announcements
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Announcements. Read Chapter 19 for Thursday – we will discuss it. HW 10: Due Tuesday Dec. 6 Final project: Due Friday Dec. 9 Volunteers for project demos? . Benford’s law: Distribution of leading digits. Explanation of Benford’s law. Explanation of Benford’s law. - PowerPoint PPT PresentationTRANSCRIPT
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Announcements
• Read Chapter 19 for Thursday – we will discuss it.
• HW 10: Due Tuesday Dec. 6
• Final project: Due Friday Dec. 9
• Volunteers for project demos?
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Benford’s law: Distribution of leading digits
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Explanation of Benford’s law
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Explanation of Benford’s law
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X = r ×10n (scientific notation)1 ≤ r <10The leading digit of X is 1 when 1 ≤ r < 2The leading digit of X is 1 when 2 ≤ r < 3and so on.
log10 X = log10(r ×10n )
= log10(r) + log10(10n )= log10(r) + nThe leading digit of X is 1 when 1≤ r < 2, or whenn = 0 : 0 ≤ log10 X < 0.301n =1: 1 ≤ log10 X <1.301n = 2 : 2 ≤ log10 X < 2.301etc.(30.1% of the time)
The leading digit of X is 2 when 2 ≤ r < 3, or whenn = 0 : .301≤ log10 X < 0.477n =1: 1.301≤ log10 X <1.477n = 2 : 2.301≤ log10 X < 2.477etc.(17.6% of the time)
€
The leading digit of X is 9 when 9 ≤ r < 10 or whenn = 0 : .954 ≤ log10 X <1n =1: 1.954 ≤ log10 X < 2n = 2 : 2.954 ≤ log10 X < 3etc.(4.6% of the time)
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1. Global information is encoded as statistics and dynamics of patterns over the systems components.
2. Randomness and probabilities are essential
3. The system carries out a fine-grained parallel search of possibilities.
4. The system exhibits a continual interplay of bottom-up and top-down processes.
Four Principles of Information Processing In Living Systems
(Complexity: A Guided Tour, Chapter 12)
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Consider the following cognitive activities
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• Recognition:
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• Recognition:– A child learns to recognize cats and dogs in books as
well as in real life.
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• Recognition:– A child learns to recognize cats and dogs in books as
well as in real life.
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– People can recognize letters of the alphabet, e.g., ‘A’, in many different typefaces and handwriting styles.
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– People can recognize letters of the alphabet, e.g., ‘A’, in many different typefaces and handwriting styles.
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– People can recognize styles of music:
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– People can recognize styles of music:
• “That sounds like Mozart”
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– People can recognize styles of music:
• “That sounds like Mozart”
• “That’s a muzak version of ‘Hey Jude’”
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– People can recognize styles of music:
• “That sounds like Mozart”
• “That’s a muzak version of ‘Hey Jude’”
– People can recognize abstract situations:
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– People can recognize styles of music:
• “That sounds like Mozart”
• “That’s a muzak version of ‘Hey Jude’”
– People can recognize abstract situations:
• A “Cinderella story”
• “Another Vietnam”
• “Monica-gate”
• “Shop-aholic”
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• People make scientific analogies:
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• People make scientific analogies:– “Biological competition is like economic competition” (Darwin)
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• People make scientific analogies:– “Biological competition is like economic competition” (Darwin)
– “The nuclear force is like the electromagnetic force” (Yukawa)
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• People make scientific analogies:– “Biological competition is like economic competition” (Darwin)
– “The nuclear force is like the electromagnetic force” (Yukawa)
– “The computer is like the brain” (von Neumann)
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• People make scientific analogies:– “Biological competition is like economic competition” (Darwin)
– “The nuclear force is like the electromagnetic force” (Yukawa)
– “The computer is like the brain” (von Neumann)
– “The brain is like the computer” (Simon, Newell, etc.)
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• People make unconscious analogies
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• People make unconscious analogiesMan: “I’m going shopping for a valentine for my wife.”
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• People make unconscious analogiesMan: “I’m going shopping for a valentine for my wife.”
Female colleague: “I did that yesterday.”
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Main idea is that we understandabstract concepts by analogy with the concrete physical world.
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Some examples
• Happy/Good = up– “My mood has risen since yesterday.”– “Things have been going up lately”– “I like to get high.”
• Sad/Bad = down– “My work is going downhill.”– “She’s feeling depressed.”– “That’s a real downer.”
