representing representers and what they represent kathryn blackmond laskey george mason university...
TRANSCRIPT
Representing Representers
and What They Represent
Representing Representers
and What They Represent
Kathryn Blackmond Laskey
George Mason UniversityDepartment of Systems Engineering and Operations Research
Krasnow Institute
GMUGMUQMind IIQMind II
Note change to less Note change to less pretentious and more pretentious and more
accessible titleaccessible title
This talk is dedicated to the memory of This talk is dedicated to the memory of journalist Danny Pearl, murdered in journalist Danny Pearl, murdered in
Pakistan in February 2002, and to the Pakistan in February 2002, and to the pioneering research of his father Judea pioneering research of his father Judea Pearl. Judea Pearl’s research has the Pearl. Judea Pearl’s research has the
potential to create unprecedented advances potential to create unprecedented advances in our ability to anticipate and prevent in our ability to anticipate and prevent
future terrorist incidents.future terrorist incidents.
This talk is dedicated to the memory of This talk is dedicated to the memory of journalist Danny Pearl, murdered in journalist Danny Pearl, murdered in
Pakistan in February 2002, and to the Pakistan in February 2002, and to the pioneering research of his father Judea pioneering research of his father Judea Pearl. Judea Pearl’s research has the Pearl. Judea Pearl’s research has the
potential to create unprecedented advances potential to create unprecedented advances in our ability to anticipate and prevent in our ability to anticipate and prevent
future terrorist incidents.future terrorist incidents.
RepresentationRepresentation
• A representation consists of:– A representing system
– A represented system
– A mapping between the representing system and the represented system
• Important properties of the represented system correspond to features in the representation
• A conscious organism– Represents its environment and possibly itself to itself
– Uses its representations to engage in adaptive behavior with respect to its environment
» Sense
» Recognize
» Plan and act
ObservationsObservations
ActionsActions
Real WorldReal WorldRepresentationRepresentation
Science and Representation
Science and Representation
• Elements of a representation– Reality to represent
– Space of possible representations of reality
– Correspondence between aspects of reality and features in representation space
• Important considerations– By whom is representation being used?
– For what purpose?
– How to measure how good it is?
• Scientists study a phenomenon by– Building a representation of the phenomenon
– Manipulating the representation
– Comparing non-obvious features of the representation to corresponding features in reality
• How do we study representationHow do we study representation??
ObservationsObservations
ActionsActions
Real world with real Real world with real representationrepresentationcreated by real conscious created by real conscious subsystemsubsystem
Artificial world with Artificial world with simulated representationsimulated representationcreated by simulated created by simulated conscious subsystemconscious subsystem
Representing RepresentationRepresenting
Representation
Physics, Representation and LearningPhysics, Representation and Learning
• Cross-fertilization from physics to statistics and machine learning has created rapid progress
• Recipe for creating a good learning algorithm– Represent the learning problem as a physical system in
which “low action” or “low free energy” maps to good representation
– Simulate the physical system on a computer
– Let the simulation evolve according to (simulated) laws of physics
– Presto! Out comes a good solution to your problem
• The opposite direction:– Can ideas from learning theory give insights for a physics of
consciousness?
Learners and Learnable PhenomenaLearners and Learnable Phenomena
• Good learners– Loosely coupled local learners– Multi-resolution representations– Bias toward simple representations– Compose elements to form complex representations– Adjust appropriately to environmental feedback– Intrinsic randomness to bump out of locally but not globally
optimal representations
• Learnable systems– Repeated structure– Complexity built up out of simple pieces– Not too much randomness
• A system capable of self-representation must be– Simple enough to exhibit learnable regularities– Complex enough to form and evolve representations of itself
ObservationsObservations
ActionsActions
20th Century Science20th Century Science
Real WorldReal World
?
