[Author Login]
Title:OT grammars don't count, but make errors: The consequences of strict domination for simulated annealing
Authors:Tamas Biro
Comment:Published in: Beata Gyuris, Katalin Mady and Gabor Recski (eds.), K + K = 120. Papers dedicated to Laszlo Kalman and Andras Kornai on the occasion of their 60th birthdays (Research Institute for Linguistics, Hungarian Academy of Sciences, Budapest, 2017).
Abstract:Our goal is to compare Optimality Theory (OT) to Harmonic Grammar (HG) with respect to simulated annealing, a heuristic optimization algorithm. First, a few notes on Smolensky's ICS Architecture will bridge the gap between connectionist HG and symbolic HG. Subsequently, the latter is connected to OT via q-HG grammars, in which constraint C_i has weight q^i. We prove that q-HG converges to OT if q → +∞, even if constraint violations have no upper bound. This limit shall be referred to as the strict domination limit. Finally we argue that q-HG in the strict domination limit shares with OT a remarkable feature: simulated annealing does not always converge to 100% precision, even if the algorithm is offered ample time. Globally non-optimal local optima produced at slow pace will be viewed as irregular forms.
Type:Paper/tech report
Area/Keywords:formal analysis, implementation, simulated annealing, q-HG grammar, OT-HG connection, strict domination, ICS Architecture
Article:Version 1