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Categorical Perception and the Convergence of Social Learning

Categorical Perception and the Convergence of Social Learning. Mark Y. Liberman University of Pennsylvania http://www.ling.upenn.edu/~myl. Acoustical Society of America Fall meeting 2000. The problem of vocabulary consensus. 10K-100K arbitrary pronunciations

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Categorical Perception and the Convergence of Social Learning

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  1. Categorical Perceptionandthe Convergence of Social Learning Mark Y. LibermanUniversity of Pennsylvaniahttp://www.ling.upenn.edu/~myl Acoustical Society of America Fall meeting 2000

  2. The problem of vocabulary consensus • 10K-100K arbitrary pronunciations • How is consensus established and maintained? Genesis 2:19-20 And out of the ground the Lord God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof. And Adam gave names to the cattle, and to the fowl of the air, and to every beast of the field...

  3. Possible solutions Initial naming authority (Adam) Natural names (“ding-dong” etc.) Explicit negotiation ???? Emergent structure

  4. Buridan’s Ants make a decision Percentage of Iridomyrex Humulis workers passing each (equal) arm of bridge per 3-minute period

  5. Agent-based modeling • AKA “individual-based modeling” Ensembles of parameterized entities ("agents") interact in algorithmically-defined ways. Individual interactions depend (stochastically) on the current parameters of the agents involved; these parameters are in turn modified (stochastically) by the outcome of the interaction.

  6. Key ideas of ABM • Complex structure emerges from the interaction of simple agents • Agents’ algorithms evolve in a context they create collectively • Thus behavior is like organic form BUT • ABM is a form of programming, so just solving a problem via ABM has no scientific interest • We must show relevant general property of some wide class of models • Paradigmatic example is Axelrod’s work on reciprocal altruism in the iterated prisoner’s dilemma

  7. Emergence of shared pronunciations • Definition of success: • Social convergence (“people are mostly the same”) • Lexical differentiation (“words are mostly different”) • These two propertiesare required for successful communication

  8. A simple sample model • Individual belief about word pronunciation: vector of binary random variables e.g. feature #1 is 1 with p=.9, 0 with p=.1 feature #2 is 1 with p=.3, 0 with p=.7 • (Instance of) word pronunciation: (random) binary vector e.g. 1 0 • Initial conditions: random assignment of binary values to beliefs • Channel effect: additive noise • Perception: assign input feature-wise to nearest binary vector i.e. categorical perception • Conversational geometry: circle of errorless pairwise naming among N people • Update method: linear combination of belief and perception “leaky integration” of perceptions

  9. It works! • Channel noise = .4 • Update constant = .8 • 10 people (#1 and #4 shown)

  10. Gradient output = faster convergence Instead of saying 1 or 0 for each feature, speakers emit real numbers (plus noise) proportional to their belief about the feature. Perception is still categorical. Result is faster convergence, because better information is provided about speaker’s internal state.

  11. Gradient input = no convergence If we make perception gradient, then (whether or not production is categorical) social convergence does not occur.

  12. What’s going on? • Input categorization creates “attractors” that trap beliefs despite channel noise • Positive feedback creates social consensus • Random effects generate lexical differentiation • Assertion: any model of this general type needs categorical perception to achieve social consensus with lexical differentiation

  13. Divergence with population size With gradient perception, it is not just that pronunciation beliefscontinue a random walk over time. They also diverge increasinglyat a given time, as group size increases. 40 people: 20 people:

  14. Pronunciation differentiation • There is nothing in this model to keep words distinct • But words tend to fill the space randomly (vertices of an N-dimensional hypercube) • This is fine if the space is large enough • Behavior is rather lifelike with word vectors of 19-20 bits

  15. Homophony comparison English is plotted with triangles (97K pronouncing dictionary). Model vocabulary with 19 bits is X’s. Model vocabulary with 20 bits is O’s.

  16. Conclusions • As others have argued, categorical (digital) perception is crucial for a communication system with many well-differentiated words • Previous arguments had mainly to do with individual perception • There may be arguments of equal force in the area of collective phenomena

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