RepresentationRepresentation
• Physical reality- Wave function- Deterministic evolution
punctuated by “jumps”
• No consensus on- How and why “jumps” occur- How consciousness
interacts with physical world
Stapp Theory of ConsciousnessStapp Theory of Consciousness
• Timing of reduction and choice of operator occur by conscious choice
• Efficacious conscious choice enters where physics currently lacks a theory
• Comments on Stapp theory– Stapp does not demand that all state vector reductions involve
conscious choice
– Theory and experiment verify that macroscopic evolution of physical system can depend on choice and timing of reductions
– Experimentally verified quantum Zeno effect is one potential mechanism by which conscious choice might operate
– Stapp argues that operation of quantum Zeno effect is plausible in conditions occurring in brains
Paradigm Shift in ComputingParadigm Shift in Computing
• Old paradigm: Algorithms running on Turing machines– Deterministic– Based on Boolean logic
• New paradigm: Economy of software agents executing on a physical symbol system
– Agents make decisions (deterministic or stochastic) to achieve objectives
– “Program” is replaced by dynamic system evolving better solutions– Based on decision theory / game theory / stochastic processes
• Hardware realizations of physical symbol systems– Physical systems minimize action– Decision theoretic systems maximize utility / minimize loss– Hardware realization of physical symbol system maps action to utility– Programming languages are replaced by specification / interaction
languages– Software designer specifies goals, rewards and information flows– Unified theory spans sub-symbolic to cognitive levels
• Old paradigm is limiting case of new paradigm
Decision Graph: An ExampleDecision Graph: An Example
• Maria is visiting a friend when she Maria is visiting a friend when she suddenly begins sneezing. suddenly begins sneezing.
• "Oh dear, I'm getting a cold," she "Oh dear, I'm getting a cold," she thinks. “I had better not visit Grandma.”thinks. “I had better not visit Grandma.”
• Then she notices scratches on the Then she notices scratches on the furniture. She sighs in relief. "I'm not furniture. She sighs in relief. "I'm not getting a cold! It's only my cat allergy getting a cold! It's only my cat allergy acting up!”acting up!”
• Maria is visiting a friend when she Maria is visiting a friend when she suddenly begins sneezing. suddenly begins sneezing.
• "Oh dear, I'm getting a cold," she "Oh dear, I'm getting a cold," she thinks. “I had better not visit Grandma.”thinks. “I had better not visit Grandma.”
• Then she notices scratches on the Then she notices scratches on the furniture. She sighs in relief. "I'm not furniture. She sighs in relief. "I'm not getting a cold! It's only my cat allergy getting a cold! It's only my cat allergy acting up!”acting up!”
Allergic_Reaction
TrueFalse
3.2296.8
Sneezing
TrueFalse
15.384.7
Scratches_on_Furniture
TrueFalse
2.7797.2
Cold
TrueFalse
8.0092.0
Cat_Nearby
TrueFalse
3.0097.0
HealthOfGrandmother
VisitGrandmother
GoStayHome
117.000100.000
Pleasure
Allergic_Reaction
TrueFalse
3.2296.8
Sneezing
TrueFalse
15.384.7
Scratches_on_Furniture
TrueFalse
2.7797.2
Cold
TrueFalse
8.0092.0
Cat_Nearby
TrueFalse
3.0097.0
HealthOfGrandmother
VisitGrandmother
GoStayHome
117.000100.000
Pleasure
11
Plausible inferencePlausible inference
Allergic_Reaction
TrueFalse
20.879.2
Sneezing
TrueFalse
100 0
Scratches_on_Furniture
TrueFalse
9.9590.1
Cold
TrueFalse
51.748.3
Cat_Nearby
TrueFalse
15.284.8
HealthOfGrandmother
VisitGrandmother
GoStayHome
73.2510100.000
Pleasure
Allergic_Reaction
TrueFalse
20.879.2
Sneezing
TrueFalse
100 0
Scratches_on_Furniture
TrueFalse
9.9590.1
Cold
TrueFalse
51.748.3
Cat_Nearby
TrueFalse
15.284.8
HealthOfGrandmother
VisitGrandmother
GoStayHome
73.2510100.000
Pleasure
22
The evidence for cat allergy The evidence for cat allergy ““explains away” sneezingexplains away” sneezing
and cold is no longer needed and cold is no longer needed as an explanationas an explanation
Allergic_Reaction
TrueFalse
88.411.6
Sneezing
TrueFalse
100 0
Scratches_on_Furniture
TrueFalse
100 0
Cold
TrueFalse
14.485.6
Cat_Nearby
TrueFalse
91.58.53
HealthOfGrandmother
VisitGrandmother
GoStayHome
110.592100.000
Pleasure
Allergic_Reaction
TrueFalse
88.411.6
Sneezing
TrueFalse
100 0
Scratches_on_Furniture
TrueFalse
100 0
Cold
TrueFalse
14.485.6
Cat_Nearby
TrueFalse
91.58.53
HealthOfGrandmother
VisitGrandmother
GoStayHome
110.592100.000
Pleasure 33Does Maria have a Does Maria have a
“grandmother “grandmother neuron”?neuron”?
