1. The Concrete Substrates of Abstract Rule Use Bradley Love www.ccc.utexas.edu

2. Three Domains • Tracking basic statistics in our environment. • Learning seemingly abstract rules. • Learning and reasoning about future rewards in dynamic environments.

3. Basic Story • Learning is constrained by • non-rational mechanisms • the nature of domain representations • trial-by-trial updates with regards to current representations in memory. • Seemingly abstract or rational explanations prove not to be upon closer inspection.

4. Tracking Basic Statistics • Variance • Mean

5. Tracking Variability

6. Tracking Variability

7. Rational Models • Fried and Holyoak (1984) • Maximum likelihood • unbiased estimator/consistent • Tenenbaum and Griffiths (2001) • Bayesian updating • Globally Bayesian

8. Tracking Variability

9. Obvious Mechanistic Approach • Error driven learning of cluster position and variance. • updates are trial by trial • are with regard to a memory representation of each category

10. Formally..

11. Mechanistic Model

12. Rational or Mechanistic? • Trial by trial error-driven learning makes local updates. • all statistics are local in error-driven learning • We can use this to disentangle the competing explanations.

15. Tracking Variability (locally)

17. What about the mean?

18. What about the mean?

19. Tracking Statistics • People appear to update with regards to representations in memory in a trial-by-trial fashion. • Learning is error-driven and sensitive to the error term (i.e., task goal) • we see this in many domains (e.g., inference vs. classification learning)

20. Verbal Rules? • Certainly, we can implement and report strategies, but that doesn’t imply categories are represented as rules. • Are rules more concrete than they appear?

21. Are people really using rules? • Rules aren’t always rules (e.g., Allen & Brooks, 1991; Ramscar, 2002). • One alternative is clusters with selective attention. • more schema-like

24. Value 2 2 1 1 1 2 A 2 2 1 2 2 B 2 1 2 1 1 B 2 2 2 1 1 B 2 1 1 2 2 B Value 1 1 1 1 2 1 B 1 2 1 2 2 A 1 1 2 1 1 A 1 2 2 1 1 A 1 1 1 2 2 A 1 2 1 1 1 A 1 1 2 2 2 A 1 1 2 1 2 A 1 2 1 2 1 A Sakamoto and Love (2004)

25. Value 2 2 1 1 1 2 A 2 2 1 2 2 B 2 1 2 1 1 B 2 2 2 1 1 B 2 1 1 2 2 B Value 1 1 1 1 2 1 B 1 2 1 2 2 A 1 1 2 1 1 A 1 2 2 1 1 A 1 1 1 2 2 A 1 2 1 1 1 A 1 1 2 2 2 A 1 1 2 1 2 A 1 2 1 2 1 A Sakamoto and Love (2004) Rule Route If small, then A. If large, then B. Exception Route memorize item

26. Value 2 2 1 1 1 2 A 2 2 1 2 2 B 2 1 2 1 1 B 2 2 2 1 1 B 2 1 1 2 2 B Value 1 1 1 1 2 1 B 1 2 1 2 2 A 1 1 2 1 1 A 1 2 2 1 1 A 1 1 1 2 2 A 1 2 1 1 1 A 1 1 2 2 2 A 1 1 2 1 2 A 1 2 1 2 1 A Sakamoto and Love (2004)

27. Following-A Violating-B Following-A

28. Following-A Violating-B Following-A

29. Value 2 2 1 1 1 2 A 2 2 1 2 2 B 2 1 2 1 1 B 2 2 2 1 1 B 2 1 1 2 2 B Value 1 1 1 1 2 1 B 1 2 1 2 2 A 1 1 2 1 1 A 1 2 2 1 1 A 1 1 1 2 2 A 1 2 1 1 1 A 1 1 2 2 2 A 1 1 2 1 2 A 1 2 1 2 1 A Sakamoto and Love (2004)

30. “Abstract” Rules • Abstract rules are not specified by fixed-values. • e.g., learning an abstract notion of same and different • Could abstract responding be grounded in concrete episodes and trial-by-trial learning?

31. Exemplar Model Kruschke’s (1992) ALCOVE

32. Category association Learns association and attention weights Luminance Size

33. Attention Learns association and attention weights Luminance Size

34. Adding Structure: Chase Chase Chased Chased Chaser Chaser

35. one-to-one correspondence Chase Chase Chased Chased Chaser Chaser One or the other, not both

36. Parallel Connectivity Chase Chase Perfect relational match, but feature mismatches. Parallel connectivity satisfied.

37. Parallel Connectivity Chase Chase Two relational mismatches, but high feature match. Parallel Connectivity violated.

38. Disambiguation: Attention Chase Chase Attention determines the trade-off.

39. BRIDGES

40. Do, Do, Re (pause) Me, Me, Fa (pause) Ti, Ti, Sa (pause) ... Learning Abstract Rules • Marcus et al. showed infants can learn to distinguish simple grammars. • AAB pattern vs. ABB pattern • No diagnostic features • Infants habituated to one grammar, then tested with novel sounds from both grammars

41. Representation • Attention on position constrained • Only type-token relation used a a b Type_of( , ) Type_of( , ) Type_of( , ) a1 A a2 A b1 B

42. Same grammar • Relations: perfect similarity, parallel connectivity preserved a a b c c d Type_of( , ) Type_of( , ) Type_of( 1, ) Type_of( , ) Type_of( , ) Type_of( , ) a1 A c1 C a2 A c2 C b B d1 D

43. Opposite grammar • Relations: 1 mismatch, parallel connectivity not preserved a a b e f f Type_of( , ) Type_of( , ) Type_of( , ) Type_of( , ) Type_of( , ) Type_of( , ) a1 A e E a2 A f1 F b1 B f2 F

44. Learning • Attention shifts from inconsistent features to predictive relations • Concrete exemplar-based memory and attention shifting to relations explains performance

45. Lurking Concreteness in Abstract Concepts • Pigeons appear to learn the concept of same and different. Same Different Young, Wasserman and others - 1997, 2001, 2004

46. Experimental Details • 16 “Same” grids, 16 “Different” grids -> 4 x 4 • Pigeons trained to peck green for same, red for different • Then tested with novel icons and old icons • accuracy was 83% with old icons, 71% with new BRIDGES captures this pattern...

47. Concrete basis revealed in graded structure Shades of grey Same Different

48. Determining relational similarity Shades of grey Match Match Same Different Mismatch Mismatch 13 Mismatches 2 Mismatches

49. Relational categories are graded Shades of grey Shades of grey Same Different

50. Relational categories are graded Shades of grey Same Different