HG Has No Computational Advantages over OT: Toward a New Toolkit for Computational OT

Abstract

Various authors have recently endorsed Harmonic Grammar (HG) as a replacement for Optimality Theory (OT). One argument for this move is that OT seems not to have close correspondents within machine learning while HG allows methods and results from machine learning to be imported into computational phonology. Here, I prove that this argument in favor of HG and against OT is wrong. In fact, I show that any algorithm for HG can be turned into an algorithm for OT. Hence, HG has no computational advantages over OT. This result allows tools from machine learning to be systematically adapted to OT. As an illustration of this new toolkit for computational OT, I prove convergence for a slight variant of Boersma’s (1998) (nonstochastic) Gradual Learning Algorithm.

Does MaxEnt Overgenerate? Implicational Universals in Maximum Entropy Grammar

“…The algebraic characterization provided by (5) is instead easy to check with readily available linear programming tools. In Anttila & Magri (2018b) we extend this result from HG to OT using the HG-to-OT portability observation in Magri (2013). Thus, also in the case of OT, T-orders can be established without computing the entire OT typology by checking a simple condition on the antecedent and consequent difference vectors analogous to (5).…”

Error-driven learning in Optimality Theory and Harmonic Grammar: a comparison

“…As just noted, one crucial property of counterexample (9) is that the size of the negative entries is always equal to the number of positive entries in the corresponding row. This property ensures that gang-up effects are impossible, as explained in Appendix C (this is a special case of an argument from Magri 2013b: §4). The OT and HG update conditions thus collapse: whenever the OT learner would update the current vector θ , the HG learner would update it as well.…”

Noise robustness and stochastic tolerance of OT error-driven ranking algorithms

“…The idea is to evaluate the two frameworks apart from their typological predictions, by distilling their algorithmic implications for modelling the production perception and acquisition of phonology. For instance, Riggle [29] and Bane et al [1] compare the two frameworks from the perspective of learning-theoretic complexity measures such as their VC-dimension; Magri [23] compares them from the perspective of the computational problem of finding a consistent grammar; Jesney and Tessier [15] compare them from the perspective of the problem of finding a restrictive grammar. This article contributes to this enterprise from the perspective of the theory of error-driven learning.…”

“…In other words, the inequality (12) holds no matter whether the update has been triggered by a pristine or by a corrupted triplet and, therefore, extends to the noisy learning setting considered here. The two inequalities (23) and (12) can then be combined into the error bound (24).…”