What Happened Under the Hood? What Happened Under the Hood?
• A decision graph is both a knowledge representation and a computational architecture
– Represents knowledge about variables and their interactions– Modular elements with defined interconnections– Computation can exploit loosely coupled structure for efficiency– Parsimony
» Probability distributions on 5 binary variables 31-dimensional space» Probability distributions for Maria’s Bayesian network 9-dimensional space
• Learning about one variable affects likelihood of other variables– Evidence “flows” along the arcs– Bidirectional inference– Learn structure and probabilities as cases accumulate
• The information update operation is called Bayes Rule – Bayesian inference is belief dynamics– Within-case evidence accumulation– Cross-case learning
Subjective ProbabilitySubjective Probability
• PS(E|B) is system’s degree of belief that E will occur given background information B
– In subjectivist theory there is no one “correct” probability
– Viewpoints vary on whether “objective probabilities” exist
• Probability as belief dynamics– If new information N is added to background information B then
belief in E changes to PS(E|B&N)
– Probability updating follows the dynamic equation known as Bayes rule
€
PS (E1 |B & N)
PS (E2 |B & N)=
PS (E1 |B)
PS (E2 |B)×
PS (N |B & E1)
PS (N |B & E2 )
€
PS (E1 |B & N)
PS (E2 |B & N)=
PS (E1 |B)
PS (E2 |B)×
PS (N |B & E1)
PS (N |B & E2 )
Prior odds ratioPrior odds ratioPosterior odds ratioPosterior odds ratio Likelihood ratioLikelihood ratio
- Belief in E1 increases relative to E2 if N was more likely to co-occur with E1 than with E2
Maria’s Continuing Saga…Maria’s Continuing Saga…
• Variation 1:– Tran is sneezing and saw scratches– Tran was recently exposed to a cold and probably is not
allergy prone
• Variation 2:– Tran saw scratches– Maria did not see scratches– Tran is in room with Maria
• Variation 3:– Tran and Maria both are sneezing, are allergy prone, and
saw scratches– Tran and Maria are a continent apart
Variation 1Variation 1
AllergyProne(Maria)
TrueFalse
100 0
AllergicReaction(Mar ...
TrueFalse
88.211.8
Sneezing(Maria)
TrueFalse
100 0
SeesScratches(Mar...
TrueFalse
100 0
ExposedToCold(Maria)
TrueFalse
15.784.3
ColdStatus(Maria)
TrueFalse
15.085.0
NearCat(Maria)
TrueFalse
91.48.63
Health(Grandmother1)
Pleasure(Maria,Grandmother1)Visit(Maria,Grandmother1)
GoStayHome
109.977100.000
AllergyProne(Maria)
TrueFalse
100 0
AllergicReaction(Mar ...
TrueFalse
88.211.8
Sneezing(Maria)
TrueFalse
100 0
SeesScratches(Mar...
TrueFalse
100 0
ExposedToCold(Maria)
TrueFalse
15.784.3
ColdStatus(Maria)
TrueFalse
15.085.0
NearCat(Maria)
TrueFalse
91.48.63
Health(Grandmother1)
Pleasure(Maria,Grandmother1)Visit(Maria,Grandmother1)
GoStayHome
109.977100.000
Allergy_Prone(Tran)
TrueFalse
5.7194.3
Allergic_Reaction(Tran)
TrueFalse
4.4395.6
Sees_Scratches(Tran)
TrueFalse
100 0
Cold_Status(Tran)
TrueFalse
97.32.69
Exposed_to_Cold(Tran)
TrueFalse
100 0
Near_Cat(Tran)
TrueFalse
65.534.5
Sneezing(Tran)
TrueFalse
100 0
Visit(Tran,Grandmother2)
GoStayHome
27.6902100.000
Health(Grandmother2)
Pleasure(Tran,Grandmother2)
Allergy_Prone(Tran)
TrueFalse
5.7194.3
Allergic_Reaction(Tran)
TrueFalse
4.4395.6
Sees_Scratches(Tran)
TrueFalse
100 0
Cold_Status(Tran)
TrueFalse
97.32.69
Exposed_to_Cold(Tran)
TrueFalse
100 0
Near_Cat(Tran)
TrueFalse
65.534.5
Sneezing(Tran)
TrueFalse
100 0
Visit(Tran,Grandmother2)
GoStayHome
27.6902100.000
Health(Grandmother2)
Pleasure(Tran,Grandmother2)
• Add background variables to specialize model to different individuals
• Still a “template model” with limited expressive power
Variation 2Variation 2
• Decision graph has replicated sub-parts
• Different kinds of entities (cats and people)
SeesScratches(Mar...
