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					         Unified Cognitive Science
• Neurobiology
• Psychology
• Computer Science
• Linguistics
• Philosophy
• Social Sciences
• Experience

Take all the Findings and Constraints Seriously
What are schemas?
•   Regularities in our perceptual, motor and
    cognitive systems
•   Structure our experiences and interactions
    with the world.
•   May be grounded in a specific cognitive
    system, but are not situation-specific in their
    application (can apply to many domains of
    experience)
      Basis of Image
        schemas
• Perceptual systems
• Motor routines
• Social Cognition
• Image Schema properties depend on
  • Neural circuits
  • Interactions with the world
    Spatial schemas
• TR/LM relation
• Boundaries, bounded region
• Topological relations
• Orientational Axes
• Proximal/Distal
    Trajector/Landmark
         Schema

• Roles:
 Trajector (TR) – object being located
 Landmark (LM) – reference object
   TR and LM may share a location (at)
    TR/LM -- asymmetry

• The cup is on the table
• ?The table is under the cup.

• The skateboard is next to the post.
• ?The post is next to the skateboard.
Topological Relations


• Separation
Topological Relations


• Separation
• Contact
Topological Relations
• Separation
• Contact
• Coincidence:
  - Overlap
  - Inclusion
         Orientation
• Vertical axis -- up/down
 up
               above


                             upright
               below
 down
         Orientation
Horizontal plane – Two axes:
Language and Frames
    of Reference
• There seem to be three prototypical
  frames of reference in language
  (Levinson)
 • Intrinsic
 • Relative
 • Absolute
Intrinsic frame of
     reference

               left

back                  front

       right
Relative frame of
   reference

                right??

back                      front


       left??
Absolute frame of
   reference

               west

south                 north

        east
    Representing image
         schemas
semantic schema Source-Path-Goal    semantic schema Container
   roles:                              roles:
        source                              interior
        path                                exterior
        goal                                portal
        trajector                           boundary


                                   Boundary
                                              Interior
           Trajector
Source                   Goal                             Portal
             Path
                                                         Exterior


   These are abstractions over sensorimotor experiences.
           Language and Spatial Schemas
•   People say that they look up to some people, but look down on
    others because those we deem worthy of respect are somehow
    “above” us, and those we deem unworthy are somehow “beneath”
    us.
•   But why does respect run along a vertical axis (or any spatial axis,
    for that matter)? Much of our language is rich with such spatial talk.
•   Concrete actions such as a push or a lift clearly imply a vertical or
    horizontal motion, but so too can more abstract concepts.
•   Metaphors: Arguments can go “back and forth,” and hopes can get
    “too high.”
Regier Model Lecture

   Jerome A. Feldman
          March 4, 2008
   With help from Matt Gedigian
Neural Theory of Language
       Language Development in Children


• 0-3 mo: prefers sounds in native language
• 3-6 mo: imitation of vowel sounds only
• 6-8 mo: babbling in consonant-vowel segments
• 8-10 mo: word comprehension, starts to lose sensitivity to
  consonants outside native language
• 12-13 mo: word production (naming)
• 16-20 mo: word combinations, relational words (verbs, adj.)
• 24-36 mo: grammaticization, inflectional morphology
• 3 years – adulthood: vocab. growth, sentence-level
  grammar for discourse purposes
  Trajector/Landmark
        Schema

• Roles:
 Trajector (TR) – object being located
 Landmark (LM) – reference object
   TR and LM may share a location (at)
      Language and Frames of
            Reference

