What a Perceptron Reveals about Metrical Phonology

Metrical phonology is a relatively successful theory that attempts to explain stress systems in language. This paper discusses a perceptron model of stress, pointing out interesting parallels between certain aspects of the model and the constructs and predictions of metrical theory. The distribution of learning times obtained from perceptron experiments corresponds with theoretical predictions of “markedness.” In addition, the weight patterns developed by perceptron learning bear a suggestive relationship to features of the linguistic analysis, particularly with regard to iteration and metrical feet. Our results suggest that simple statistical learning techniques have the potential to complement, and provide computational validation for, abstract theoretical investigations of linguistic domains. Basics of metrical theory This section outlines the structure of the syllable and the basics of metrical theory1. A syllable is composed of an onset, which contains the material before the vowel, and a rime. The rime is composed of a nucleus, which contains the vocalic material, and a coda, which contains any remaining non-vocalic material. A syllable may be open (ends in a vowel) or closed (ends in a consonant). Viewing syllable structures as trees, an open syllable has a non-branching rime (the rime has a nucleus, but not a coda), while a closed syllable has a branching rime (the rime has both a nucleus and a coda). A syllable may also have a long vowel, in which case the nucleus is considered to branch. In many languages, stress tends to be placed on certain kinds of syllables rather than on others; the former are termed heavy syllables, and the latter light syllables. What counts as heavy or lightdiffers across languages but, most commonly, a heavy syllable is one with a branching rime ([Goldsmith 1990, p. 113]). However, it is possible for other properties to contribute to syllable weight. For example, in some languages, only syllables with a long vowel (i.e., branching nucleus) count as heavy. Closed syllables with short vowels do not count as heavy, as they would in the more commonly-occurring heavy/light distinction ([Goldsmith 1990, p. 179]). Languages that distinguish between heavy and light syllables are termed quantity-sensitive, while languages that do not make this distinction are termed quantity-insensitive. There seems to be theoretical agreement that, in quantity-sensitive systems, the placement of stress is sensitive to the structure of the rime, but not the onset. We follow this assumption 2. The second author was supported by a grant from Hughes Aircraft Corporation, and by the Office of Naval Research under contract number N0001486-K-0678. 1For an overview of metrical phonology, see [Goldsmith 1990, chapter 4], [Kaye 1989, pp. 139-145], [van der Hulst & Smith 1982] or [Dresher & Kaye 1990, pp. 140-147]. 2See, for example, ([Dresher & Kaye 1990, p. 141] or [Goldsmith 1990, p. 170]). However, both [Davis 1988] and [Everett & Everett 1984] present evidence that onsets may in fact be relevant to the placement of stress. Thus rime structure is taken to be the basic level at which accounts of stress systems are formulated. Stress patterns are controlled by metrical structures built on top of rime structures. The version of metrical structure adopted here is metrical feet. We assume the parameters formulated by Dresher & Kaye ([Dresher & Kaye 1990, p. 142]): (P1) The word-tree is strong on the [Left/Right] (P2) Feet are [Binary/Unbounded] (P3) Feet are built from the [Left/Right] (P4) Feet are strong on the [Left/Right] (P5) Feet are Quantity-Sensitive (QS) [Yes/No] (P6) Feet are QS to the [Rime/Nucleus] (P7) A strong branch of a foot must itself branch [No/Yes] (P8) There is an extra-metrical syllable [Yes/No] (P9) It is extra-metrical on the [Left/Right] (P10) A weak foot is defooted in clash [No/Yes] (P11) Feet are non-iterative [No/Yes] As an example of the application of these parameters, consider the stress pattern of Maranungku, in which primary stress falls on the first syllable of the word and secondary stress on alternate succeeding syllables. Figure 1 shows an abstract representation of a six-syllable word, with each syllable represented as . The assignment of stress is characterized as follows. Binary, quantity-insensitive, left-dominant