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Bayesian Language Games Unifying and evaluating agent-based models - - PowerPoint PPT Presentation

Bayesian Language Games Unifying and evaluating agent-based models of horizontal and vertical language evolution Bas Cornelissen The (Little) Tower of Babel by Pieter Bruegel the Elder (c. 1563) oil on panel; 60 cm 74.5 cm; Museum Boijmans


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Bayesian Language Games

Bas Cornelissen Unifying and evaluating agent-based models

  • f horizontal and vertical language evolution
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The (Little) Tower of Babel by Pieter Bruegel the Elder (c. 1563) oil on panel; 60 cm × 74.5 cm; Museum Boijmans Van Beuningen, Rotterdam

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Sound does not fossilise.

;<= >=?;@AB C@DEB=F

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biology cognitive science archeology linguistics anthropology unifying and evaluating
 agent-based models of cultural language evolution computational modelling

The origins

  • f language?
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?D BA?LMAL= BA?LMAL=

time

biological evolution cultural evolution cultural evolution

adapted from Tamariz & Kirby (2016) 
 NOP 10.1016/j.copsyc.2015.09.003

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NSTS USVW NSTS USVW NSTS USVW NSTS WXVXYSTPOV Z WXVXYSTPOV [ WXVXYSTPOV \

Iterated learning
 Every generation learns the language spoken by the previous generation. Vertical transmission across generations

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SLIDE 7

27 objects different colour, shape and movement with random names

  • 1. Train subject to learn the

names of a subset m i t u v i mituvi k i h e m i w i t a k u p i

  • 2. Test the subject on the

full set of of objects Use the reproduced names, including errors, to train the next subject. Emerging compositionality

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F Transmission pressures for learnable languages, resulting in systematic underspecification (left). Introducing a pressure for ex- pressivity results in compositional structure (right). Figure reproduced from Kirby, Cor- nish, and Smith () without permission.

n-ere-ki l-ere-ki renana n-ehe-ki l-aho-ki r-ene-ki n-eke-ki l-ake-ki r-ahe-ki n-ere-plo l-ane-plo r-e-plo n-eho-plo l-aho-plo r-eho-plo n-eki-plo l-aki-plo r-aho-plo n-e-pilu l-ane-pilu r-e-pilu n-eho-pilu l-aho-pilu r-eho-pilu n-eki-pilu l-aki-pilu r-aho-pilu

  • Compositional language

Meaning of a signal determined by meaning

  • f parts

Cultural processes (transmission & communication) pressure for compositional languages

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lamp!

Naming game Population negotiates a shared convention via local interactions:

  • 1. Select random speaker & hearer
  • 2. The hearer utters a word.
  • 3. Both agents ‘align’ languages

mothership! hat!

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lamp!

VC=AW=@ <=A@=@

hat lamp ship hat lamp

VC=AW=@ <=A@=@

lamp lamp

VC=AW=@ <=A@=@

hat hat ship lamp

VC=AW=@ <=A@=@

hat hat ship lamp lamp

Success Failure Minimal NG Every agent can invent, add and remove words to its vocabulary

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lamp!

VC=AW=@ <=A@=@

hat 0.4 lamp 0.1 ship 0.3 hat 0.2 lamp 0.2

VC=AW=@ <=A@=@

hat 0.3 lamp 0.3 ship 0.2 hat 0.1 lamp 0.4

Success Lateral inhibition After success, decrease the scores of competing words

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F The dynamics of the mini- mal naming game. An sharp transi- tion leads to convergence and the emergence of consensus. Results shown for ;

  • avg. of runs, std. shaded.
  • Dynamics of the minimal NG

Three stages lead to the convergence to a single word:

  • 1. Invention of words
  • 2. Spread through population
  • 3. Elimination of words

Cultural process of social negotiation leads to shared emergence of a convention

F The dynamics of the mini- mal naming game. An sharp transi- tion leads to convergence and the emergence of consensus. Results shown for ;

  • avg. of runs, std. shaded.
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unifying and evaluating
 agent-based models of cultural language evolution cognitive science linguistics computational modelling The origins

  • f language?

jXYTPkSU iterated learning lOYPmOVTSU naming game

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jXYTPkSU iterated learning lOYPmOVTSU naming game

iterated learning naming games

ɣ

  • 1. shared formalism 2. population model
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jXYTPkSU iterated learning lOYPmOVTSU naming game

Bayesian IL Bayesian NG

ɣ

  • SpXqPSV 


USVWrSWX WSsX

  • 1. shared formalism 2. population model
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  • 2. Population model
  • 1. Shared (Bayesian) formalism

NSTS USVW NSTS USVW NSTS USVW NSTS

biases of 
 the learners probability of adopting a language

  • ( | ) ∝ ( | ) · ()
  • ∝ ( | ) ·
  • production algorithm

learning algorithm

  • ( | )
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probability of language after previous interaction

NSTS USVW NSTS USVW NSTS USVW NSTS

  • ( | ) ∝ ( | ) · ()
  • ∝ ( | ) ·
  • production algorithm

learning algorithm

  • ( | )
  • 2. Population model
  • 1. Shared (Bayesian) formalism
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<D@`aD?;AB homogeneous mixing b=@;`>AB transmission chain

Iterated learning Naming Game Bayesian Naming Game

  • Iterated learning

Naming Game Bayesian Naming Game

  • Iterated learning

Naming Game Bayesian Naming Game

  • ED;<

random walk ∞ 1 B`c= =dC=>;A?>e ɣ The age at which a speaker dies

ɣ

  • 2. Population model
  • 1. Shared (Bayesian) formalism
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NSTS USVW NSTS USVW NSTS USVW NSTS

  • ∝ ( | ) ·
  • production algorithm

learning algorithm

  • ( | )
  • 0,1

0,2 0,3 0,4 0,5 hat mothership lamp

A language is a distribution over words (or e.g. linguistic features) The Bayesian Naming Game

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The Bayesian Naming Game

  • Lineage specificity
  • Reflection of the bias 


(rather than convergence to the prior)

  • Language stability
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The Bayesian Naming Game

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The Bayesian Naming Game On average, the Bayesian Naming Game reproduces the innate biases. Reminiscent of “wide but constrained variation” (e.g. colour terms)

Regier et al. (2015). NOP 10.1002/9781118346136.ch11

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Different strategies But why this? Shouldn’t we expect this?

  • ∝ ( | ) ·
  • production algorithm

0,1 0,2 0,3 0,4 0,5 hat mothership lamp

Strategies One can vary the ‘production strategy’ and ‘language strategy’ sample or maximise

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l i f e e x p e c t a n c y

  • l

a n g u a g e s t r a t e g y

  • production strategy

– – – – – – –

  • IL

NG

ɣ

Different strategies

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Different strategies

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biology cognitive science archeology linguistics anthropology unifying and evaluating
 agent-based models of cultural language evolution computational modelling

The origins

  • f language?
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archeology unifying and evaluating
 agent-based models of cultural language evolution Iterated learning and the naming game closely related: language evolution through frequency tracking and innate biases. Realistic? Lineage-specific languages reflecting innate biases in the Bayesian naming game. Take home messages

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The (Little) Tower of Babel by Pieter Bruegel the Elder (c. 1563) oil on panel; 60 cm × 74.5 cm; Museum Boijmans Van Beuningen, Rotterdam