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Stable Heteroclinic Sequences as a Paradigm for Dynamic Psycholinguistics

Stable Heteroclinic Sequences as a Paradigm for Dynamic Psycholinguistics. ZAS Tandem Workshop December, 11 – 13, 2010. Peter beim Graben Department of German Language and Linguistics Humboldt-Universität zu Berlin peter.beim.graben@hu-berlin.de. Overview. linguistic ambiguity

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Stable Heteroclinic Sequences as a Paradigm for Dynamic Psycholinguistics

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  1. Stable Heteroclinic Sequences as a Paradigm for Dynamic Psycholinguistics ZAS Tandem Workshop December, 11 – 13, 2010 Peter beim Graben Department of German Language and Linguistics Humboldt-Universität zu Berlin peter.beim.graben@hu-berlin.de

  2. Overview • linguistic ambiguity • geometric representations • heteroclinic dynamics • disambiguation by bifurcation

  3. Linguistic Ambiguity (1) The forester watched the bird with binoculars. (2) The bird watched the forester with binoculars.

  4. PP Attachment instrumentalattributive semantic biases

  5. Context Free Grammar (1) instrumental: (2) attributive:

  6. state description Syntactic Parsing bottom-up architecture

  7. Sequence Generation 1 2 3 4 6 8 10

  8. Filler / Role Binding filler: categories represented by vectors roles: vectors Smolensky & Legendre (2006) beim Graben et al. (2008) beim Graben & Potthast (2009)

  9. Tensor Product Representation 1. tree 2. parser state description p3p2p1 : stack position roles

  10. Tensor Product Parser instrumental attributive

  11. State Descriptions stationary states are “vertices” in state space

  12. Continuous Dynamics

  13. Saddle Node

  14. Saddle Node

  15. Saddle Node

  16. Saddle Node saddle unstable manifold stable manifold

  17. Saddle Node saddle unstable manifold stable manifold

  18. Heteroclinic Dynamics

  19. Stable Heteroclinic Sequence SHS Afraimovich et al. (2004) Rabinovich et al. (2008)

  20. ith stationary pattern (“factor”) Order Parameters amplitude of ith pattern (“load”) Haken (1983) beim Graben et al. (2009)

  21. Order Parameter Dynamics network of competing neural populations 1 5 2 generalized Lotka-Volterra model 4 3

  22. Sequence Generation 1 2 3 4 6 8 10

  23. Disambiguation by Bifurcation unstable fixpoints

  24. Disambiguation by Bifurcation new unstable fixpoints

  25. Control Parameter convex combination instrumental: attributive:

  26. Bifurcation Scenario 1 2 3 4 6 8 10

  27. Bifurcation Scenario

  28. Bifurcation Scenario 1 2 3 5 7 9 11

  29. Conclusion • complex symbolic data structures geometrically represented by tensor products • syntactic parsing represented by time-discrete sequences in geometric space • continuous time through competitive order parameter dynamics • representational states as saddle nodes connected through stable heteroclinic sequences • syntactic reanalysis as bifurcation of SHS

  30. Acknowledgements Thank you for your attention! Funding: DFG-Heisenbergstipendium GR 3711/1-1

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