TrueFalse
54.945.1
AllergicReaction(Tran)
TrueFalse
5.6694.3
ColdStatus(Tran)
TrueFalse
97.02.98
Sneezing(Tran)
TrueFalse
100 0
AllergyProne(Maria)
TrueFalse
100 0
AllergicReaction(Mar ...
TrueFalse
88.111.9
Sneezing(Maria)
TrueFalse
100 0
ExposedToCold(Maria)
TrueFalse
15.884.2
ColdStatus(Maria)
TrueFalse
15.085.0
Near(Tran,Cat1)
TrueFalse
91.48.59
Near(Maria,Cat1)
TrueFalse
91.38.68
Sees_Scratches(Tran)
TrueFalse
100 0
AllergyProne(Tran)
TrueFalse
5.9994.0
ExposedToCold(Tran)
TrueFalse
100 0
Loc(Tran) Loc(Maria)Loc(Cat1)
Near(Maria,Tran)
TrueFalse
100 0
Health(Grandmother,T1)
Pleasure(Maria,Grandmother,T1)Visit(Maria,Grandmother, ...
GoStayHome
109.950100.000
SeesScratches(Mar...
TrueFalse
54.945.1
AllergicReaction(Tran)
TrueFalse
5.6694.3
ColdStatus(Tran)
TrueFalse
97.02.98
Sneezing(Tran)
TrueFalse
100 0
AllergyProne(Maria)
TrueFalse
100 0
AllergicReaction(Mar ...
TrueFalse
88.111.9
Sneezing(Maria)
TrueFalse
100 0
ExposedToCold(Maria)
TrueFalse
15.884.2
ColdStatus(Maria)
TrueFalse
15.085.0
Near(Tran,Cat1)
TrueFalse
91.48.59
Near(Maria,Cat1)
TrueFalse
91.38.68
Sees_Scratches(Tran)
TrueFalse
100 0
AllergyProne(Tran)
TrueFalse
5.9994.0
ExposedToCold(Tran)
TrueFalse
100 0
Loc(Tran) Loc(Maria)Loc(Cat1)
Near(Maria,Tran)
TrueFalse
100 0
Health(Grandmother,T1)
Pleasure(Maria,Grandmother,T1)Visit(Maria,Grandmother, ...
GoStayHome
109.950100.000
Variation 3 Done WrongVariation 3 Done Wrong
• Variation 2 model gets wrong answer if Maria and Tran are not near each other and both are near cats!
• We need to be able to hypothesize additional cats if and when necessary
SeesScratches(Mar...
TrueFalse
100 0
AllergicReaction(Tran)
TrueFalse
51.049.0
ColdStatus(Tran)
TrueFalse
35.964.1
Sneezing(Tran)
TrueFalse
100 0
AllergyProne(Maria)
TrueFalse
100 0
AllergicReaction(Mar ...
TrueFalse
51.049.0
Sneezing(Maria)
TrueFalse
100 0
ExposedToCold(Maria)
TrueFalse
33.866.2
ColdStatus(Maria)
TrueFalse
35.964.1
Near(Tran,Cat1)
TrueFalse
49.550.5
Near(Maria,Cat1)
TrueFalse
49.550.5
Sees_Scratches(Tran)
TrueFalse
100 0
AllergyProne(Tran)
TrueFalse
100 0
ExposedToCold(Tran)
TrueFalse
33.866.2
Loc(Tran) Loc(Maria)Loc(Cat1)
Near(Maria,Tran)
TrueFalse
0 100
Health(Grandmother,T1)
Pleasure(Maria,Grandmother,T1)Visit(Maria,Grandmother, ...
GoStayHome
89.1446100.000
SeesScratches(Mar...
TrueFalse
100 0
AllergicReaction(Tran)
TrueFalse
51.049.0
ColdStatus(Tran)
TrueFalse
35.964.1
Sneezing(Tran)
TrueFalse
100 0
AllergyProne(Maria)
TrueFalse
100 0
AllergicReaction(Mar ...
