer the questions that you know first, and only after answering them, go back to the questions that you are less certain about.

Answer all questions on the examination paper. If you need additional space use the back of the paper or an additional exam booklet and clearly label each answer.

Question 1

marks

a) Consider an interactive activation and competition (IAC) network that represents clothing outfits. The network has pools of features for {tshirt, business shirt}, {shorts, jeans}, {thongs, running shoes}, {socks, no socks} and people’s names. Draw an IAC network that will represent the patterns for (1) Alice’s clothing (tshirt, shorts, running shoes and socks) (2) Bob’s clothing (tshirt, jeans and thongs).

6

b) How many positive and negative weights does your network have? Explain your answer.

1

c) If another 50 clothing patterns were added to your IAC network, it would be possible to use the network to generate prototypes. Explain how you would use the network to generate the typical shoes worn with jeans.

3

Question 2

marks

a) Describe the Stroop effect.

4

b) Explain the role learning plays in Cohen, Dunbar and McClelland’s theory of the Stroop effect, and how it was implemented in the model.

3

c) Explain what training and test patterns were used in the model, and why they were used.

3

Question 3

marks

a) Explain the difference between distributed and local representations in the input and hidden layers of a neural network.

2

b) List one advantage of each for input patterns.

2

c) Give an example of an error correcting learning rule for a one layer neural network.

2

d) Consider a feedforward network that has one input, one hidden and one output unit (a 1-1-1 network). The training patterns are the identity patterns (0,0) and (1,1).

i How many local minima does this network have?

ii How many of these are global minima?

2

e) From a memory modeling perspective, what problems would prevent adding a hidden layer to a matrix memory model?

2

Question 4

marks

a) Explain what the XOR problem is, and why it is relevant to machine learning.

3

b) Can a one-layer feedforward neural network learn the XOR problem? Justify your answer

2

c) In general, is backpropagation guaranteed to converge to

i. A local minima

ii. A global minima

Justify your answers.

3

d) Would the Hebbian learning rule be appropriate for training the 1-1-1 network? Justify your answer.

2

Question 5

marks

a) Consider four patterns, (0,0), (1,0), (0,1) and (1,1). If a 3x3 self-organizing map (SOM) were trained on these patterns, what would a likely SOM layer look like? (Draw the input and map layers)

5

b) What would the trained SOM do with the patterns:

i. (0.5, 0.5) Justify your answer

ii. (1.5, 1.5) Justify your answer

3

c) Explain what the neighbourhood parameter does in a SOM.

2

Question 6

Marks

a) Explain what an analogy is in cognitive science.

2

b) The structure mapping engine (SME) is an analogical mapper that takes hand-coded representations of source and target domains and finds mappings based on the similarities between the given representations. How does Copycat differ from this approach when making an analogy with respect to its mapping and representation formation?

2

c) Is the parallel terraced scan in Copycat a strategy that searches breadth first, depth first or neither?

1

Copycat question continued:

A possible solution derived by Copycat to the problem abc : abd, ijjkkk : ? is ijjlll. This solution is driven by the fact that both abc and ijjkkk are successor groups to the right, allowing a correspondence to be formed between them. For the solution ijjlll to be formed in the Workspace:

d) what initial and modified rule would allow this to occur ?

1

initial rule: replace ________________________ by _______________________

modified rule: replace ________________________ by ________________________

e) The slippages between the concepts used in the initial and modified rule are either implied by or incorporated in the correspondence that is built between the groups abc and ijjkkk. Denote what descriptions would be attached to the two groups, the slippages that occur when the two groups are mapped, and what implied slippages are required to derive the modified from the initial rule above.

1

Copycat question continued:

f) In the following diagram, fill in the missing descriptions, groups, bonds and correspondences that are consistent with your answers above.

3

i

j

j

k

k

k

Question 7

marks

1. Given the 1D cellular automata (CA) shown below and the seven bit starting pattern, apply the rules to shade in the next two rows of the CA (assume the ends of the CA wrap around).

4

2. What classes of patterns are possible in a 3-bit CA?:

3

3. Why are CAs relevant to the study of complex systems?

3

Question 8

marks

a) Give an example of a small world network in real life.

2

b) Describe how a small world network differs from a random network.

3

c) If you were told that a particular disease spread in a way that was similar to information spread on a small world network, what conclusions could be drawn about the rate of transmission of the disease?

4

d) Consider a second disease that spread uniformly across a grid. How would its rate of transmission compare to the first disease?

1

Question 9

Marks

Consider the task of finding the sequence of 20 bits for which each of the following functions is maximal. x is a 20 bit string.

a) F(x) = 100 if x=0000 0000 0000 0000 0000

0 otherwise

b) F(x) = the number of 1s in x

c) F(x) = 100 if x=0000 0000 0000 0000 0000

the number of 1s in x otherwise

d) F(x) = 7 if x contains 7 consecutive 0s

7 if x contains 7 consecutive 1s

14 if x contains 7 consecutive 0s and 7 consecutive 1s.

0 otherwise

For each of these four functions

1. Would an evolutionary algorithm with crossover and mutation be expected to find the solution faster, slower, or at about the same amount of time compared to a completely random search?
2. For which of these functions would you expect an evolutionary algorithm with crossover and mutation to be significantly faster than one with mutation alone?

10

Question 10

marks

a) Describe the Prisoner’s Dilemma (PD) and Iterated prisoner’s dilemma (IPD) problems in game theory. What critical factors distinguish IPD from PD? Include a sample payoff matrix and explain the relationship between the values in each cell of the matrix.

4

b) Give real world example that have been considered as good examples of PD and IPD (two examples of each). What conclusions for agents (societies as a whole, individual humans, animals and synthetic agents) that trade together can be drawn from PD and IPD?

2

c) Illustrate the concept of “strategy” in game theory by explaining the nice (always cooperate), nasty (always defect), and tit-for-tat strategies in the IPD.

2

d) Consider two simulations:
1. a population of 30 nice, 30 nasty and 30 tft
2. a population of 45 nice and 45 tft.
What differences would you expect in the number of nice in the population over time in the first simulation compared to the second? Explain you answer.

2

Question 11

marks

a) Explain the basic steps involved in an evolutionary algorithm.

4

b) Given an initial population or 100 individuals. Describe how (i) roulette wheel and (ii) tournament selection algorithms would be used to generate the next generation.

4

c) What role does mutation play in an EA?

2

Question 12

marks

a) Define “embodied cognition”?

2

b) Give examples of models relevant to cognitive science designed using embodied cognition principles?

2

c) Describe how a model based on the idea of embodied cognition would differ from one based on the view of a general artificial intelligence.

2

d) Would evolutionary psychologists such as Tooby and Cosmides support or reject the idea of a general purpose rational reasoning? Justify your answer.

2

e) What is a “unified theory of cognition”?

2

End of Exam

Question	Marks /10
1
2
3
4
5
6
7
8
9
10
11
12
Total/120