The Dynamics of Iterated Learning

Simon Kirby

LEC, Edinburgh

What is Iterated Learning?

An approach to understanding language evolution

A way of relating properties of the learners and users of language to language structure

A type of cultural evolution

The mechanism whereby knowledge is passed-on through observation of behaviour resulting from that knowledge

Iterated learning as evolutionary system

There are important differences between iterated learning and biological evolution

The main difference: possibility of discontinuity

The main similarity: link between stability and reproductive success?

Question: is there selection (for learnability and/or usability)?

Iterated learning models

Two broad classes:

Complex simulation models – target specific features of language

Minimal idea models – understand evolutionary principles

Components of ILMs:

Learning mechanism

Production mechanism

Invention mechanism

What is being learned?

Sets of strings

Parameter settings

Morphology

Meaning-signal mappings

Main ILM results so far

Languages can adapt to pressures on production and parsing

Generalisations are better replicators

Given structured meaning-spaces:

Compositional languages are more stable

Compositional languages can emerge with invention. Depends on:

Size of signal space

Size of “bottleneck”

Population structure

Environment structure

Meaning-space structure

What can we conclude from ILM results?

General methodological approach:

Discover which simulation parameters lead to language-like systems

Hypothesise that these parameters are necessary (and sufficient?) precursors for language

Sufficiency conditions: tells us how much we need to explain

Necessity conditions: helps solve the uniqueness problem.

Example: structured meaning-spaces

How does the structure of meaning-space affect the structure of the languages that emerge in an ILM?

Henry’s approach:

Construct languages that reflect structure of meaning-spaces

Compare the expressivity of these languages after learning

Equate expressivity and stability through iterated learning

Languages that reflect highly structured meaning-spaces most stable

General idea: highly-structured meaning spaces are part of our biological endowment.

Two problems…

Model looks at what happens to a language that is completely compositional vs. completely holistic

i.e., Lyapunov local stability

Note: same problem for Nowak et. al in Nature

What about partially compositional systems?

Model assumes that meaning-space is fixed and provided by some other evolutionary mechanism

Seems to run counter to the “spirit” of adaptation through iterated learning

What if the meaning-space coevolves with the syntactic system?

A really simple model

What is language?

A system for mediating between interfaces

Meanings

Simple feature-vectors

Multiple spaces

Many-to-one mapping from meanings to objects in environment

Objects as sets of feature-vectors

Each object is associated with one feature-vector per meaning space.

Key point: agents are prompted to express signals for each object (not each meaning!)

Big Assumption

If a learner is presented with a language that is compositional for some part of meaning space,
then the learner will learn a compositional system.

Can be justified on MDL grounds?

Model of learning simply needs to keep track of each feature-value heard.

Exactly the same as Henry’s model

Stability relates to the probability of hearing each feature-value

Differences…

Potentially more than one subsystem operating at the same time

Only looking at the stability of compositional systems

BUT… holistic system is identical to a 1-dimensional compositional system

What this allows us to do:

Deal with mixed systems (i.e., move beyond Lyapunov)

Look at evolution of meaning-space usage

Simulation

Agent knowledge:
list of feature-values

Production:
prompted by an object, pick any way of expressing it

An object can be expressed in a meaning space if the corresponding feature vector <v1, v2, …> contains only feature-values that the agent knows how to express.

Learning:
add the feature-values heard to knowledge

Parameters:
environment, meaning spaces, bottleneck

Experiments

Stability of different meaning-spaces

Relative stability of different meaning-spaces against holistic system

Complete dynamics with two meaning-spaces

Iterated learning with multiple meaning-spaces

What next?

Holistic vs. Compositional

Holistic with differing bottlenecks

Differing meaning-spaces

Relative stability for differing meaning spaces (compared with holistic)

Iterated learning with mixed system

Complete dynamics for mixed system

Invention

Effect of low bottleneck

Low bottleneck with invention

Multiple systems

Inexpressive meaning-spaces

Problem – no pressure for expressivity

The key bias: avoidance of many to one mapping between meanings and signals

BUT – many to one mapping between environment and meanings

Solution – discrimination and contexts

Currently: speakers only presented with target object

Add: a context of other objects

Obverter: only produce signals that will discriminate target from context

Selection for contextual discrimination

Summary

We can extend Henry’s model to mixed-systems

Linking objects to multiple meaning-structures leads to competition between meaning-spaces

Evolution through Iterated Learning extends to semantics

Key point:

What’s next?