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• Understanding/Knowledge = seeing / light– “I see what you mean.”– “Thanks for enlightening me.”– “Can you shed any light on this situation?.”
• Confusion/Ignorance = blindness/dark– “I can’t see my way through his argument.”– “She left me in the dark.”– “I have brainfog in the morning.”
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• Love/Attraction = physical force– “I’m falling in love.”– “There’s a strong chemistry between us.”– “I could feel the electricity between them; there were a lot of
sparks.”– “He has a lot of magnetism.”– “When I’m with him, the atmosphere is charged.”
• Ideas = food– “I need some time to digest that idea.”– “Your idea is half-baked.”– “That’s a theory you can sink your teeth into.”– “That gave me some food for thought.”
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• Significant/Important = large– “He’s a big name in the field.”– “He’s a giant among writers.”– “What are the big ideas in your field?”– “Her accomplishments tower over those of others in her area.”
• Vitality / Energy = a substance ; people = containers– “He’s brimming with spirit.”– “She’s overflowing with vitality.”– “He’s devoid of energy.”– “I’m always drained at the end of the day.”
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• Emotional effect = physical contact– “Getting fired hit him hard.”– “That movie bowled me over.”– “She made a big impression on me”– “That blew me away.”– “I was really struck by his sincerity.”
• Vitality / Energy = a substance ; people = containers– “He’s brimming with spirit.”– “She’s overflowing with vitality.”– “He’s devoid of energy.”– “I’m always drained at the end of the day.”
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Copycat: A computer program that models human analogy-making
(Douglas Hofstadter, Melanie Mitchell, Jim Marshall)
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Idealizing analogy-making
abc ---> abdijk --->
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Idealizing analogy-making
abc ---> abdijk ---> ijl (replace rightmost
letter by successor)
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Idealizing analogy-making
abc ---> abdijk ---> ijl (replace rightmost
letter by successor) ijd (replace rightmost
letter by ‘d’)
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Idealizing analogy-making
abc ---> abdijk ---> ijl (replace rightmost
letter by successor) ijd (replace rightmost
letter by ‘d’) ijk (replace all
‘c’s by ‘d’s)
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Idealizing analogy-making
abc ---> abdijk ---> ijl (replace rightmost
letter by successor) ijd (replace rightmost
letter by ‘d’) ijk (replace all
‘c’s by ‘d’s) abd (replace any
string by ‘abd’)
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Idealizing analogy-making
abc ---> abdiijjkk ---> ?
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Idealizing analogy-making
abc ---> abdiijjkk ---> iijjklReplace rightmost letter by successor
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Idealizing analogy-making
abc ---> abdiijjkk ---> ?
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Idealizing analogy-making
abc ---> abdiijjkk ---> iijjllReplace rightmost “letter” by successor
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Idealizing analogy-making
abc ---> abdkji ---> ?
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Idealizing analogy-making
abc ---> abdkji ---> kjjReplace rightmost letter by successor
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Idealizing analogy-making
abc ---> abdkji ---> ?
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Idealizing analogy-making
abc ---> abdkji ---> ljiReplace “rightmost” letter by successor
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Idealizing analogy-making
abc ---> abdkji ---> ?
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Idealizing analogy-making
abc ---> abdkji ---> ?
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Idealizing analogy-making
abc ---> abdkji ---> kjhReplace rightmost letter by “successor”
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Idealizing analogy-making
abc ---> abdmrrjjj ---> ?
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Idealizing analogy-making
abc ---> abdmrrjjj ---> mrrjjkReplace rightmost letter by successor
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Idealizing analogy-making
abc ---> abdmrrjjj ---> ?
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Idealizing analogy-making
abc ---> abdmrrjjj ---> ? 1 2 3
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Idealizing analogy-making
abc ---> abdmrrjjj ---> ? 1 2 3 1 2 4
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Idealizing analogy-making
abc ---> abdmrrjjj ---> mrrjjjj 1 2 3Replace rightmost “letter” by successor
1 2 4
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Idealizing analogy-making
abc ---> abdxyz ---> ?
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Idealizing analogy-making
abc ---> abdxyz ---> xyaReplace rightmost letter by successor
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Idealizing analogy-making
abc ---> abdxyz ---> xya (not allowed)
Replace rightmost letter by successor
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Idealizing analogy-making
abc ---> abdxyz ---> ?
