The Concrete Substrates of Abstract Rule Use Bradley Love www ccc utexas edu Three 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 Mean Tracking Variability Tracking Variability Rational Models Fried and Holyoak 1984 Maximum likelihood unbiased estimator consistent Tenenbaum and Griffiths 2001 Bayesian updating Globally Bayesian Tracking Variability 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 Formally Mechanistic Model 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 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 bytrial 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 like Sakamoto and Love 2004 Value 2 Value 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 2 1 1 2 2 1 1 2 2 1 2 2 1 1 2 1 2 1 2 1 2 1 1 2 1 2 2 1 B A A A A A A A A 2 2 2 2 2 1 2 1 2 1 1 1 2 2 1 1 2 1 1 2 2 2 1 1 2 A B B B B Sakamoto and Love 2004 Value 2 Value 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 2 1 1 2 2 1 1 2 2 1 2 2 1 1 2 1 2 1 2 1 2 1 1 2 1 2 2 1 B A A A A A A A A 2 2 2 2 2 1 2 1 2 1 1 1 2 2 1 1 2 1 1 2 2 2 1 1 2 A B B B B Rule Route If small then A If large then B Exception Route memorize item Sakamoto and Love 2004 Recognition Value 2 Value 1 100 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 2 1 1 2 2 1 1 2 2 1 2 2 1 1 2 1 2 1 2 1 2 1 1 2 1 2 2 1 B A A A A A A A A 2 2 2 2 2 1 2 1 2 1 1 1 2 2 1 1 2 1 1 2 2 2 1 1 2 A B B B B 90 80 70 2AFC 60 Accuracy 50 Small Large Inconsistent Small Large Consistent Following A Violating B Following A Following A Violating B Following A Sakamoto and Love 2004 Recognition Value 2 Value 1 100 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 2 1 1 2 2 1 1 2 2 1 2 2 1 1 2 1 2 1 2 1 2 1 1 2 1 2 2 1 B A A A A A A A A 2 2 2 2 2 1 2 1 2 1 1 1 2 2 1 1 2 1 1 2 2 2 1 1 2 A B B B B 90 80 70 2AFC 60 Accuracy 50 Small Large Inconsistent Small Large Consistent Abstract Rules Abstract rules are not specified by fixedvalues e g learning an abstract notion of same and different Could abstract responding be grounded in concrete episodes and trial by trial learning Exemplar Model Kruschke s 1992 ALCOVE Category association Luminance Learns association and attention weights Size Attention Luminance Learns association and attention weights Size Adding Structure Chase Chased Chase Chaser Chased Chaser one to one correspondence Chase Chased Chase Chaser Chased One or the other not both Chaser Parallel Connectivity Chase Chase Perfect relational match but feature mismatches Parallel connectivity satisfied Parallel Connectivity Chase Chase Two relational mismatches but high feature match Parallel Connectivity violated Disambiguation Attention Chase Attention determines the trade off Chase BRIDGES Learning Abstract Rules Marcus et al showed infants can learn to distinguish simple grammars AAB pattern vs ABB pattern Do Do Re pause Me Me Fa pause Ti Ti Sa pause No diagnostic features Infants habituated to one grammar then tested with novel sounds from both grammars Representation Attention on position constrained Only type token relation used a a b Type of a1 A Type of a2 A Type of b1 B Same grammar Relations perfect similarity parallel connectivity preserved a a b c c d Type of a1 A Type of c1 C Type of a2 A Type of c2 C Type of b1 B Type of d1 D Opposite grammar Relations 1 mismatch parallel connectivity not preserved a a b e f f Type of a1 A Type of e E Type of a2 A Type of f1 F Type of b1 B Type of f2 F Learning Attention shifts from inconsistent features to predictive relations Concrete exemplar based memory and attention shifting to relations explains performance Lurking Concreteness in Abstract Concepts Pigeons appear to learn the concept of same and different QuickTime QuickTime QuickTime and athis and athisdecompressor QuickTime QuickTime QuickTime and athis and asee athis TIFF Uncompressed TIFF Uncompressed TIFF Uncompressed decompressor TIFF Uncompressed TIFF TIFF 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