Niyogi, P., & Sonderegger, M. When does variation lead to change? [PDF]

Department of Computer Science, University of Chicago, USA; [email protected]. Introduction. All language change be

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Laboratory Phonology 11

103

Niyogi & Sonderegger

When does variation lead to change? A dynamical systems model of a stress shift in English Partha Niyogi* & Morgan Sonderegger# *Departments of Computer Science and Statistics, University of Chicago, USA; [email protected] # Department of Computer Science, University of Chicago, USA; [email protected] Introduction All language change begins with variation, but most variation does not lead to change. In fact significant phonetic variation occurs even within the speech of single speakers (Pierrehumbert, 2003), suggesting a restatement of the “actuation problem”: why does language change happen at all, why does it arise from variation, and what determines whether a pattern of variation between several forms is stable or unstable (leads to change)? To address these questions we present a case study of prosodic change in English between multiple forms, and model its dynamics using dynamical systems models for a population of learners (Niyogi, 2006). We propose that the distinction between unstable and stable variation corresponds to the distinction between models which show bifurcations (or “phase transitions”) as model parameters change, and those which do not. These classes correspond to models with or without “ambiguity”, meaning that learners receive some examples which are not clearly heard as one form or another. Data The English lexicon contains approximately 1000–2000 bisyllabic words with both noun and verb forms (contest, contrast, cement). The stress for a N/V pair is denoted (N, V) here (e.g. (1, 1) means doubly- initial stress). There are four possibilities for each pair: (1,1), (1,2), (2,2), or (2,1). Sherman (1975) found that approximately 150 N/V pairs have shifted stress since 1600, many to (1,2). Combining Sherman’s data (1600-1800) with our own (1800-2005), we recorded the stress of these 150 words in 85 British and American dictionaries from 1600-2005. These sources often report variation. Considering the trajectories formed by the moving average of each word’s reported stress, we found: 1. (2,1) is never attested. 2. The changes (2, 2) → (1, 2), (1, 1) → (1, 2), (1, 2) → (2, 2), (1, 2) → (1, 1) occur (in decreasing order of frequency), and (1, 1) ↔ (2, 2) do not occur. 3. Synchronic variation (for a particular N/V pair) is widespread, but long-term variation is rare. 4. Classes of words sharing a prefix (such as con-) have more similar trajectories than random classes (analogy), but only for larger prefix classes We also found 5. that (1, 1), (1, 2), and (2, 2) are stable states: in a random subset of 100 of all N/V pairs, most have shown little synchronic variation, and no change, over 400 years. Many linguistic explanations for (1)-(5) are possible, but testing whether a proposed theory diachronically explains (1)-(5) involves building formal models of the interplay between acquisition, variation, and change. Models In order to reason about the possible trajectories of language change in a population, we constructed a variety of models; here we focus on two classes of models. Both assume a probabilistic characterization of the internal variation on the part of speakers, and a population of learners each of whom learns from the population at large during a learning period. We use a probabilistic characterization based on evidence from a corpus of radio speech showing speaker-level variation in stress placement for N/V pairs.

LabPhon11 abstracts edited by Paul Warren

Wellington, New Zealand 30 June - 2 July 2008

Abstract accepted after review

104

Niyogi & Sonderegger

Laboratory Phonology 11

Models with Phonological Ambiguity Assume a word has two forms (say 1 and 2, the two stress patterns). Let each mature speaker have a value x ∈ [0, 1] that characterizes the probability with which they produce form 1. Let the distribution of x values in the adult population be given by a probability distribution P(x). Learning is the mechanism by which this variation is transmitted to the next generation. A learner situated in this population hears k utterances of the word from the population at large. On the basis of his/her experience, the learner develops a value of x which is used as a mature speaker. Ambiguity, for us, means the following. If a speaker intended form 1, then with probability a, the hearer perceives form 1 but with probability (1 - a), the hearer is unable to determine whether form 1 or 2 was intended. Similarly, form 2 is heard correctly with probability (1 − b), and is heard as ambiguous with probability b. Then, if the learner hears form i ki times and ambiguous forms k − k1 − k2 times, a natural probability matching algorithm on the part of the learner would be to use an internal variation x given by x = k1 /(k1 + k2) (provided k1 + k2 > 0; say x=0.5 otherwise). Then, if ut is the average value of x in the generation t, one can calculate ut+1 , the average value in the next generation. In this case, for large k we have

u t+1 =

au t au t + b(1 − u t )

This dynamics is (i) nonlinear (ii) has stable points where the population uses either form 1 or form 2 exclusively (iii) bifurcations between the two stable points as a function of (a − b). We elaborate on this basic insight by considering the effects of (a) coupling between words (analogy between words during learning) (b) finite k (word frequency) (c) finite population size (d) mixed misperception and ambiguity. Models without Phonological Ambiguity In contrast, one might consider models without ambiguity. The setup is exactly as before except learners always interpret the acoustic stimulus categorically. In other words, if the speaker intended form 1, the learner will either hear it as form 1 or 2: there is no “ambiguous” state. Thus there may be misperceptions but none of the primary linguistic data is actually thrown out during the learning period. We consider models with this character and show that the dynamics that arise have very different properties. In particular, there is always one stable attractor that corresponds to a mixed state, i.e., stable variation persists. Further there are no bifurcations. Conclusions and Contributions Our main contribution is to collect a corpus of empirical data on phonological change over time, to expose the important aspects of language change in this corpus, to construct a variety of models of language acquisition, variation, and change to understand and reason about the trends we see in this corpus. Our main result is that if learners perceived their input with the possibility of phonological ambiguity, then the dynamics is nonlinear, there are bifurcations (“phase transitions”) that may explain the actuation problem, and the stable modes of the population are close to homogeneous. In contrast, if learners perceived their input in a purely categorical way, this is not true and in particular stable variation is possible. There are many subtle aspects of the dynamics of linguistic populations that we wish to expose through this kind of a case study of phonetic variation and phonological change. References Niyogi, P. (2006). The Computational Nature of Language Learning and Evolution. Cambridge: MIT Press. Pierrehumbert, J. (2003). Phonetic diversity, statistical learning, and acquisition of phonology. Language and Speech, 46, 115-154. Sherman, D. (1975). Noun-verb stress alternation: An example of the lexical diffusion of sound change in English. Linguistics, 159, 43–71.

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