The Neural Basis of Thought and Language

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The Neural Basis ofThought and Language

• Week 11
• Metaphor and Bayes Nets

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Schedule

• Assignment 7 extension, due Wednesday night
• Last Week
• Aspect and Tense
• Event Structure Metaphor
• This Week
• Frames how it maps to X-schemas
• Inference, KARMA Knowledge-based Action
  Representations for Metaphor and Aspect
• Next Week
• Grammar

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Announcement

• Panel "Cruise Control" Careers in Artificial
  Intelligence.
• Friday, April 16th from 3-430 in Bechtel Hall
  120A/B.
• The panel is an informal session, where
  professionals in the field of AI will answer
  general questions about their entry into the
  field, trends, etc.
• Panelists will be
• Peter Norvig from Google
• Charlie Ortiz of Teambotics at SRI
• Nancy Chang from ICSI.
• Moderator will be
• Barbara Hightower, CS advisor.

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Quiz

1. What are metaphors? Give two examples of Primary
   Metaphors and sentences using them.
2. What are Event Structure Metaphors? Give an
   example.
3. How do Bayes Nets fit into the simulation story?
   What are the benefits of that model?
4. What are Dynamic Bayesian Networks?

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Going from motor control to abstract reasoning

• The sensory-motor system is directly engaged in
  abstract reasoning
• Both the physical domain and abstract domain are
  structured by schemas and frames, i.e. there are
• semantic roles, and
• relation between semantic roles
• schemas generally refer to embodied, universal
  knowledge, whereas frames are generally
  culturally specific

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Frames and FrameNet

• Formalizes links between semantics and syntax
• FrameNet
• For every target word (ideally word sense)
• Describes underlying frames or conceptual
  structures
• Semantic frames are schemas
• Frame elements (roles)
• Participants, props, etc...
• Event Frames
• Temporal structure
• Constraints on before/during/after
• E.g. Commercial Transaction

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The Commercial-Transaction schema
schema Commercial-Transaction subcase of
Exchange roles customer participant1 vend
or participant2 money entity1
Money goods entity2 goods-transfer
transfer1 money-transfer transfer2
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Quiz

1. What are metaphors? Give two examples of Primary
   Metaphors and sentences using them.
2. What are Event Structure Metaphors? Give an
   example.
3. How do Bayes Nets fit into the simulation story?
   What are the benefits of that model?
4. What are Dynamic Bayesian Networks?

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Metaphors

• metaphors are mappings from a source domain to a
  target domain
• metaphor maps specify the correlation between
  source domain entities / relation and target
  domain entities / relation
• they also allow inference to transfer from source
  domain to target domain (possibly, but less
  frequently, vice versa)

ltTARGETgt is ltSOURCEgt
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Primary Metaphors

• The key thing to remember about primary metaphors
  is that they have an experiential basis

• Affection Is Warmth
• Important is Big
• Happy is Up
• Intimacy is Closeness
• Bad is Stinky
• Difficulties are Burdens
• More is Up
• Categories are Containers
• Similarity is Closeness

• Linear Scales are Paths
• Organization is Physical Structure
• Help is Support
• Time Is Motion
• Relationships are Enclosures
• Control is Up
• Knowing is Seeing
• Understanding is Grasping
• Seeing is Touching

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Affection is Warmth

• Subjective Judgment Affection
• Sensory-Motor Domain Temperature
• Example They greeted me warmly.
• Primary Experience Feeling warm while being held
  affectionately.
• more examples
• She gave me a cold shoulder
• Now that I've known such-and-such for a while,
  he's finally warming up to me.

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Important is Big

• Subjective Judgment Importance
• Sensory-Motor Domain Size
• Example Tomorrow is a big day.
• Primary experience As a child, important things
  in your environment are often big, e.g., parents,
  but also large things that exert a force on you
• more examples
• Don't sweat the small stuff.
• I'll have a meeting with the big boss today.

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How are these metaphors developed?