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Idealizing analogy-making
abc ---> abdxyz ---> ?
last letter in alphabet
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Idealizing analogy-making
abc ---> abdxyz ---> ?
last letter in alphabet
first letter in alphabet
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Idealizing analogy-making
abc ---> abdxyz ---> ?
last letter in alphabet
first letter in alphabet
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Idealizing analogy-making
abc ---> abdxyz ---> wyz
last letter in alphabet
first letter in alphabet
Replace “rightmost” letter by “successor”
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Idealizing analogy-making
abc ---> abdxyz ---> wyz
last letter in alphabet
first letter in alphabet
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The Copycat program(Hofstadter and Mitchell)
• Inspired by collective behavior in complex systems (e.g., ant colonies)
• Understanding and perception of similarity is built up collectively by many independent simple “agents” working in parallel
• Each agent’s job is to explore a possible way of describing an object or relationship between objects
• Each agent has very limited perceptual and communication abilities
• Each agent makes its decisions (about what to explore probabilistically, based on what it perceives in its environment and on its interaction with other agents.
• In this way the resources (agent time) allocated to a possible exploration depends on its promise, as assessed dynamically as exploration proceeds.
• The agents working together produce an “emergent” understanding of the analogy.
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Architecture of Copycat
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Concept network
Architecture of Copycat
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a b c ---> a b di i j j k k --> ?
Architecture of Copycat
Workspace
Concept network
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a b c ---> a b di i j j k k --> ?
Architecture of Copycat
Workspace
Perceptual agents (codelets)
Concept network
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a b c ---> a b di i j j k k --> ?
Perceptual agents (codelets)
Architecture of Copycat
Temperature
Workspace
Concept network
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Workspace
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a b c --> a b d
m r r j j j --> ?
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a b c --> a b d
m r r j j j --> ?
Codelet actions
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a b c --> a b d
m r r j j j --> ?
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a b c --> a b d
m r r j j j --> ?
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a b c --> a b d
m r r j j j --> ?
successorship
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a b c --> a b d
m r r j j j --> ?
successorship
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• Codelets make probabilistic decisions:
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• Codelets make probabilistic decisions:– What to look at next
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• Codelets make probabilistic decisions:– What to look at next– Whether to build a structure there
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• Codelets make probabilistic decisions:– What to look at next– Whether to build a structure there– How fast to build it
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• Codelets make probabilistic decisions:– What to look at next– Whether to build a structure there– How fast to build it– Whether to destroy an existing structure there
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a b c --> a b d
m r r j j j --> ?
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a b c --> a b d
m r r j j j --> ? rightmost --> rightmost??
letter --> letter??
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a b c --> a b d
m r r j j j --> ? rightmost --> rightmost?
letter --> letter?
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a b c --> a b d
m r r j j j --> ? rightmost --> rightmost?
letter --> letter?leftmost --> leftmost??letter --> letter??
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a b c --> a b d
m r r j j j --> ? rightmost --> rightmost
letter --> letterleftmost --> leftmost??letter --> letter??
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a b c --> a b d
m r r j j j --> ? rightmost --> rightmost
letter --> letterleftmost --> leftmost??letter --> letter??
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a b c --> a b d
m r r j j j --> ? rightmost --> rightmost
letter --> letterleftmost --> leftmost??letter --> letter??
rightmost --> rightmost??letter --> group??
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a b c --> a b d
m r r j j j --> ? rightmost --> rightmost
letter --> letterleftmost --> leftmost??letter --> letter??
rightmost --> rightmost?letter --> group?
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a b c --> a b d
m r r j j j --> ? leftmost --> leftmost?
letter --> letter?rightmost --> rightmostletter --> group
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a b c --> a b d
m r r j j j --> ? leftmost --> leftmost?
letter --> letter?rightmost --> rightmostletter --> groupleftmost --> rightmost??
letter --> letter??
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a b c --> a b d
m r r j j j --> ? leftmost --> leftmost?
letter --> letter?rightmost --> rightmostletter --> group
high prob.
low prob.
leftmost --> rightmost??letter --> letter??
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Concept Network
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Part of Copycat’s Concept Network
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• Concepts are activated as instances are noticed in workspace.
Concept Network
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a b c --> a b d
x y z --> ?
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a b c --> a b d
x y z --> ?
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Part of Copycat’s Concept Network
successor
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• Activation of concepts feeds back into “top-down” pressure to notice instances of those concepts in the workspace.