• There seem to be three prototypical frames of
  reference in language (Levinson)
 • Intrinsic
 • Relative
 • Absolute
                      English „on‟
     1. The computer is on the desk
     2. The picture is on the wall
     3. The projector is on the ceiling
UP
             TR                     TR          LM
                                                  TR
           LM
                                 LM
DN
     TR/LM, verticality,   TR/LM, contact,   TR/LM, contact,
     contact, support      attaching force   attaching force
          Image schemas
•   Trajector / Landmark (asymmetric)
    • The bike is near the house               TR         LM
    • ? The house is near the bike
•   Boundary / Bounded Region
                                                       boundary
                                                bounded region
    •   bounded region has a closed boundary
•   Topological Relations
    • Separation, Contact, Overlap, Inclusion, Surround
•   Orientation
    • Vertical (up/down), Horizontal
    • Absolute (E, S, W, N)
    Spatial schemas
• TR/LM relation
• Boundaries, bounded region
• Topological relations
• Orientational Axes
• Proximal/Distal
        Regier‟s Model
 above below      left    right   in     out   on   off



                    Learning System


                           TR
         Input:                        above
                          LM


• Training input: configuration of TR/LM and the correct
  spatial relation term
• Learned behavior: input TR/LM, output spatial relation
            Issue #1: Implicit Negatives


•   Children usually do not get explicit negatives
•   But we won‟t know when to stop generalizing if we don‟t
    have negative evidence
•   Yet spatial relation terms aren‟t entirely mutually
    exclusive
•   The same scene can often be described with two or
    more spatial relation terms (e.g. above and outside)
•   How can we make the learning problem realistic yet
    learnable?
       Dealing with Implicit Negatives

•   Explicit positive for above
•   Implicit negatives for below, left, right, etc


•   in Regier:
       E = ½ ∑i,p (( ti,p – oi,p) * βi,p )2,

       where i is the node, p is the pattern,
       βi,p = 1 if explicit positive,
       βi,p < 1 if implicit negative
above – positive examples
above – negative examples
above – after training
above – test examples
Learning
System
dynamic relations
(e.g. into)


structured connectionist
network (based on
visual system)
           Issue #2: Shift Invariance



•   Backprop cannot handle shift invariance (it cannot
    generalize from 0011, 0110 to 1100)
•   But the cup is on the table whether you see it right
    in the center or from the corner of your eyes (i.e. in
    different areas of the retina map)
•   What structure can we utilize to make the input
    shift-invariant?
Topological Relations
• Separation
• Contact
• Coincidence:
  - Overlap
  - Inclusion
- Encircle/surround
        Limitations
• Scale
• Uniqueness/Plausibility
• Grammar
• Abstract Concepts
• Inference
• Representation
    Demo of the
   Regier System
• on the English above
     Language and
       Thought
   Language           •   We know thought (our cognitive
                          processes) constrains the way
                          we learn and use language
                      •   Does language also influence
                          thought?
                      •   Benjamin Whorf argues yes
                      •   Psycholinguistics experiments
    Thought               have shown that linguistics
                          categories influence thinking
                          even in non-linguistics task
cognitive processes
              Image schemas
• Trajector / Landmark (asymmetric)
   • The bike is near the house
   •   ?   The house is near the bike
                                              TR       LM

• Boundary / Bounded Region                           boundary


   • a bounded region has a closed boundary    bounded region


• Topological Relations
   • Separation, Contact, Overlap, Inclusion, Surround
• Orientation
   • Vertical (up/down), Horizontal (left/right, front/back)
   • Absolute (E, S, W, N)
      More image schemas
• Proximal / Distal
   • distance from center (near/far)
• Part / Whole
   • top of the hill, cover of the magazine
• Container
   • interior, exterior, boundary, portal
• Source-Path-Goal                                 P
   • source, path, goal, trajector        S   TR       G

• Force-Dynamics
   • support, force
        Regier‟s Model
 above below      left    right   in     out   on   off



                    Learning System


                           TR
         Input:                        above
                          LM


• Training input: configuration of TR/LM and the correct
  spatial relation term
• Learned behavior: input TR/LM, output spatial relation
Learning
System
dynamic relations
(e.g. into)


structured connectionist
network (based on
visual system)

  We‟ll look at the
  details next lecture

				
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posted:7/27/2011
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