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

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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:


Syntactic parsing

state description

Syntactic Parsing

bottom-up architecture


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


Continuous dynamics

Continuous Dynamics


Saddle node

Saddle Node


Saddle node1

Saddle Node


Saddle node2

Saddle Node


Saddle node3

Saddle Node

saddle

unstable manifold

stable manifold


Saddle node4

Saddle Node

saddle

unstable manifold

stable manifold


Heteroclinic dynamics

Heteroclinic Dynamics


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 bifurcation

Disambiguation by Bifurcation

unstable

fixpoints


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 scenario1

Bifurcation Scenario


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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