• Conflation HypothesisChildren hypothesize an
  early meaning for a source domain word that
  conflates meanings in both the literal and
  metaphorical senses
• experiencing warmth and affection when being held
  as a child
• observing a higher water level when there's more
  water in a cup

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The Dual Metaphors for Time

• Time is stationary and we move through it
• It takes a long time to write a book
• We are behind schedule
• schedules are landmarks on this landscape that we
  have to be at by a certain time
• Time is a moving object
• The deadline is approaching
• He is forever chasing his past
• the past is an object that has come by and moved
  past him

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A different experiment by Boroditsky Ramscar,
2002

• Next Wednesday's meeting has been moved forward
  two days. What day is the meeting now that it has
  been rescheduled?
• Is the meeting Monday? or Friday?

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Results of the experiment

• two spatial primes
• participant sitting in an office chair moving
  through space. (ego-moving prime)
• participant pulling an office chair towards
  himself with a rope. (time-moving prime)
• results
• more likely to say Friday
• more likely to say Monday

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Quiz

1. What are metaphors? Give two examples of Primary
   Metaphors and sentences using them.
2. What are Event Structure Metaphors? Give an
   example.
3. How do Bayes Nets fit into the simulation story?
   What are the benefits of that model?
4. What are Dynamic Bayesian Networks?

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Event Structure Metaphor

• Target Domain event structure
• Source Domain physical space
• States are Locations
• Changes are Movements
• Causes are Forces
• Causation is Forced Movement
• Actions are Self-propelled Movements
• Purposes are Destinations
• Means are Paths
• Difficulties are Impediments to Motion
• External Events are Large, Moving Objects
• Long-term Purposeful Activities are Journeys

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The Dual of the ESM

• Attributes are possessions
• Changes are Movements of Possessions
  (acquisitions or losses)
• Causes are forces
• Causation is Transfer of Possessions (giving or
  taking)
• Purposes are Desired Objects
• Achieving a Purpose Is Acquiring a Desired Object

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Examples of the Dual

• I have a headache.
• I got a headache.
• My headache went away.
• The noise gave me a headache.
• The aspirin took away my headache.
• I'm in trouble. (Location ESM)
• The programming assignment gave me much trouble.
  (Object ESM)

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Quiz

1. What are metaphors? Give two examples of Primary
   Metaphors and sentences using them.
2. What are Event Structure Metaphors? Give an
   example.
3. How do Bayes Nets fit into the simulation story?
   What are the benefits of that model?
4. What are Dynamic Bayesian Networks?

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Simulation-based Understanding
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Semantic Analysis

• Takes in constructions
• pairing of form and meaning
• Form pole syntax
• Meaning pole frames and other schemas
• Spits out semantic specification
• schemas with bound roles

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What exactly is simulation?

• Belief update plus X-schema execution

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Bayes Nets Take away points

• Computational technique to capture best fit
• Probabilistic
• Approximation to neural spreading activation
• Easy to write down (intuitive)
• Nodes in terms of explicit causal relations
• Efficient
• Much smaller than full joint...
• Known mechanisms to do inference

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Review Probability

• Random Variables
• Boolean/Discrete
• True/false
• Cloudy/rainy/sunny
• Continuous
• 0,1 (i.e. 0.0 lt x lt 1.0)

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Priors/Unconditional Probability

• Probability Distribution
• In absence of any other info
• Sums to 1
• E.g. P(SunnyT) .8 (thus, P(SunnyF) .2)
• This is a simple probability distribution
• Joint Probability
• P(Sunny, Umbrella, Bike)
• Table 23 in size
• Full Joint is a joint of all variables in model
• Probability Density Function
• Continuous variables
• E.g. Uniform, Gaussian, Poisson

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Conditional Probability

• P(Y X) is probability of Y given that all we
  know is the value of X
• E.g. P(cavityT toothacheT) .8
• thus P(cavityF toothacheT) .2
• Product Rule
• P(Y X) P(X Y) / P(X) (normalizer to add up to
  1)

Y
X
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Inference
Toothache Cavity Catch Prob
False False False .576
False False True .144
False True False .008
False True True .072
True False False .064
True False True .016
True True False .012
True True True .108
P(ToothacheT)?P(ToothacheT, CavityT)?
P(ToothacheT CavityT)?
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Bayes Nets
P(B)
0.001
P(E)
0.002
B E P(A)
TTFF TFTF 0.950.940.290.001
A P(J)
TF 0.900.05
A P(M)
TF 0.700.01
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Graphical Models

• P(Y X)
• P(X Y) P(Y)
• P(X)
• What is P(YFXT)?
• What is P(XTYF)?
• What does it mean to have evidence?

