1. Split-Brain Studies What do you see? “Nothing”
Left Visual Field-> Right Hemisphere -> Can’t Speak

2. Split-Brain Studies What do you see? “Triangle”
Right Visual Field-> Left Hemisphere -> Can Speak

3. Split-Brain Studies Point to correct match “Heart”
Left Visual Field-> Right Hemisphere -> Can understand
Simple words -> Can Point

4. Language in both hemispheres
Split-Brain Studies
Language in both hemispheres
“What is your name?”
“Bob”

5. Language in both hemispheres
Split-Brain Studies
Language in both hemispheres
“What is your name?”
“Bob”

6. Language in both hemispheres
Split-Brain Studies
Language in both hemispheres
“What do you want to be
When you grow up?”
“I want to be a director of independent films
And then sell out to major studios and
Make a bundle”

7. Language in both hemispheres
Split-Brain Studies
Language in both hemispheres
“What do you want to be
When you grow up?”
“I want to be a professional hockey player”

8. Language in both hemispheres
Split-Brain Studies
Language in both hemispheres
“What’s your favorite CD?
“Brittany Spears”

9. Language in both hemispheres
Split-Brain Studies
Language in both hemispheres
“What’s your favorite CD?
“Ozzy Osbourne – Heavy Metal”

10. Split-Brain Studies Two people in this guys head?
More than two people?
How many in your head?
“Feels like” one person, but is this an illusion?

11. Studying “Experience” or “Consciousness”
Measurement Problems
Measure experience by reports of subject
Reports of experience are pretty fuzzy
Can study our own experience
But this is pretty limited
What’s it like to be a split-brain patient?
Only real way to know is to zap your cortex
There are limits to curiosity

12. What’s a model? A system is a structure that provides a mapping to
the thing being modelled
A model of solar system
Big center thing (maps to sun)
Small things going around big thing
(maps to planets)
Leaves some stuff out
Paths of objects are elliptical
Solar flares

13. 3 FROG Symbolic Models What are symbols?
Symbols are things that represent something else 3
(the number three)
FROG

14. Symbolic Models What are symbols?
Symbols are things that represent something else
Semantics /
Intentionality
one
“one”
two
“two”
three
“three”
four
“four”
numbers
marks on paper

15. Symbolic Models What are symbols?
Symbols are things that represent something else
isomorphic relationship
one
“I”
two
“II”
three
“III”
four
“IV”
numbers
marks on paper

16. Symbolic Models What are symbols?
Symbols are things that represent something else
homomorphic relationship
“cat”
“bird”
animals
marks on paper

17. Symbolic Models What are symbols?
Symbols are things that represent something else
“chicken (McNuggets)”
“chicken (bird)”
animals
marks on paper

18. Symbolic Models What are symbols?
Symbols are things that represent something else x
“chicken (McNuggets)”
“chicken (bird)”
animals
marks on paper

19. Symbolic Models What are symbols?
Symbols are things that represent something else
quasi-homomorphic relationship
(Q-morph)
“chicken (McNuggets)”
“chicken (bird)”
animals
marks on paper

20. Symbolic Models What are symbols?
Symbols are things that represent something else.
A set of symbols and a set of items in the world.
A correspondence can be drawn between elements
in each set.
This correspondence can be:
Isomorphic (one-to-one)
Homomorphic (many-to-one)
Q-morphic (approximate many-to-one, with errors)

21. Symbolic Models The first symbolic computational model:
General Problem Solver (GPS)
(by Simon and Newell)
But first, an example problem...

22. Tower of Hanoi Puzzle

23. Symbolic Models General Problem Solver (GPS)
Uses IF-THEN rules, called productions
Uses goals, and breaks them into sub-goals.
Back to the example problem...

