Connectionist Models of Analogical Reasoning

1. Connectionist ModelsofAnalogical Reasoning Cesare Bianchi

2. Overview • Symbolic and Connectionist Models • The Binding Problem • LISA Model • Leech’s Model

3. Symbolic SME IAM I-SME SEQL ACT-R BORIS MORRIS … Hybrid COPYCAT TABLETOP LETTER-SPIRIT METACAT AMBR and AMBR-2 ASTRA ABR-conposit … Models of Analogical Reasoning 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 Sub Proposition (SB) Units John-loves1 Mary-loves2 loves1 John Mary loves2 Predicate and Object Units Semantic Units actor emotion1 positive1 male human female patient emotion2 positive2

11. LISA Architecture Firing Scheme John loves Mary John-loves1 Mary-loves2 loves1 John Mary loves2 actor emotion1 positive1 male human female patient emotion2 positive2

12. LISA Architecture Firing Scheme John loves Mary John-loves1 Mary-loves2 loves1 John Mary loves2 actor emotion1 positive1 male human female patient emotion2 positive2

13. LISA Architecture Firing Scheme John loves Mary John-loves1 Mary-loves2 loves1 John Mary loves2 actor emotion1 positive1 male human female patient emotion2 positive2

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

15. 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. Leech’s Model “ [...] there is no explicit coding of the relation itself. The similarity between two different examples of a relation (e.g. the similarity between apple:cut-apple and bread:cutbread) lies in how the perceptual features of the objects involved are transformed. (Leech et al., 2003) ”

18. Leech’s Model Output 1: Transformed Object Output 2: Causal Agent Hidden Input 1: Object Input 2: Causal Agent

19. Leech’s 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

20. Leech’s Model Priming Output 1: Cut Apple Output 2: Nothing Hidden Input 1: Apple Input 2: Nothing

21. Leech’s Model Priming Output 1: Cut Apple Output 2: Knife Hidden Input 1: Apple Input 2: Knife

22. Leech’s Model Retrieval Output 1: Nothing Output 2: Nothing Hidden Input 1: Bread Input 2: Nothing

23. Leech’s 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 Leech’s model • Try to add synchronized patterns to Leech’s 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. 6:200-205 • Hummel and Holyoak, 1997. "Distributed representations of structure: A theory of analogical access and mapping." Psychological Review. 104:427-466 • 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