Connectionist Models of Analogical Reasoning

1
Connectionist ModelsofAnalogical Reasoning

• Cesare Bianchi

2
Overview

• Symbolic and Connectionist Models
• The Binding Problem
• LISA Model
• Leechs Model

3
Models of Analogical Reasoning

• Symbolic
• SME
• IAM
• I-SME
• SEQL
• ACT-R
• BORIS
• MORRIS

• Hybrid
• COPYCAT
• TABLETOP
• LETTER-SPIRIT
• METACAT
• AMBR and AMBR-2
• ASTRA
• ABR-conposit

• Connectionist
• ACME
• STAR-1 and STAR-2
• DRAMA
• Analogator

(French, 2002)
4
Differences

• symbolic systems readily model structure
  sensitivity but often fail to demonstrate
  humanlike flexibility, whereas connectionist
  systems exhibit flexibility in pattern matching
  and generalization but have great difficulty in
  forming or manipulating structured
  representations
• (Hummel and Holyoak, 1997)

5
The binding problem

• Representing a proposition entails binding the
  argument roles of the proposition to their
  fillers
• (ibidem)

John loves Mary
Loves
John
Mary
lover
beloved
6
The binding problem

• Symbolic solution

John loves Mary
Loves
lover
beloved
John
Mary
7
The binding problem

• Connectionist solution

John loves Mary
Loves
Hates
Mary
Lucy
John
Sam
8
The binding problem

• Adding Synchronicity

Loves
Mary
John loves Mary
John
lover
beloved
9
LISA

• LISA (Learning and Inference with Schemas and
  Analogies), represents propositions (predicates
  and their arguments) as distributed patterns of
  activation over units representing semantic
  primitives.
• (ibidem)

10
LISA Architecture
Structure Units
John loves Mary
P Units
John-loves1
Mary-loves2
Sub Proposition (SB) Units
loves1
loves2
John
Mary
Predicate and Object Units
Semantic Units
actor
emotion1
positive1
patient
emotion2
positive2
male
human
female
11
LISA Architecture
Firing Scheme
John loves Mary
John-loves1
Mary-loves2
loves1
loves2
John
Mary
actor
emotion1
positive1
patient
emotion2
positive2
male
human
female
12
LISA Architecture
Firing Scheme
John loves Mary
John-loves1
Mary-loves2
loves1
loves2
John
Mary
actor
emotion1
positive1
patient
emotion2
positive2
male
human
female
13
LISA Architecture
Firing Scheme
John loves Mary
John-loves1
Mary-loves2
loves1
loves2
John
Mary
actor
emotion1
positive1
patient
emotion2
positive2
male
human
female
14
LISA Architecture
likes1
Analogical Mapping
loves1
Bill
likes2
Bill likes Susan
John
Susan
loves2
fears1
John loves Mary
Peter fears Beth
Peter
Mary
fears2
Driver
Recipients
Beth
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LISA strength

• unlike virtually all current analogy models
  in which mapping is treated as an explicit
  comparison between analogs (based on symbols
  representing hypothesized correspondences),
  mapping in LISA is a much more implicit process
  in which the recipient reacts to semantic
  patterns created by the driver.
• (ibidem)

16
LISA limitations

• LISA has a number of inherent limitations,
  including capacity limits, sensitivity to the
  manner in which a problem is represented, and
  sensitivity to strategic factors such as the
  order in which elements of a problem are
  processed.
• (ibidem)

17
Leechs Model

• ... there is no explicit coding of the relation
  itself. The similarity between two different
  examples of a relation (e.g. the similarity
  between applecut-apple and breadcutbread) lies
  in how the perceptual features of the objects
  involved are transformed.
• (Leech et al., 2003)

18
Leechs Model
Output 1 Transformed Object
Output 2 Causal Agent
Hidden
Input 1 Object
Input 2 Causal Agent
19
Leechs Model
Training Contrastive Hebbian Learning

• Random Patterns
• 20 Objects
• 4 Causal Agents
• 4 Transformation Vectors

Transformation Vector Cutting
Output 1 Cut Apple
Output 2 Knife
Hidden
Input 1 Apple
Input 2 Knife
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Leechs Model
Priming
Output 1 Cut Apple
Output 2 Nothing
Hidden
Input 1 Apple
Input 2 Nothing
21
Leechs Model
Priming
Output 1 Cut Apple
Output 2 Knife
Hidden
Input 1 Apple
Input 2 Knife
22
Leechs Model
Retrieval
Output 1 Nothing
Output 2 Nothing
Hidden
Input 1 Bread
Input 2 Nothing
23
Leechs Model
Retrieval
Transformation Vector Cutting
Output 1 Cut Bread
Output 2 Nothing
Hidden
Input 1 Bread
Input 2 Nothing
24
Future directions

• Use real distributed representation in LISA
  model
• Use features (instead of random patterns) in
  Leechs model
• Try to add synchronized patterns to Leechs model
• Test both models with larger knowledge base and
  more complex problems

25
References

• French, 2002. "The computational modeling of
  analogy-making." Trends in Cognitive Sciences.
  6200-205
• Hummel and Holyoak, 1997. "Distributed
  representations of structure A theory of
  analogical access and mapping." Psychological
  Review. 104427-466
• Leech, Mareschal and Cooper, 2003. "A
  connectionist account of analogical development"
  in R. Altman D. Kirsch (Eds.), Proceedings of
  the twenty-fifth annual conference of the
  Cognitive Science Society. 710-715. London LEA