24. Tower of Hanoi Puzzle Goal: Move stack[1] to peg C
Production: disk[1] is not on peg C, and is not free
 subgoal: move stack[2] to peg B 4 3
Stack[1] 2 1 A B C

25. Tower of Hanoi Puzzle Goal: Move stack[2] to peg B
Production: disk[2] is not on peg B, and is not free
 subgoal: move stack[3] to peg C 4
Stack[2] 3 2 1 A B C

26. Tower of Hanoi Puzzle Goal: Move stack[3] to peg C
Production: disk[3] is not on peg C, and is not free
 subgoal: move stack[4] to peg B 4
Stack[3] 3 2 1 A B C

27. Tower of Hanoi Puzzle Goal: Move stack[4] to peg B
Production: disk[4] is not on peg B, but is free!
 so move disk[4] to peg B
Stack[4] 4 3 2 1 A B C

28. Tower of Hanoi Puzzle Goal: Move stack[4] to peg B
Production: disk[4] is on peg B, and is free, but there is no stack[5]
 so we’re done with this goal! 3 2 1 4 A B C

29. Tower of Hanoi Puzzle Previous Goal: Move stack[3] to peg C
Production: disk[3] is not on peg C, but it is free
 so move disk[3] to peg C 2 1 4 3 A B C

30. Tower of Hanoi Puzzle Previous Goal: Move stack[3] to peg C
Production: disk[3] is on peg C, and it is free
 so subgoal: move stack[4] to peg C 2 1 4 3 A B C

31. Tower of Hanoi Puzzle Goal: Move stack[4] to peg C
Production: disk[4] is not on peg C, and it is free
 so move disk[4] to peg C 2 1 4 3 A B C

32. Tower of Hanoi Puzzle Goal: Move stack[4] to peg C
Production: disk[4] is not on peg C, and it is free
 so move disk[4] to peg C 2 4 1 3 A B C

33. Tower of Hanoi Puzzle Goal: Move stack[4] to peg C
Production: disk[4] is on peg C, and is free, but there is no stack[5]
 so done with this goal! 2 4 1 3 A B C

34. Tower of Hanoi Puzzle Previous Goal: Move stack[3] to peg C
Production: disk[3] is on peg C and has stack[4] on top of it
 so done with this goal! 2 4 1 3 A B C

35. Tower of Hanoi Puzzle Previous Goal: Move stack[2] to peg B
Production: disk[2] is not on peg B, and is free,
 so move disk[2] to peg B 4 1 2 3 A B C

36. Tower of Hanoi Puzzle Previous Goal: Move stack[2] to peg B
Production: disk[2] is on peg B, and is free,
 so set up a subgoal to move stack[3] onto peg B 4 1 2 3 A B C

37. Tower of Hanoi Puzzle
….and so on….. 4 1 2 3 A B C

38. Tower of Hanoi Puzzle
DONE! 4 3 2 1 A B C

39. Symbolic Models General Problem Solver (GPS)
Uses IF-THEN rules, called productions
Uses goals, and breaks them into sub-goals.
ACT*
Three components:
Production Memory (IF-THEN rules)
Declarative Memory (facts about the world)
Working Memory (information currently being processed)

40. ACT* Declarative Memory Production Memory retrieval storage execution
match
Working
Memory
perception
action

41. ACT* Declarative Memory Production Memory retrieval storage execution
busy intersection
IF (driving) and (stop sign)
THEN
brake!
retrieval
storage
execution
match
Working
Memory
I’m driving!
Brake!
Stop sign!
perception
action

42. Symbolic Models General Problem Solver (GPS)
Uses IF-THEN rules, called productions
Uses goals, and breaks them into sub-goals.
ACT*
Production Memory, Declarative Memory, Working Memory

43. Symbolic Models: Summary
The basic units of computation are symbols
Decisions, actions, and problem-solving are accomplished through productions: IF-THEN like statements in memory
Usually they divide up memory into different kinds, like production memory, declarative memory, working memory.
All thought is seen as manipulation of symbols in these different areas of memory.
WHAT THEY ARE GOOD AT: Problem solving, reasoning, language, logic.
WHAT THEY ARE BAD AT: Perception, memory storage and retrieval, low-level processing.

