1. Richard Sproat University of Illinois at Urbana-Champaign rws@uiuc.edu 3rd Workshop on "Quantitative Investigations in Theoretical Linguistics" (QITL-3) Helsinki, 2-4 June 2008 (Preliminary)Experiments in Morphological Evolution

2. Overview • The explananda • Previous work on evolutionary modeling • Computational models and preliminary experiments

3. Phenomena • How do paradigms arise? • Why do words fall into different inflectional “equivalence classes” • Why do stem alternations arise? • Why is there syncretism? • Why are there “rules of referral”?

4. Stem alternations in Sanskrit zero guna Examples from: Stump, Gregory (2001) Inflectional Morphology: A Theory of Paradigm Structure. Cambridge University Press.

5. Stem alternations in Sanskrit morphomic(Aronoff, M. 1994. Morphology by Itself. MIT Press.) vrddhi lexeme-class particular lexeme-class particular

6. Evolutionary Modeling (A tiny sample) • Hare, M. and Elman, J. L. (1995) Learning and morphological change. Cognition, 56(1):61--98. • Kirby, S. (1999) Function, Selection, and Innateness: The Emergence of Language Universals. Oxford • Nettle, D. "Using Social Impact Theory to simulate language change". Lingua, 108(2-3):95--117, 1999. • de Boer, B. (2001) The Origins of Vowel Systems. Oxford • Niyogi, P. (2006) The Computational Nature of Language Learning and Evolution. Cambridge, MA: MIT Press.

7. Experiment 1: Rules of Referral

8. Rules of referral • Stump, Gregory (1993) “On rules of referral”. Language. 69(3), 449-479 • (After Zwicky, Arnold (1985) “How to describe inflection.” Berkeley Linguistics Society. 11, 372-386.)

9. Latin declensions

10. Are rules of referral interesting? • Are they useful for the learner? • Wouldn’t the learner have heard instances of every paradigm? • Are they historically interesting: • Does morphological theory need mechanisms to explain why they occur?

11. Another example: Böğüstani nominal declension sSg Du Pl sSg Du Pl sSg Du Pl Nom Acc Gen Dat Loc Inst Abl Illat • Böğüstani • A language of Uzbekistan ISO 639-3: bgs Population 15,500 (1998 Durieux). Comments Capsicum chinense and Coffea arabica farmers

12. Monte Carlo simulation(generating Böğüstani) • Select a re-use bias B • For each language: • Generate a set of vowels, consonants and affix templates • a, i, u, e • n f r w B s x j D • V, C, CV, VC • Decide on p paradigms (minimum 3), r rows (minimum 2), c columns (minimum 2)

13. Monte Carlo simulation • For each paradigm in the language: • Iterate over (r, c): • Let α be previous affix stored for r: with p = B retain α in L • Let β be previous affix stored for c: with p = B retain β in L • If either L is non-empty, set (r, c) to random choice from L • Otherwise generate a new affix for (r, c) • Store (r, c)’s affix for r and c • Note that P(new-affix) = (1-B)2

14. Sample language: bias = 0.04 Consonants x n p w j B t r s S m Vowels a i u e Templates V, C, CV, VC

15. Sample language: bias = 0.04 Consonants n f r w B s x j D Vowels a i u e Templates V, C, CV, VC

16. Sample language: bias = 0.04 Consonants r p j d G D Vowels a i u e o y O Templates V, C, CV, VC,CVC, VCV, CVCV, VCVC

17. Sample language: bias = 0.04 Consonants D k S n b s l t w j B g G d Vowels a i u e Templates V, C, CV, VC

18. Results of Monte Carlo simulations(8000 runs, 5000 languages per run)

19. Interim conclusion • Syncretism, including rules of referral, may arise as a chance byproduct of tendencies to reuse inflectional exponents --- and hence reduce the number of exponents needed in the system. • Side question: is the amount of ambiguity among inflectional exponents statistically different from that among lexemes? (cf. Beard’s Lexeme-Morpheme-Base Morphology) • Probably not since inflectional exponents tend to be shorter, so the chances of collisions are much higher

