Lexical and Grammatical
Convergence within Communities
Chris Schmader
EECS 470
Northwestern University
June 10, 2011
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)
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:
1) Create a large community of artificial agents
2) Observe thousands of attempts to communicate
among agents within community
Lexical Convergence
•
•
Barr (2004) used ABM to show that large
communities of agents were able to
converge on a common lexicon in a bottomup 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
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?
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)
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 ]
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)
At Each Tick
• Each person ("speaker") communicates with closest other
person (“interlocutor”) who hasn’t already spoken on that 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
Person 0's sentence: "A"
Person 63's sentence: "D"
At Each Tick
• Training phase of model run ends when people have
converged on common lexicon
• Next, people produce twoword 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
Person 0's sentence: "C" "D"
Person 63's sentence: "C" "D"
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
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 memorysize and neighborhood-size settings
• Predictions: lexical & grammatical convergence will
occur more quickly at low settings of memory-size
and middle settings of neighborhood-size
Results (Lexical Convergence)
Mean Ticks to Converge on a Lexicon
6000
Neighborhood Size = 16
Neighborhood Size = 10
5000
Neighborhood Size = 2
Ticks
4000
3000
2000
1000
0
-1000
2
3
4
5
6
7
8
9
10
Memory Size
• 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
Results (Grammatical Convergence)
Mean Ticks to Converge on a Grammar
1000
Neighborhood Size = 16
Neighborhood Size = 10
800
Neighborhood Size = 2
Ticks
600
400
200
0
2
3
4
5
6
7
8
9
10
-200
Memory Size
• 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
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
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
References
• Barr, D. J. (2004). Establishing
conventional communication systems:
Is common knowledge necessary?
Cognitive Science, 28, 937-962.
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