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 [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 Psycholinguistics

  • linguistic ambiguity

  • geometric representations

  • heteroclinic dynamics

  • disambiguation by bifurcation


Linguistic ambiguity
Linguistic Ambiguity Psycholinguistics

(1) The forester watched the bird with binoculars.

(2) The bird watched the forester with binoculars.


Pp attachment
PP Attachment Psycholinguistics

instrumentalattributive

semantic biases


Context free grammar
Context Free Grammar Psycholinguistics

(1) instrumental:

(2) attributive:


Syntactic parsing

state description Psycholinguistics

Syntactic Parsing

bottom-up architecture


Sequence generation
Sequence Generation Psycholinguistics

1 2 3 4 6 8 10


Filler role binding
Filler / Role Binding Psycholinguistics

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 Psycholinguistics

1. tree

2. parser state description

p3p2p1 : stack position roles


Tensor product parser
Tensor Product Parser Psycholinguistics

instrumental

attributive


State descriptions
State Descriptions Psycholinguistics

stationary states are “vertices” in state space


Continuous dynamics
Continuous Dynamics Psycholinguistics


Saddle node
Saddle Node Psycholinguistics


Saddle node1
Saddle Node Psycholinguistics


Saddle node2
Saddle Node Psycholinguistics


Saddle node3
Saddle Node Psycholinguistics

saddle

unstable manifold

stable manifold


Saddle node4
Saddle Node Psycholinguistics

saddle

unstable manifold

stable manifold


Heteroclinic dynamics
Heteroclinic Dynamics Psycholinguistics


Stable heteroclinic sequence
Stable Heteroclinic Sequence Psycholinguistics

SHS

Afraimovich et al. (2004)

Rabinovich et al. (2008)


Order parameters

i Psycholinguisticsth stationary pattern (“factor”)

Order Parameters

amplitude of ith pattern (“load”)

Haken (1983)

beim Graben et al. (2009)


Order parameter dynamics
Order Parameter Dynamics Psycholinguistics

network of competing neural populations

1

5

2

generalized Lotka-Volterra model

4

3


Sequence generation1
Sequence Generation Psycholinguistics

1 2 3 4 6 8 10


Disambiguation by bifurcation
Disambiguation by Bifurcation Psycholinguistics

unstable

fixpoints


Disambiguation by bifurcation1
Disambiguation by Bifurcation Psycholinguistics

new unstable

fixpoints


Control parameter
Control Parameter Psycholinguistics

convex combination

instrumental:

attributive:


Bifurcation scenario
Bifurcation Scenario Psycholinguistics

1 2 3 4 6 8 10


Bifurcation scenario1
Bifurcation Scenario Psycholinguistics


Bifurcation scenario2
Bifurcation Scenario Psycholinguistics

1 2 3 5 7 9 11


Conclusion
Conclusion Psycholinguistics

  • 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 Psycholinguistics

Thank you for your attention!

Funding: DFG-Heisenbergstipendium GR 3711/1-1


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