Environment is random and smooth

Adaptation of semantics to environment structure?

Problem: why aren’t languages all binary?

Populations

Need to add explicit lexicon

Still need more realistic model of meaning flexibility

Final questions


	An approach to understanding language evolution
	A way of relating properties of the learners and users of language to language structure
	A type of cultural evolution

	The mechanism whereby knowledge is passed-on through observation of behaviour resulting from that knowledge


	There are important differences between iterated learning and biological evolution







	The main difference: possibility of discontinuity
	The main similarity: link between stability and reproductive success?
	Question: is there selection (for learnability and/or usability)?


	Two broad classes:
		Complex simulation models – target specific features of language
		Minimal idea models – understand evolutionary principles
	Components of ILMs:
		Learning mechanism
		Production mechanism
		Invention mechanism
	What is being learned?
		Sets of strings
		Parameter settings
		Morphology
		Meaning-signal mappings


Languages can adapt to pressures on production and parsing
Generalisations are better replicators
Given structured meaning-spaces:
	Compositional languages are more stable
	Compositional languages can emerge with invention. Depends on:
		Size of signal space
		Size of “bottleneck”
		Population structure
		Environment structure
		Meaning-space structure


	General methodological approach:
		Discover which simulation parameters lead to language-like systems
		Hypothesise that these parameters are necessary (and sufficient?) precursors for language

	Sufficiency conditions: tells us how much we need to explain
	Necessity conditions: helps solve the uniqueness problem.


	How does the structure of meaning-space affect the structure of the languages that emerge in an ILM?
	Henry’s approach:
		Construct languages that reflect structure of meaning-spaces
		Compare the expressivity of these languages after learning
		Equate expressivity and stability through iterated learning
		Languages that reflect highly structured meaning-spaces most stable
	General idea: highly-structured meaning spaces are part of our biological endowment.


	Model looks at what happens to a language that is completely compositional vs. completely holistic
		i.e., Lyapunov local stability
		Note: same problem for Nowak et. al in Nature
	What about partially compositional systems?
	Model assumes that meaning-space is fixed and provided by some other evolutionary mechanism
		Seems to run counter to the “spirit” of adaptation through iterated learning
	What if the meaning-space coevolves with the syntactic system?


	Simple feature-vectors
	Multiple spaces
	Many-to-one mapping from meanings to objects in environment


	Each object is associated with one feature-vector per meaning space.






	Key point: agents are prompted to express signals for each object (not each meaning!)


	If a learner is presented with a language that is compositional for some part of meaning space, then the learner will learn a compositional system.

	Can be justified on MDL grounds?
	Model of learning simply needs to keep track of each feature-value heard.
	Exactly the same as Henry’s model
		Stability relates to the probability of hearing each feature-value


	Potentially more than one subsystem operating at the same time
	Only looking at the stability of compositional systems
	BUT… holistic system is identical to a 1-dimensional compositional system

	What this allows us to do:
		Deal with mixed systems (i.e., move beyond Lyapunov)
		Look at evolution of meaning-space usage


	Agent knowledge: list of feature-values
	Production: prompted by an object, pick any way of expressing it
		An object can be expressed in a meaning space if the corresponding feature vector <v1, v2, …> contains only feature-values that the agent knows how to express.
	Learning: add the feature-values heard to knowledge

	Parameters: environment, meaning spaces, bottleneck



	Stability of different meaning-spaces
	Relative stability of different meaning-spaces against holistic system
	Complete dynamics with two meaning-spaces
	Iterated learning with multiple meaning-spaces


	What next?


	The key bias: avoidance of many to one mapping between meanings and signals
	BUT – many to one mapping between environment and meanings


	Currently: speakers only presented with target object
	Add: a context of other objects
	Obverter: only produce signals that will discriminate target from context


	We can extend Henry’s model to mixed-systems
	Linking objects to multiple meaning-structures leads to competition between meaning-spaces
	Evolution through Iterated Learning extends to semantics
	Key point:


	Environment is random and smooth
		Adaptation of semantics to environment structure?

	Problem: why aren’t languages all binary?

	Populations
		Need to add explicit lexicon

	Still need more realistic model of meaning flexibility