X
Sneezing
P(XT) .3
Y
P(YTXT) .7 P(YTXF) .2
Cold
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Independence
X independent of Z? X conditionally
independent of Z given Y?
X
Y
Z
X
Y
Z
No
Yes
X
Z
X
Z
No
Yes
Y
Y
Y
Y
Yes
Or below
X
Z
X
Z
No
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Markov Blanket
X
X is independentof everything else
givenParents, Children, Parents of Children
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Reference Joints

• Representation of entire network
• P(X1x1 ? X2x2 ? ... Xnxn) P(x1, ..., xn)
  ?i1..n P(xiparents(Xi))
• How? Chain Rule
• P(x1, ..., xn) P(x1x2, ..., xn) P(x2, ..., xn)
  ... ?i1..n P(xixi-1, ..., x1)
• Now use conditional independences to simplify

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Reference Joint, cont.

• P(x1, ..., x6) P(x1) P(x2x1) P(x3x2, x1)
  P(x4x3, x2, x1) P(x5x4, x3, x2, x1)
  P(x6x5, x4, x3, x2, x1)

X4
X2
X6
X1
X3
X5
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Reference Joint, cont.

• P(x1, ..., x6) P(x1) P(x2x1) P(x3x2, x1)
  P(x4x3, x2, x1) P(x5x4, x3, x2, x1)
  P(x6x5, x4, x3, x2, x1)

X4
X2
X6
X1
X3
X5
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Reference Inference

• General case
• Variable Eliminate
• P(Q E) when you have P(R, Q, E)
• P(Q E) ?R P(R, Q, E) / ?R,Q P(R, Q, E)
• ?R P(R, Q, E) P(Q, E)
• ?Q P(Q, E) P(E)
• P(Q, E) / P(E) P(Q E)

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Reference Inference, cont.

• Q X1, E X6
• R X \ Q,E
• P(x1, ..., x6) P(x1) P(x2x1) P(x3x1)
  P(x4x2) P(x5x3) P(x6x5, x2)

P(x1, x6) ?x2 ?x3 ?x4 ?x5 P(x1) P(x2x1)
P(x3x1) P(x4x2) P(x5x3) P(x6x5, x2) P(x1)
?x2 P(x2x1) ?x3 P(x3x1) ?x4 P(x4x2) ?x5
P(x5x3) P(x6x5, x2) P(x1) ?x2 P(x2x1) ?x3
P(x3x1) ?x4 P(x4x2) m5(x2, x3) P(x1) ?x2
P(x2x1) ?x3 P(x3x1) m5(x2, x3) ?x4 P(x4x2)
...
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Approximation Methods

• Simple
• no evidence
• Rejection
• just forget about the invalids
• Likelihood Weighting
• only valid, but not necessarily useful
• MCMC
• Best only valid, useful, in proportion

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Stochastic Simulation
P(WetGrassCloudy)?
P(WetGrassCloudy) P(WetGrass ? Cloudy) /
P(Cloudy)
1. Repeat N times 1.1. Guess Cloudy at
random 1.2. For each guess of Cloudy, guess
Sprinkler and Rain, then WetGrass 2.
Compute the ratio of the runs where
WetGrass and Cloudy are True over the runs
where Cloudy is True
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Quiz

1. What are metaphors? Give two examples of Primary
   Metaphors and sentences using them.
2. What are Event Structure Metaphors? Give an
   example.
3. How do Bayes Nets fit into the simulation story?
   What are the benefits of that model?
4. What are Dynamic Bayesian Networks?

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DBNs

• Explicit causal relations full joint table ?
  Bayes Nets
• Sequence of full joint states over time ? HMM
• HMM BN ? DBNs
• DBNs are a generalization of HMMs which capture
  sparse causal relationships of full joint

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Dynamic Bayes Nets