20. Experiment 2:Stabilizing Multiple Paradigms in a Multiagent Network

21. Paradigm Reduction in Multi-agent Models with Scale-Free Networks • Agents connected in scale-free network • Only connected agents communicate • Agents more likely to update forms from interlocutors they “trust” • Each individual agent has pressure to simplify its morphology by collapsing exponents: • Exponent collapse is picked to minimize an increase in paradigm entropy • Paradigms may be simplified – removing distinctions and thus reducing paradigm entropy • As the number of exponents decreases so does the pressure to reduce • Agents analogize paradigms to other words

22. Scale-free networks

23. Scale-free networks • Connection degrees follow the Yule-Simon distribution: where for sufficiently large k: i.e. reduces to Zipf’s law (cf. Baayen, Harald (2000) Word Frequency Distributions. Springer.)

24. Scale-free vs. Random:1000 nodes

25. Relevance of scale-free networks • Social networks are scale-free • Nodes with multiple connections seem to be relevant for language change. • cf: James Milroy and Lesley Milroy (1985) “Linguistic change, social network and speaker innovation.” Journal of Linguistics, 21:339–384.

26. Scale-free networks in the model • Agents communicate individual forms to other agents • When two agents differ on a form, one agent will update its form with a probability p proportional to how well connected the other agent is: • p = MaxP X ConnectionDegree(agent)/MaxConnectionDegree • (Similar to Page Rank)

27. Paradigm entropy • For exponents φ and morphological functions μ, define the Paradigm Entropy as: (NB: this is really just the conditional entropy) • If each exponent is unambiguous, the paradigm entropy is 0

28. Example

29. Syncretism tends to be most common in “rarer” parts of paradigm

30. Old Latin 1st/2nd Declensions

31. Simulation • 100 agents in scale-free or random network • Roughly 250 connections in either case • 20 bases • 5 “cases”, 2 “numbers”: each slot associated with a probability • Max probability of updating one’s form for a given slot given what another agent has is 0.2 or 0.5 • Probability of analogizing within one’s own vocabulary is 0.01, 0.02 or 0.05 • Also a mode where we force analogy every 50 iterations • Analogize to words within same “analogy group” (4 such groups in current simulation) • Winner-takes all strategy • (Numbers in the titles of the ensuing plots are given as UpdateProb/AnalogyProb (e.g. 0.2/0.01)) • Run for 1000 iterations

32. Features of simulation • At nth iteration, compute: • The paradigm distribution over agents for each word. • Paradigm purity is the proportion of the “winning paradigm” • The number of distinct winning paradigms

33. Scale-free Network: 0.2/0.01

34. Scale-free network: 0.5/0.05

35. Random network: 0.5/0.05

36. Scale-free network: 0.5/0.055000 runs

37. Random network: 0.5/0.055000 runs

38. Scale-free network: 0.5/0.005000 runs: No analogy

39. Scale-free network: 0.5/0.0030,000 runs: No analogy

40. Sample final state 0.24 0.21 0.095 0.095 0.06 0.12 0.095 0.048 0.024 0.012

41. Adoption of acc/acc/acc/acc/acc/ACC/ACC/ACC/ACC/ACCin a 0.5/0.05 run

42. Interim conclusions • Scale-free networks don’t seem to matter: convergence behavior seems to be no different from a random network • Is that a big surprise? • Analogy matters • Paradigm entropy (conditional entropy) might be a model for paradigm simplification

43. Experiment 3:Large-scale multi-agent evolutionary modeling with learning(work in progress…)

44. Synopsis • System is seeded with a grammar and small number of agents • Initial grammars all show an agglutinative pattern • Each agent randomly selects a set of phonetic rules to apply to forms • Agents are assigned to one of a small number of social groups • 2 parents “beget” child agents. • Children are exposed to a predetermined number of training forms combined from both parents • Forms are presented proportional to their underlying “frequency” • Children must learn to generalize to unseen slots for words • Learning algorithm similar to: • David Yarowsky and Richard Wicentowski (2001) "Minimally supervised morphological analysis by multimodal alignment." Proceedings of ACL-2000, Hong Kong, pages 207-216. • Features include last n-characters of input form, plus semantic class • Learners select the optimal surface form to derive other forms from (optimal = requiring the simplest resulting ruleset – a Minimum Description Length criterion) • Forms are periodically pooled among all agents and the n best forms are kept for each word and each slot • Population grows, but is kept in check by “natural disasters” and a quasi-Malthusian model of resource limitations • Agents age and die according to reasonably realistic mortality statistics

