Lexical and Grammatical Convergence within Communities

2. Lexical and Grammatical Convergence within Communities Chris Schmader EECS 470 Northwestern University June 10, 2011

3. Linguistic Convergence • Occurs when a community arrives at a common set of linguistic conventions • e.g., using "dog" to refer to a certain type of animal • using word order to encode who/what performed an action & who/what was acted upon • Question: how does convergence occur, given that… • These conventions are arbitrary (i.e., no inherent connection between words & their meanings) • Communication within large communities typically occurs at the level of dyads (i.e., two people)

4. Agent-Based Modeling • Some types of linguistic convergence are difficult to study using experimental methods • Occur over many interactions between large numbers of people • Costs of assembling large groups of participants are prohibitive • ABM allows us to: • Create a large community of artificial agents • Observe thousands of attempts to communicate among agents within community

5. Lexical Convergence • Barr (2004) used ABM to show that large communities of agents were able to converge on a common lexicon in a bottom-up fashion • Barr’s (2004) findings: agents converged more quickly on a lexicon when…. • Number of previous communicative outcomes agents could store (i.e., memory size) was small • Number of distinct agents within the community each agent communicated with (i.e., neighborhood size) was relatively small

6. Grammatical Convergence • Current model: investigated whether communities of agents would converge on a common lexicon and grammar • If so, will memory size and neighborhood size also affect grammatical convergence?

7. The Current Model • Contains “people” and “objects” • People communicate about objects that appear in the center of model environment • Objects vary along two dimensions: shape (circle or square) and color (blue or yellow)

8. The Current Model • People have lists representing: • lexicons of four words (“A,” “B,” “C,” and “D”) mapped to four meanings (circle, square, blue and yellow) • two-position grammars, in which 1st sentence position encodes shape and 2nd position encodes color, or vice versa • Memories for how well lexical mappings and grammars have performed Lexicon: [ "A" yellow false] [ "B" "square" false] …. Grammar: [ "shape" "color" ] Lex-memory: ["A" false true] [ "B" true true ]…. Gram-memory: [ false true false ]

9. At Setup • 100 people created and randomly scattered throughout environment • Each person’s lexicon and grammar are randomly initialized “A” = circle “A” = square “A” = yellow “A” = blue (Different colors for agents indicate different lexicons)

10. At Each Tick • Training phase: people generate one-word sentences • Sentences refer to object’s shape or its color • If speaker & interlocutor's sentences mismatch, they switch word's meaning based on number of failures stored in memory • If switch occurs, word’s meaning is exchanged with the meaning of least successful other word • Each person ("speaker") communicates with closest other person (“interlocutor”) who hasn’t already spoken on that tick Person 0's sentence: "A" Person 63's sentence: "D"

11. At Each Tick • Next, people produce two-word sentences based on their grammars • If grammar is “shape-first,” first word refers to shape; “color-first,” first word refers to color • If at least one sentence position contains same word across speaker and interlocutor, it's a success • If not, they record a failure and follow switching algorithm similar to that used for lexicon • Training phase of model run ends when people have converged on common lexicon Person 0's sentence: "C" "D" Person 63's sentence: "C" "D"

12. Sliders • Memory-size: varies number of previous outcomes stored in memories for lexical mappings & grammar • Ranges from 2 to 10 • Neighborhood-size: varies radius, in patches, within which a person can move • Ranges from 1 to 16 • Smaller radius means people will interact with smaller number of distinct others during model run

13. Experiment • Attempted to replicate Barr’s (2004) findings on lexical convergence & extend them to grammatical convergence • Conducted BehaviorSpace experiment measuring number of ticks to lexical convergence & grammatical convergence • Varied memory-size from 2 to 10 • Varied neighborhood-size, with settings of 2, 4, 6, 8, 10, 12, 14, and 16 • Conducted 10 model runs at each combination of memory-size and neighborhood-size settings • Predictions: lexical & grammatical convergence will occur more quickly at low settings of memory-size and middle settings of neighborhood-size

14. Results (Lexical Convergence) • Trend toward slower convergence at smallest neighborhood size • Trend toward quicker convergence at smallest memory sizes • Reliably slower convergence at neighborhood size 2 when memory size was 2 or 3

15. Results (Grammatical Convergence) • Analyzed ticks needed after lexical convergence for grammatical convergence to occur • Small trend toward slower grammatical convergence at neighborhood size 2 • No indication of differences in convergence across different levels of memory size

16. Discussion • Results replicated Barr's (2004) findings on effect of memory size on lexical convergence • Smaller memory sizes led to quicker convergence • Likely due to fact that storing too many failures leads people to switch mappings too often • Results did not replicate Barr's findings on neighborhood size • May be due to differences across studies in how models operationalized neighborhood size

17. Discussion • No indication that memory size or neighborhood size affect grammatical convergence • Likely due to fact that grammars in current model were too simple for these effects to emerge • Future work will attempt to extend model to more complex grammars • Overall, results demonstrate that communities can converge on lexicon & grammar in bottom-up fashion, provided they establish lexical mappings first

18. References • Barr, D. J. (2004). Establishing conventional communication systems: Is common knowledge necessary? Cognitive Science, 28, 937-962.