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The Concrete Substrates of Abstract Rule UseThree DomainsBasic StoryTracking Basic StatisticsTracking VariabilitySlide 6Rational ModelsSlide 8Obvious Mechanistic ApproachFormally..Mechanistic ModelRational or Mechanistic?PowerPoint PresentationSlide 14Tracking Variability (locally)Slide 16What about the mean?Slide 18Tracking StatisticsVerbal Rules?Are people really using rules?Slide 22Slide 23Sakamoto and Love (2004)Slide 25Slide 26Slide 27Slide 28Slide 29“Abstract” RulesExemplar ModelCategory associationAttentionAdding Structure:one-to-one correspondenceParallel ConnectivitySlide 37Disambiguation: AttentionBRIDGESLearning Abstract RulesRepresentationSame grammarOpposite grammarLearningLurking Concreteness in Abstract ConceptsExperimental DetailsConcrete basis revealed in graded structureDetermining relational similarityRelational categories are gradedSlide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Learning Abstract ConceptsLearning in Dynamic EnvironmentsMelioration/MaximizationSlide 63Slide 64Slide 65Slide 66Slide 67Slide 68ResultsSlide 70Slide 71Slide 72Slide 73Slide 74ConclusionsOverall ConclusionsAcknowledgementsSlide 78Slide 79Slide 80Slide 81Slide 82Slide 83Slide 84Beyond Classification LearningInference vs. ClassificationSlide 87Slide 88Slide 89Sakamoto and Love (submit.)Slide 91Slide 92Slide 93Slide 94Slide 95Slide 96Slide 97Slide 98Slide 99Slide 100Slide 101Slide 102Slide 103Slide 104Slide 105Slide 106The Concrete Substrates of Abstract Rule UseBradley Lovewww.ccc.utexas.eduThree Domains•Tracking basic statistics in our environment.•Learning seemingly abstract rules.•Learning and reasoning about future rewards in dynamic environments.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.Tracking Basic Statistics•Variance•MeanTracking VariabilityTracking VariabilityRational Models•Fried and Holyoak (1984)–Maximum likelihood–unbiased estimator/consistent•Tenenbaum and Griffiths (2001)–Bayesian updating–Globally BayesianTracking VariabilityObvious Mechanistic Approach•Error driven learning of cluster position and variance.–updates are trial by trial–are with regard to a memory representation of each categoryFormally..Mechanistic ModelRational 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.Tracking Variability (locally)What about the mean?What about the mean?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)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?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-likeSakamoto and Love (2004)Value 22 1 1 1 2 A2 2 1 2 2 B2 1 2 1 1 B2 2 2 1 1 B2 1 1 2 2 BValue 11 1 1 2 1 B1 2 1 2 2 A1 1 2 1 1 A1 2 2 1 1 A1 1 1 2 2 A1 2 1 1 1 A1 1 2 2 2 A1 1 2 1 2 A1 2 1 2 1 ASakamoto and Love (2004)Value 22 1 1 1 2 A2 2 1 2 2 B2 1 2 1 1 B2 2 2 1 1 B2 1 1 2 2 BValue 11 1 1 2 1 B1 2 1 2 2 A1 1 2 1 1 A1 2 2 1 1 A1 1 1 2 2 A1 2 1 1 1 A1 1 2 2 2 A1 1 2 1 2 A1 2 1 2 1 ARule RouteIf small, then A.If large, then B.Exception Routememorize itemSakamoto and Love (2004)Recognition5060708090100Small Large Small LargeInconsistent Consistent2AFC AccuracyValue 22 1 1 1 2 A2 2 1 2 2 B2 1 2 1 1 B2 2 2 1 1 B2 1 1 2 2 BValue 11 1 1 2 1 B1 2 1 2 2 A1 1 2 1 1 A1 2 2 1 1 A1 1 1 2 2 A1 2 1 1 1 A1 1 2 2 2 A1 1 2 1 2 A1 2 1 2 1 AViolating-BFollowing-A Following-AViolating-BFollowing-A Following-ASakamoto and Love (2004)Recognition5060708090100Small Large Small LargeInconsistent Consistent2AFC AccuracyValue 22 1 1 1 2 A2 2 1 2 2 B2 1 2 1 1 B2 2 2 1 1 B2 1 1 2 2 BValue 11 1 1 2 1 B1 2 1 2 2 A1 1 2 1 1 A1 2 2 1 1 A1 1 1 2 2 A1 2 1 1 1 A1 1 2 2 2 A1 1 2 1 2 A1 2 1 2 1 A“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?Exemplar ModelKruschke’s (1992) ALCOVECategory associationLearns association and attention weights SizeLuminanceAttentionSizeLuminanceLearns association and attention weightsAdding Structure:ChaseChaseChaser ChaserChased Chasedone-to-one correspondenceChaseChaseOne or the other, not bothChaser ChaserChased ChasedParallel ConnectivityChaseChasePerfect relational match, but feature mismatches.Parallel connectivity satisfied.Parallel ConnectivityTwo relational mismatches, but high feature match.Parallel Connectivity violated.ChaseChaseDisambiguation: AttentionChaseChaseAttention determines the trade-off.BRIDGESLearning 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 grammarsDo, Do, Re (pause) Me, Me, Fa (pause) Ti, Ti, Sa (pause) ...Representation•Attention on position constrained•Only type-token relation useda a bType_of( , )Type_of( , )Type_of( , )AABa1a2b1Same grammar•Relations: perfect similarity, parallel connectivity preserveda a bType_of( , )Type_of( , )Type_of( 1, )c c dType_of( , )Type_of( , )Type_of( , )AABCCDa1a2bc1c2d1Opposite grammar•Relations: 1 mismatch, parallel connectivity not preserveda a bType_of( , )Type_of( , )Type_of( , )e f fType_of( , )Type_of( , )Type_of( , )AABEFFa1a2b1ef1f2Learning•Attention shifts from inconsistent features to predictive relations•Concrete exemplar-based memory and attention shifting to relations explains performanceLurking Concreteness in Abstract Concepts•Pigeons appear to learn the concept of same and different.Same DifferentQuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this
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