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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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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

  • geometric representations

  • heteroclinic dynamics

  • disambiguation by bifurcation


Linguistic Ambiguity

(1) The forester watched the bird with binoculars.

(2) The bird watched the forester with binoculars.


PP Attachment

instrumentalattributive

semantic biases


Context Free Grammar

(1) instrumental:

(2) attributive:


state description

Syntactic Parsing

bottom-up architecture


Sequence Generation

1 2 3 4 6 8 10


Filler / Role Binding

filler: categories represented by vectors

roles: vectors

Smolensky & Legendre (2006)

beim Graben et al. (2008)

beim Graben & Potthast (2009)


Tensor Product Representation

1. tree

2. parser state description

p3p2p1 : stack position roles


Tensor Product Parser

instrumental

attributive


State Descriptions

stationary states are “vertices” in state space


Continuous Dynamics


Saddle Node


Saddle Node


Saddle Node


Saddle Node

saddle

unstable manifold

stable manifold


Saddle Node

saddle

unstable manifold

stable manifold


Heteroclinic Dynamics


Stable Heteroclinic Sequence

SHS

Afraimovich et al. (2004)

Rabinovich et al. (2008)


ith stationary pattern (“factor”)

Order Parameters

amplitude of ith pattern (“load”)

Haken (1983)

beim Graben et al. (2009)


Order Parameter Dynamics

network of competing neural populations

1

5

2

generalized Lotka-Volterra model

4

3


Sequence Generation

1 2 3 4 6 8 10


Disambiguation by Bifurcation

unstable

fixpoints


Disambiguation by Bifurcation

new unstable

fixpoints


Control Parameter

convex combination

instrumental:

attributive:


Bifurcation Scenario

1 2 3 4 6 8 10


Bifurcation Scenario


Bifurcation Scenario

1 2 3 5 7 9 11


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


Acknowledgements

Thank you for your attention!

Funding: DFG-Heisenbergstipendium GR 3711/1-1


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