44. Where do symbols come from?
These systems assume symbols are fully-formed
But where do we get our symbols?
Born with this mass of cortex
Somehow we end up with symbols that map to things in world
Big problem
We need a model for how we learn things

45. Artificial Brains?
input
input layer
hidden layer
output layer

46. Artificial Neural Nets
Some Properties of
Artificial Neural Nets
Distributed Representation: Ideas, thoughts, concepts,
memories, are all represented in the brain as patterns of
activation across a large number of neurons. As a result,
there is a lot of redundancy in neural representation.
Graceful Degradation: Performance of the system
decreases gradually as the system is damaged.
Learning: When neurons are active at the same time,
the strength of the connection between them to increase.
In artificial nets, this is called the Hebb Rule.

47. Artificial Neural Nets
More Properties of
Artificial Neural Nets
Generalization: Because of how the network learns,
and its distributed representation, it can respond to
inputs that it was never officially trained on, generalizing
based on similarity to things it was trained on.
Distributed Processing: Not only representation, but
processing is distributed, too, so there is no central
controlling function, or CPU, in the brain. It is more
cooperative.

48. Another Approach + Lets look at the biology of the eye!
The first artificial neural model: The Perceptron +

49. The Basic Perceptron a 1 1 a b 1 b
a AND b

50. The Basic Perceptron a 1 1 1 a b 1 1 b
a OR b

51. The Basic Perceptron a 1 1 a b 1 1 b
a XOR b

52. The Basic Perceptron a 1 1 a b
linearly separable 1 b
a AND b

53. The Basic Perceptron a 1 1 1 a b 1
linearly separable 1 b
a OR b

54. The Basic Perceptron a a b 1 b
NOT linearly separable
a XOR b

55. The Basic Perceptron What the perceptron can’t do: Exclusive OR 1 1 aa 1 1 b

56. The Basic Perceptron What the perceptron can’t do: Exclusive OR
Even/Odd discrimination
Total inputs:
ouput:

57. The Basic Perceptron What the perceptron can’t do: Exclusive OR
Even/Odd discrimination
Inside/Outside discrimination

58. The Basic Perceptron What the perceptron can’t do: Exclusive OR
Even/Odd discrimination
Inside/Outside discrimination
Open/Closed discrimination

59. The Basic Perceptron BIG PROBLEMS What the perceptron can’t do:
Exclusive OR
Even/Odd discrimination
Inside/Outside discrimination
Open/Closed discrimination
BIG PROBLEMS

60. The Multi-Layer Perceptron1 1 a b 1 1 b
a XOR b

61. The Multi-Layer Perceptron
AND 1 1 - a b + 1 OR 1 b
a XOR b

62. The Three-Layer Network
input
input
input layer
input layer
hidden layer
output layer

63. The Two-Layer Network
input
input layer
output layer

64. The Two-Layer Network
input
input layer
output layer

65. The Three-Layer Network
input
input
input layer
input layer
hidden layer
output layer

66. The Three-Layer Network
input
input
input layer
input layer
hidden layer
output layer

67. The Three-Layer Network
input
input
input layer
input layer
? ? ? ? ? ? ?
hidden layer
output layer

68. The Three-Layer Network
input
input
input layer
input layer
hidden layer
output layer
Back-propagation is the learning procedure that allows you to adjust
the weights in multi-layer networks to train them to respond correctly.

69. The Hopfield Network
(not all connections are shown)

70. The Hopfield Network
THE END OF CLASS IS NEAR
Pattern Completion

71. Quick Summary Symbolic Models: Basic Units are Symbols
Local Representation: Individual elements have meaning
Use productions, goals (means-ends analysis), working memory
Two examples are GPS and ACT*
Are good at problem solving, reasoning, logic, and language
Neural Network Models:
Basic Units are artificial neurons
Distributed Representation: Patterns across elements have meaning
Use activation, learning (Hebb Rule, Backpropagation)
Two examples are layered networks and Hopfield networks
Are good at pattern matching, memory storage/retrieval