45. Population growth, 300 “years”

46. Phonological rules • c_assimilation • c_lenition • degemination • final_cdel • n_assimilation • r_syllabification • umlaut • v_nasalization • voicing_assimilation • vowel_apocope • vowel_coalescence • vowel_syncope K = [ptkbdgmnNfvTDszSZxGCJlrhX] L = [wy] V = [aeiouAEIOU&@0âêîôûÂÊÎÔÛãõÕ] ## Regressive voicing assimilation b -> p / - _ #?[ptkfTsSxC] d -> t / - _ #?[ptkfTsSxC] g -> k / - _ #?[ptkfTsSxC] D -> T / - _ #?[ptkfTsSxC] z -> s / - _ #?[ptkfTsSxC] Z -> S / - _ #?[ptkfTsSxC] G -> x / - _ #?[ptkfTsSxC] J -> C / - _ #?[ptkfTsSxC] K = [ptkbdgmnNfvTDszSZxGCJlrhX] L = [wy] V = [aeiouAEIOU&@0âêîôûÂÊÎÔÛãõÕ] [td] -> D / [aeiou&âêîôûã]#? _ #?[aeiou&âêîôûã] [pb] -> v / [aeiou&âêîôûã]#? _ #?[aeiou&âêîôûã] [gk] -> G / [aeiou&âêîôûã]#? _ #?[aeiou&âêîôûã]

47. Example run • Initial paradigm: • Abog pl+acc Abogmeon • Abog pl+dat Abogmeke • Abog pl+gen Abogmei • Abog pl+nom Abogmeko • Abog sg+acc Abogaon • Abog sg+dat Abogake • Abog sg+gen Abogai • Abog sg+nom Abogako • NUMBER 'a' sg 0.7 'me' pl 0.3 • CASE 'ko' nom 0.4 'on' acc 0.3 'i' gen 0.2 'ke' dat 0.1 • PHONRULE_WEIGHTING=0.60 • NUM_TEACHING_FORMS=1500

48. Behavior of agent 4517 at 300 “years” Abog pl+acc Abogmeon Abog pl+dat Abogmeke Abog pl+gen Abogmei Abog pl+nom Abogmeko Abog sg+acc Abogaon Abog sg+dat Abogake Abog sg+gen Abogai Abog sg+nom Abogako Abog pl+acc Abogmeô Abog pl+dat Abogmeke Abog pl+gen Abogmei Abog pl+nom Abogmeko Abog sg+acc Abogaô Abog sg+dat Abogake Abog sg+gen Abogai Abog sg+nom Abogako lArpux pl+acc lArpuxmeô lArpux pl+dat lArpuxmeGe lArpux pl+gen lArpuxmei lArpux pl+nom lArpuxmeGo lArpux sg+acc lArpuxaô lArpux sg+dat lArpuxaGe lArpux sg+gen lArpuxai lArpux sg+nom lArpuxaGo lIdrab pl+acc lIdravmeô lIdrab pl+dat lIdrabmeke lIdrab pl+gen lIdravmei lIdrab pl+nom lIdrabmeGo lIdrab sg+acc lIdravaô lIdrab sg+dat lIdravaGe lIdrab sg+gen lIdravai lIdrab sg+nom lIdravaGo 59 paradigms covering 454 lexemes

49. Another run

50. Another run • Initial paradigm: • Adgar pl+acc Adgarmeon • Adgar pl+dat Adgarmeke • Adgar pl+gen Adgarmei • Adgar pl+nom Adgarmeko • Adgar sg+acc Adgaraon • Adgar sg+dat Adgarake • Adgar sg+gen Adgarai • Adgar sg+nom Adgarako • PHONRULE_WEIGHTING=0.80 • NUM_TEACHING_FORMS=1500