Non-Adjacent Transitional Probabilities and the Induction of Grammatical Regularities

Non-adjacent Transitional Probabilities and the Induction of Grammatical Regularities Francisco Calvo Garzon (fjcalvo@um.es) Departamento de Filosofia, Campus de Espinardo Murcia, 30100 SPAIN familiarization. The results reported show that subjects favour words over part-words (P < 0.0005; see Pena et al., 2002, for details). This behaviour backs up the hypothesis that statistics alone suffice to segment a linguistic stream, since what counts as a word is defined as a function of the higher transitional probabilities between specific non- adjacent items (in this case, between Ai and Ci). Abstract According to Pena et al. (2002), statistical computations based on nonadjacent transitional probabilities of the sort that are exploited in speech segmentation cannot be used in order to induce existing grammatical regularities in the speech stream. In their view, statistics are insufficient to support the discovery of the underlying grammatical regularities. In this note I argue that a single statistical mechanism can account for the data Pena et al. report. Experiment B In experiment B, Pena et al. wanted to know whether subjects are simply segmenting the stream by exploiting differential transitional probabilities between words and part-words, or whether they are also tuning to some more abstract underlying grammatical regularity. In order to answer this question, after having been familiarized to the same speech stream of experiment A, subjects were asked to choose between a part-word and what Pena et al. dubbed a rule-word. A rule-word is a sequence of three syllables of the form AiX*Ci, where X* stands for a familiar syllable that occurs in familiarization, although never between Ai and Ci. In this way, although a rule-word represents a novelty, it is congruent with the structure of actual words by means of the preservation of a non-adjacent transitional probability of 1.0 between Ai and Ci. This time, interestingly, subjects prefer part-words over rule words. Under the light of experiments A and B, Pena et al. conclude that a “computational mechanism sufficiently powerful to support segmentation on the basis of nonadjacent transitional probabilities [experiment A] is insufficient to support the discovery of the underlying grammatical-like regularity embedded in a continuous speech stream [experiment B]” (p. 605). Keywords: statistical computations; rule-based learning; speech segmentation; neural networks. Introduction Pena et al. (2002) consider whether statistical computations based on nonadjacent transitional probabilities of the sort that are exploited in speech segmentation (Saffran et al., 1996) can be used in order to induce existing grammatical regularities in the speech stream. To answer this question, they designed an experimental paradigm and performed five different experiments. The first three are briefly reviewed here. Under the light of these experiments Pena et al. conclude that statistics are insufficient to support the discovery of the underlying grammatical regularities, and that their results imply knowledge of rules. Contra Pena et al., I shall argue that a single statistical mechanism can account for the data they report. Pena et al.’s experimental paradigm Pena et al.’s experimental paradigm involves asking adult subjects to listen to a sequence of trisyllabic artificial words for 10 minutes. Words have the form AiXCi and are identified on the basis of their nonadjacent transitional probabilities, such that the transitional probability between any Ai and the following Ci is 1.0; between Ai and the intermediate X, and between X and the final Ci is 0.33; and between Ci and the next word’s first syllable is 0.5. After familiarization, subjects are confronted with two linguistic stimuli and asked to offer a judgement as to which stimulus is more similar to chunks of the familiarization stream. Experiment A In experiment A, subjects were familiarized to a continuous speech stream as described above. In the test phase, they were exposed to a word (AiXCi) and a part-word (XCiAj) 1 , both of them contained in the stream being heard during Experiment C Pena et al. then introduced a 25-ms subliminal segmentation gap between words during familiarization. This time subjects manifested preference for rule-words over part- words, identifying them with above-chance accuracy (P < 0.0005; see Pena et al., 2002, for details). In their view, these results imply knowledge of rules insofar as the very notion of an abstract rule-word underlies the successful discrimination of rule-words and part-words. Thus, they claim: “This seems to be due to the fact that the selected items are compatible with a generalization of the kind “If there is a [pu] now, then there will be a [ki] after an intervening X” (p. 606). Part-words can also be of the form CkAiX (see below).