feet are constructed iteratively from the left edge of the word. Each foot has a “strong” and a “weak” branch (labeled “S” and “W,” respectively, in the figure). The strong, or dominant branch assigns stress to the syllable it dominates. Since the feet are leftdominant, odd-numbered syllables are assigned stress. Over the roots of these metrical feet, a left-dominant word-tree is constructed, which assigns stress to the structure dominated by its leftmost branch. The third and fifth syllables are each dominated by the dominant branch of one metrical structure (a foot), while the first syllable is dominated by the dominant branches of two structures (a foot, and the word-tree). Even-numbered syllables are dominated only by non-dominantbranches of feet. The result is that even-numbered syllables receive no stress; the third and fifth syllables receive one degree of stress (secondary stress); and the first syllable receives two degrees of stress (primary stress.) The parameter settings characterizing Maranungku are: [P1 Left], [P2 Binary], [P3 Left], [P4 Left], [P5 No], [P7 No], [P8 No], [P10 No], [P11 No]. Parameters P6 and P9 are irrelevant because of the settings of parameters P5 and P8, respectively. Sixteen stress systems Six quantity-insensitive (QI) languages and ten quantitysensitive (QS) languages were examined in our experiments. The data, summarized in Table 1, were taken primarily from [Hayes 1980]. Note that the QI stress patterns of Latvian & French, Maranungku & Weri, and Lakota & Polish are mirror images of each other. The QS stress patterns of Malayalam & Gupta & Touretzky, What a Perceptron Reveals About Metrical Phonology 2 Figure 1: Metrical structures for a six-syllable word in Maranungku. Yapese, Ossetic & Rotuman, Eastern Permyak Komi & Eastern Cheremis, and Khalka Mongolian & Aguacatec Mayan are also mirror images3. Learning stress with a perceptron In separate experiments, we taught a perceptron to produce the stress pattern of each of the sixteen languages. The domain was limited to single words, as in the previous learning models of metrical phonology developed by Dresher & Kaye, and Nyberg ([Dresher & Kaye 1990, Nyberg 1989]). Again as in the other models, the effects of morpho-syntactic information (such as lexical category) were ignored, and the simplifying assumption was made that the only relevant information about syllables was their weight. Words up to 7 syllables long were slid across a 13-element input window as shown in Figure 2. At each time step, the perceptron was trained to predict the stress of the center element. In order to distinguish heavy from light syllables, each input element consisted of two units. Thus the perceptron had a total of 26 inputs, plus a bias connection. The input patterns used were [1 0] for a heavy syllable, [0 1] for a light syllable, and [0 0] for no syllable.4 The output targets used in training were 1.0 for primary stress, 0.5 for secondary stress, and 0 for no stress. The input data set for all stress systems consisted of all 255 word-forms of up to seven syllables. Each word was processed one syllable at a time. Connection weights were adjusted at each time step using the back-propagation learning algorithm of [Rumelhart, Hinton & Williams 1986]. One epoch consisted of one presentation of the entire training set. The network was trained for as many epochs as necessary to ensure that the stress value produced by the perceptron was within 0.1 of the target value, for each syllable of the word, for all words in the training set. A learning rate of 0.05 and momentum of 0.90 was used in all simulations. Initial weights were uniformly distributed random values in the range 0:5. 3We have somewhat simplified the descriptions of Polish and Malayalam comparedwith those in [Halle & Vergnaud 1987, pp. 57-58]and [Hayes 1980, p. 66, 109]. However, this does not detract from our discussion in any way, as stress systems corresponding to our simplifications are reported to exist: Swahili ([Halle & Clements 1983, p.17]) and Gurkhali ([Hayes 1980, p.66]), corresponding to Polish and Malayalam, respectively. 4Note that the distinction between heavy and light syllables is irrelevant in a quantity-insensitive language. However, this representation was used in all simulations to maintain consistency across quantity-sensitive and quantityinsensitive systems. L