HG Has No Computational Advantages over OT

The peculiar property of Optimality Theory (OT) is that it uses constraint ranking and thus enforces strict domination, according to which the highest ranked relevant constraint “takes it all”; see Prince & Smolensky (2004). Because of this property, OT looks prima facie like an exotic combinatorial framework. Exotic in the sense that it does not seem to have any close correspondent within core Machine Learning. For this reason, the toolkit available nowadays in computational OT for modeling language acquisition, production, and perception consists of autarchic combinatorial algorithms, specifically tailored to the exotic framework of OT, developed from scratch with no connections to methods and results in Machine Learning. Tesar & Smolensky’s (1998) powerful ranking algorithms well exemplify this current approach to computational OT. In order to bridge this gap between computational Phonology and Machine Learning, various scholars have recently started to entertain and explore variants of OT that replace constraint ranking with constraint weighting and strict domination with additive interaction, and thus fall within the class of linear models very well studied in Machine Learning. An important and simple such model is Harmonic Grammar (HG); see Legendre et al. (1990b,a). For instance, Pater (2009) writes: “[I will] illustrate and extend existing arguments for the replacement of OT’s ranked constraints with [HG’s] weighted ones: that the resulting model of grammar [. . . ] is compatible with well-understood algorithms for learning and other computations. [. . . ] The strengths of HG in this area are of considerable importance” (p. 1002): “as these algorithms are broadly applied with connectionist and statistical models of cognition, this forms an important connection between the HG version of Generative Linguistics and other research in cognitive science” (p. 1021). Let me summarize this position as follows.