TrueFalse
51.049.0
Sneezing(Maria)
TrueFalse
100 0
ExposedToCold(Maria)
TrueFalse
33.866.2
ColdStatus(Maria)
TrueFalse
35.964.1
Near(Tran,Cat1)
TrueFalse
49.550.5
Near(Maria,Cat1)
TrueFalse
49.550.5
Sees_Scratches(Tran)
TrueFalse
100 0
AllergyProne(Tran)
TrueFalse
100 0
ExposedToCold(Tran)
TrueFalse
33.866.2
Loc(Tran) Loc(Maria)Loc(Cat1)
Near(Maria,Tran)
TrueFalse
0 100
Health(Grandmother,T1)
Pleasure(Maria,Grandmother,T1)Visit(Maria,Grandmother, ...
GoStayHome
89.1446100.000
But is the cat dead or alive?But is the cat dead or alive?
Variation 3 Done Right(…but what a mess!)
Variation 3 Done Right(…but what a mess!)
• This model gets the right answer on all the variations
Loc(Cat2,T1)
Near(Maria,Cat2,T1)
TrueFalse
42.957.1
AllergyProne(Maria)
TrueFalse
100 0
AllergicReaction(Maria, ...
TrueFalse
82.817.2
Sneezing(Maria,T1)
TrueFalse
100 0
SeesScratches(Maria, ...
TrueFalse
100 0
Sneezing(Tran,T1)
TrueFalse
100 0
AllergyProne(Tran)
TrueFalse
100 0
AllergicReaction(Tran,T1)
TrueFalse
82.817.2
SeesScratches(Tran, ...
TrueFalse
100 0
Near(Maria,{c}:Cat,T1)
TrueFalse
85.314.7
Near(Maria,Cat1:Cat, ...
TrueFalse
42.757.3
Near(Maria,Cat2:Cat, ...
TrueFalse
42.757.3
Type(Cat1)
CatOther
92.27.77
Near(Tran,Cat1:Cat,T1)
TrueFalse
42.757.3
Near(Tran,{c}:Cat,T1)
TrueFalse
85.314.7
Near(Tran,Cat2:Cat,T1)
TrueFalse
42.757.3
Type(Cat2)
CatOther
92.27.77
Near(Tran,Cat1,T1)
TrueFalse
42.957.1
Near(Maria,Cat1,T1)
TrueFalse
42.957.1
Near(Maria,Tran,T1)
TrueFalse
0 100
Near(Tran,Cat2,T1)
TrueFalse
42.957.1
Loc(Cat1,T1)
Loc(Tran,T1) Loc(Maria,T1)
ColdStatus(Tran,T0)
ColdExposedHealthy
13.813.073.2
ColdStatus(Tran,T1)
ColdExposedHealthy
18.08.7973.2
ColdStatus(Maria,T1)
ColdExposedHealthy
18.08.7973.2
ColdStatus(Maria,T0)
ColdExposedHealthy
13.813.073.2
Visit(Maria,Grandmother, ...
GoStayHome
107.03399.9999
Pleasure(Maria,Grandmother,T1)
Health(Grandmother,T1)
Loc(Cat2,T1)
Near(Maria,Cat2,T1)
TrueFalse
42.957.1
AllergyProne(Maria)
TrueFalse
100 0
AllergicReaction(Maria, ...
TrueFalse
82.817.2
Sneezing(Maria,T1)
TrueFalse
100 0
SeesScratches(Maria, ...
TrueFalse
100 0
Sneezing(Tran,T1)
TrueFalse
100 0
AllergyProne(Tran)
TrueFalse
100 0
AllergicReaction(Tran,T1)
TrueFalse
82.817.2
SeesScratches(Tran, ...
TrueFalse
100 0
Near(Maria,{c}:Cat,T1)
TrueFalse
85.314.7
Near(Maria,Cat1:Cat, ...
TrueFalse
42.757.3
Near(Maria,Cat2:Cat, ...
