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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 [email protected] Overview. linguistic ambiguity

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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

[email protected]

overview
Overview
  • linguistic ambiguity
  • geometric representations
  • heteroclinic dynamics
  • disambiguation by bifurcation
linguistic ambiguity
Linguistic Ambiguity

(1) The forester watched the bird with binoculars.

(2) The bird watched the forester with binoculars.

pp attachment
PP Attachment

instrumentalattributive

semantic biases

context free grammar
Context Free Grammar

(1) instrumental:

(2) attributive:

sequence generation
Sequence Generation

1 2 3 4 6 8 10

filler role binding
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
Tensor Product Representation

1. tree

2. parser state description

p3p2p1 : stack position roles

tensor product parser
Tensor Product Parser

instrumental

attributive

state descriptions
State Descriptions

stationary states are “vertices” in state space

saddle node3
Saddle Node

saddle

unstable manifold

stable manifold

saddle node4
Saddle Node

saddle

unstable manifold

stable manifold

stable heteroclinic sequence
Stable Heteroclinic Sequence

SHS

Afraimovich et al. (2004)

Rabinovich et al. (2008)

order parameters
ith stationary pattern (“factor”)Order Parameters

amplitude of ith pattern (“load”)

Haken (1983)

beim Graben et al. (2009)

order parameter dynamics
Order Parameter Dynamics

network of competing neural populations

1

5

2

generalized Lotka-Volterra model

4

3

sequence generation1
Sequence Generation

1 2 3 4 6 8 10

disambiguation by bifurcation1
Disambiguation by Bifurcation

new unstable

fixpoints

control parameter
Control Parameter

convex combination

instrumental:

attributive:

bifurcation scenario
Bifurcation Scenario

1 2 3 4 6 8 10

bifurcation scenario2
Bifurcation Scenario

1 2 3 5 7 9 11

conclusion
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
Acknowledgements

Thank you for your attention!

Funding: DFG-Heisenbergstipendium GR 3711/1-1

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