1	The Dynamics of Iterated Learning Simon Kirby LEC, Edinburgh
2	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
3	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)?
4	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
5	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
6	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.
7	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.
8	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?
9	A really simple model What is language? A system for mediating between interfaces
10	Meanings Simple feature-vectors Multiple spaces Many-to-one mapping from meanings to objects in environment
11	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!)
12	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
13	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
14	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
15	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?
16	Holistic vs. Compositional
17	Holistic with differing bottlenecks
18	Differing meaning-spaces
19	Relative stability for differing meaning spaces (compared with holistic)
20	Iterated learning with mixed system
21	Complete dynamics for mixed system
22	Invention
23	Effect of low bottleneck
24	Low bottleneck with invention
25	Multiple systems
26	Multiple systems
27	Multiple systems
28	Multiple systems
29	Multiple systems
30	Multiple systems
31	Multiple systems
32	Multiple systems
33	Multiple systems
34	Inexpressive meaning-spaces
35	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
36	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
37	Selection for contextual discrimination
38	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:
39	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
40	Final questions