Concept Network
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a b c --> a b d
x y z --> ?
successor
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a b c --> a b d
x y z --> ?
successor
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a b c --> a b d
x y z --> ?
successor
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• Activated concepts spread activation to neighboring concepts.
Concept Network
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a b c --> a b d
x y z --> ?
last
last
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a b c --> a b d
x y z --> ?
last
lastfirst
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a b c --> a b d
x y z --> ?
last
lastfirst
first
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• Activation of link concepts determines current ease of slippages of that type (e.g., “opposite”).
Concept Network
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a b c --> a b d
x y z --> ?
first
lastleftmost
rightmost
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a b c --> a b d
x y z --> ?
first
lastleftmost
rightmost
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a b c --> a b d
x y z --> ?
first
last
opposite
first last
first --> last
leftmost
rightmost
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a b c --> a b d
x y z --> ?
first
last
opposite
first last
leftmost
rightmost
first --> last
leftmost
rightmost
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a b c --> a b d
x y z --> ?
first
last
opposite
first last
leftmost
rightmost
first --> last
leftmost
rightmost
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a b c --> a b d
x y z --> ?
first
last
opposite
first last
leftmost
rightmost
first --> lastrightmost --> leftmost
leftmost
rightmost
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Temperature
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• Measures how well organized the program’s “understanding” is as processing proceeds (a reflection of how good the current worldview is)
Temperature
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• Measures how well organized the program’s “understanding” is as processing proceeds (a reflection of how good the current worldview is)– Little organization —> high temperature
Temperature
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• Measures how well organized the program’s “understanding” is as processing proceeds (a reflection of how good the current worldview is)– Little organization —> high temperature– Lots of organization —> low temperature
Temperature
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a b c --> a b d
m r r j j j --> ?
High temperature
leftmost --> leftmost?letter --> letter?
rightmost --> rightmost??letter --> group??
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a b c --> a b d
m r r j j j --> ?
Medium temperature
leftmost --> leftmost?letter --> letter?
rightmost --> rightmostletter --> group
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a b c --> a b d
m r r j j j --> ? leftmost --> leftmost
letter --> grouprightmost --> rightmostletter --> group
Low temperature
middle --> middleletter --> group
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• Measures how well organized the program’s “understanding” is as processing proceeds (a reflection of how good the current worldview is)– Little organization —> high temperature– Lots of organization —> low temperature
Temperature
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• Measures how well organized the program’s “understanding” is as processing proceeds (a reflection of how good the current worldview is)– Little organization —> high temperature– Lots of organization —> low temperature
• Temperature feeds back to codelets:
Temperature
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• Measures how well organized the program’s “understanding” is as processing proceeds (a reflection of how good the current worldview is)– Little organization —> high temperature– Lots of organization —> low temperature
• Temperature feeds back to codelets: – High temperature —> low confidence in decisions
—> decisions are made more randomly
Temperature
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• Measures how well organized the program’s “understanding” is as processing proceeds (a reflection of how good the current worldview is)– Little organization —> high temperature– Lots of organization —> low temperature
• Temperature feeds back to codelets: – High temperature —> low confidence in decisions
—> decisions are made more randomly– Low temperature —> high confidence in
decisions —> decisions are made more deterministically
Temperature
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• Measures how well organized the program’s “understanding” is as processing proceeds (a reflection of how good the current worldview is)– Little organization —> high temperature– Lots of organization —> low temperature
• Temperature feeds back to codelets: – High temperature —> low confidence in decisions
—> decisions are made more randomly– Low temperature —> high confidence in
decisions —> decisions are made more deterministically
• Result: System gradually goes from random, parallel, bottom-up processing to deterministic, serial, top-down processing
Temperature
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Demo(Metacat, J. Marshall)
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1. Global information is encoded as statistics and dynamics of patterns over the systems components.
2. Randomness and probabilities are essential
3. The system carries out a fine-grained parallel search of possibilities.
4. The system exhibits a continual interplay of bottom-up and top-down processes.
Principles that inspired the Copycat program
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Applications of Ideas from Copycat
• Letter recognition (McGraw, 1995, Ph.D Dissertation, Indiana University)
• Natural language processing (Gan, Palmer, and Lua, Computational Linguistics 22(4), 1996, pp. 531-553)
• Robot control (Lewis and Lugar, Proceedings of the 22nd Annual Conference of the Cognitive Science Society, Erlbaum, 2000.)
• Image understanding (Mitchell et al.)