TrueFalse
42.757.3
Type(Cat1)
CatOther
92.27.77
Near(Tran,Cat1:Cat,T1)
TrueFalse
42.757.3
Near(Tran,{c}:Cat,T1)
TrueFalse
85.314.7
Near(Tran,Cat2:Cat,T1)
TrueFalse
42.757.3
Type(Cat2)
CatOther
92.27.77
Near(Tran,Cat1,T1)
TrueFalse
42.957.1
Near(Maria,Cat1,T1)
TrueFalse
42.957.1
Near(Maria,Tran,T1)
TrueFalse
0 100
Near(Tran,Cat2,T1)
TrueFalse
42.957.1
Loc(Cat1,T1)
Loc(Tran,T1) Loc(Maria,T1)
ColdStatus(Tran,T0)
ColdExposedHealthy
13.813.073.2
ColdStatus(Tran,T1)
ColdExposedHealthy
18.08.7973.2
ColdStatus(Maria,T1)
ColdExposedHealthy
18.08.7973.2
ColdStatus(Maria,T0)
ColdExposedHealthy
13.813.073.2
Visit(Maria,Grandmother, ...
GoStayHome
107.03399.9999
Pleasure(Maria,Grandmother,T1)
Health(Grandmother,T1)
ColdStatus(h1,t)
ColdExposedHealthy
8.359.8281.8
Visit(h1,h2,t)
GoStayHome
116.651100.000
Health(h2,t)
Pleasure(h1,h2,t)
ColdStatus(h1,t)
ColdExposedHealthy
8.359.8281.8
Visit(h1,h2,t)
GoStayHome
116.651100.000
Health(h2,t)
Pleasure(h1,h2,t)
The Solution: Multi-Entity Decision Graphs
The Solution: Multi-Entity Decision Graphs
SeesScratches(h,t)
TrueFalse
2.6397.4
Near(h,:Cat,t)
TrueFalse
2.7697.2
AllergicReaction(h,t)
TrueFalse
1.1098.9
AllergyProne(h)
TrueFalse
5.0095.0
SeesScratches(h,t)
TrueFalse
2.6397.4
Near(h,:Cat,t)
TrueFalse
2.7697.2
AllergicReaction(h,t)
TrueFalse
1.1098.9
AllergyProne(h)
TrueFalse
5.0095.0
Loc(y,t)
Near(x,y,t)
TrueFalse
3.0497.0
Loc(x,t)Loc(y,t)
Near(x,y,t)
TrueFalse
3.0497.0
Loc(x,t)
Type(c)
CatOther
50.050.0
Near(x,c:Cat,t)
TrueFalse
1.5098.5
Near(x,{c}:Cat,t)
TrueFalse
2.4897.5
Near(x,c,t)
TrueFalse
3.0097.0
Type(c)
CatOther
50.050.0
Near(x,c:Cat,t)
TrueFalse
1.5098.5
Near(x,{c}:Cat,t)
TrueFalse
2.4897.5
Near(x,c,t)
TrueFalse
3.0097.0
Sneezing(h,t)
TrueFalse
17.282.8
AllergicReaction(h,t)
TrueFalse
1.1398.9
ColdStatus(h,t)
ColdExposedHealthy
12.0 0
88.0
Sneezing(h,t)
TrueFalse
17.282.8
AllergicReaction(h,t)
TrueFalse
1.1398.9
ColdStatus(h,t)
ColdExposedHealthy
12.0 0
88.0
ColdStatus(h,t-1)
ColdExposedHealthy
8.359.8281.8
ColdStatus(h,t)
ColdExposedHealthy
8.359.8281.8
ColdStatus(h,t-1)
ColdExposedHealthy
8.359.8281.8
ColdStatus(h,t)
ColdExposedHealthy
8.359.8281.8
Cats & AllergiesCats & AllergiesFragmentFragment
SpatialSpatialFragmentFragment
HypothesisHypothesisManagementManagement
FragmentFragment
Colds&Time Colds&Time FragmentFragment
ValueValueFragmentFragment
SneezingSneezingFragmentFragment
• Specify model in pieces and let the computer compose them• First-order predicate calculus plus probabilities and decisions
ObservationsObservations
ActionsActions
Representing RepresentationRepresenting
Representation
““Real” WorldReal” World
• Stochastic process• Time evolution governed by
Shrödinger equation plus “quantum jumps”
• No good theory for:- Timing of reductions- Which operator is applied
Representation of Representation of ““Real” WorldReal” World
• Decisions and actions- When to take observation- Which question to ask
• Predicted outcomes- Probability distribution for next
observable• Values
- Accurate prediction- Survival
i = wave function before observationi+ = wave function after observationMi = measurement operationTi = time since last measurementEi = current experienceVi = value to player
- decision - chance event- value -deterministic event
– “Players” choose when to cause reduction events & operator to apply
– “Players” evolve representations– Consistent with quantum mechanics
» Schrödinger evolution between reductions
» Dirac probabilities for selecting actual experience from possible experiences
– “Players” choose when to cause reduction events & operator to apply
– “Players” evolve representations– Consistent with quantum mechanics
» Schrödinger evolution between reductions
» Dirac probabilities for selecting actual experience from possible experiences
Representation of “Player’s” Choice as Decision Graph
1 1+
O1 E1
wave functionreduction
ShrödingerDynamics
T1
2 2+
wave functionreduction
T2
“Information influence”
V1
O2 E2
V2
Described in Described in psychological psychological
termsterms
Described in Described in psychological psychological
termsterms
Information Information influences and influences and value nodes are value nodes are
modeled by modeled by standard physicsstandard physics
When to Reduce?When to Reduce?
