Naive discriminative learning (NDL) and linear discriminative learning (LDL) are simple computational algorithms for lexical learning and lexical processing. Both NDL and LDL assume that learning is discriminative, driven by prediction error, and that it is this error that calibrates the association strength between input and output representations. Both words’ forms and their meanings are represented by numeric vectors, and mappings between forms and meanings are set up. For comprehension, form vectors predict meaning vectors. For production, meaning vectors map onto form vectors. These mappings can be learned incrementally, approximating how children learn the words of their language. Alternatively, optimal mappings representing the end state of learning can be estimated. The NDL and LDL algorithms are incorporated in a computational theory of the mental lexicon, the ‘discriminative lexicon’. The model shows good performance both with respect to production and comprehension accuracy, and for predicting aspects of lexical processing, including morphological processing, across a wide range of experiments. Since, mathematically, NDL and LDL implement multivariate multiple regression, the ‘discriminative lexicon’ provides a cognitively motivated statistical modeling approach to lexical processing.
Yu-Ying Chuang and R. Harald Baayen
Phonotactics is the study of restrictions on possible sound sequences in a language. In any language, some phonotactic constraints can be stated without reference to morphology, but many of the more nuanced phonotactic generalizations do make use of morphosyntactic and lexical information. At the most basic level, many languages mark edges of words in some phonological way. Different phonotactic constraints hold of sounds that belong to the same morpheme as opposed to sounds that are separated by a morpheme boundary. Different phonotactic constraints may apply to morphemes of different types (such as roots versus affixes). There are also correlations between phonotactic shapes and following certain morphosyntactic and phonological rules, which may correlate to syntactic category, declension class, or etymological origins. Approaches to the interaction between phonotactics and morphology address two questions: (1) how to account for rules that are sensitive to morpheme boundaries and structure and (2) determining the status of phonotactic constraints associated with only some morphemes. Theories differ as to how much morphological information phonology is allowed to access. In some theories of phonology, any reference to the specific identities or subclasses of morphemes would exclude a rule from the domain of phonology proper. These rules are either part of the morphology or are not given the status of a rule at all. Other theories allow the phonological grammar to refer to detailed morphological and lexical information. Depending on the theory, phonotactic differences between morphemes may receive direct explanations or be seen as the residue of historical change and not something that constitutes grammatical knowledge in the speaker’s mind.
Phonological learnability deals with the formal properties of phonological languages and grammars, which are combined with algorithms that attempt to learn the language-specific aspects of those grammars. The classical learning task can be outlined as follows: Beginning at a predetermined initial state, the learner is exposed to positive evidence of legal strings and structures from the target language, and its goal is to reach a predetermined end state, where the grammar will produce or accept all and only the target language’s strings and structures. In addition, a phonological learner must also acquire a set of language-specific representations for morphemes, words and so on—and in many cases, the grammar and the representations must be acquired at the same time. Phonological learnability research seeks to determine how the architecture of the grammar, and the workings of an associated learning algorithm, influence success in completing this learning task, i.e., in reaching the end-state grammar. One basic question is about convergence: Is the learning algorithm guaranteed to converge on an end-state grammar, or will it never stabilize? Is there a class of initial states, or a kind of learning data (evidence), which can prevent a learner from converging? Next is the question of success: Assuming the algorithm will reach an end state, will it match the target? In particular, will the learner ever acquire a grammar that deems grammatical a superset of the target language’s legal outputs? How can the learner avoid such superset end-state traps? Are learning biases advantageous or even crucial to success? In assessing phonological learnability, the analysist also has many differences between potential learning algorithms to consider. At the core of any algorithm is its update rule, meaning its method(s) of changing the current grammar on the basis of evidence. Other key aspects of an algorithm include how it is triggered to learn, how it processes and/or stores the errors that it makes, and how it responds to noise or variability in the learning data. Ultimately, the choice of algorithm is also tied to the type of phonological grammar being learned, i.e., whether the generalizations being learned are couched within rules, features, parameters, constraints, rankings, and/or weightings.
Jane Chandlee and Jeffrey Heinz
Computational phonology studies the nature of the computations necessary and sufficient for characterizing phonological knowledge. As a field it is informed by the theories of computation and phonology. The computational nature of phonological knowledge is important because at a fundamental level it is about the psychological nature of memory as it pertains to phonological knowledge. Different types of phonological knowledge can be characterized as computational problems, and the solutions to these problems reveal their computational nature. In contrast to syntactic knowledge, there is clear evidence that phonological knowledge is computationally bounded to the so-called regular classes of sets and relations. These classes have multiple mathematical characterizations in terms of logic, automata, and algebra with significant implications for the nature of memory. In fact, there is evidence that phonological knowledge is bounded by particular subregular classes, with more restrictive logical, automata-theoretic, and algebraic characterizations, and thus by weaker models of memory.