• Game theoretic semantics– Player’s utility function includes effort of applying operator and value of
result – Choose reduction policy that maximizes player’s utility– Players interact and can affect each other’s utility– Evolutionary pressure for players who “like” policies conducive to
survival• As time since last observation increases
– Probability of “termination state” increases– Fatigue decreases
• Components of uncertainty– Intrinsic stochasticity (“object level” uncertainty)– Lack of knowledge (“higher order” uncertainty)– Approximation error (“model uncertainty”)
• As players evolve more complex and more accurate models– Forecasts become more accurate– Less higher order uncertainty– Better ability to control question asking
• Players can learn to share information and effort
Direction of TimeDirection of Time
• Second law of thermodynamics: time is direction of increasing physical entropy
• “Learning universe” hypothesis: time is direction of increasing knowledge of players about the universe they inhabit
• Can these arrows be reconciled?– Expansion of physical phase space
– Contraction of information phase space
CommunicationCommunication
• Learning can be faster when players exchange information
• Communicating players exchange messages
• Players can learn each other’s representations– Efficient communication: Player 1 expresses difference
between Player 1’s knowledge and Player 2’s knowledge in language of Player 2’s representation
– Mixed motives for information sharing
• Communication respects laws of physics– Intrinsic randomness
– Prevents “freezing” at local optima
SummarySummary
• Conscious agents construct representations• Conscious agents learn better representations
over time• Common mathematics and algorithms for
– Simulating physical systems– Learning complex representations
» Many parameters» High degree of conditional independence (representation is
restricted to low-dimensional subspace of all probability distributions)
» High degree of self-similarity
• Conscious subsystems of universe evolve to construct better representations of themselves and the world around them
To Think AboutTo Think About
• Where is information technology revolution heading?– Silicon intelligence?– Symbiotic carbon/silicon intelligence?– “Earth consciousness”?
• Assertion: It is important that we– Embed (decision theoretically) coherent logic and decision making rules in
hardware of the systems we build– Base software architecture on decision and game theoretic semantics– Map the software dynamics properly to the physical dynamics– Understand the semantics of the knowledge representations we construct – Understand how they are realized in the physics– Understand the interface between the physics and the representation
• Questions to address:– What base beliefs should we embed in hardware?– What base values values should we embed in hardware?– How should we initialize decision rules?
• It is better to have our eyes open and our minds engaged in considering the possibilities than to just let it happen to us
Speculative QuestionSpeculative Question• Can “intelligent life” be modeled as attractor in
phase space? – “Players” stay alive by constructing accurate (enough)
representations – Control exercised by “players” introduces nonlinearity– “Players” guide the system toward “edge of complexity”
» Simple enough to learn» Complex enough to evolve learners» Learners cooperate to organize into mutually beneficial societies
• Could we obtain a shadowing theorem?– Unconscious Schrodinger evolution moves away from the
attractor under influence of local forces– Wave function reduction brings system back toward the
attractor– Reduction event registers in consciousness of learners and
increases their knowledge– Consciously adopting policies that keep us near attractor has
survival value
Additional Speculative QuestionsAdditional Speculative Questions
• “Mixture distributions” over models of different dimensions are active research area
• Bayes rule gives rise to “natural Occam’s razor”– Bias toward simple models (low-dimensional parameter space)
– Dimensions are included as needed to explain observations
• Tractable approximation of complex models– Algorithms imported from physics (e.g., variational methods,
Markov Chain Monte Carlo) are being applied to learn very complex models
– Can we be modeled as MCMC samplers learning a representation of the universe we live in?
• If we average over models of different dimensions the parameter space is not a smooth manifold
– Image: quantum foam
– Might there be something to this image?
