Speaker: Jon Rawski (MIT) and Zhouyi Sun (MIT)
Title: Tensor Product Representations of Phonological Constraints and Transformations
Time: Monday, April 29th, 5pm – 6:30pm
Location: 32-D831
Abstract: A crowning achievement of connectionist modeling in phonology embedded symbolic structures using tensors as an intermediary to neural computation, and used optimization over such structures to compute well-formedness (a la OT, HG, etc). However, there has been considerable difficulty restricting these models to match the upper computational bounds of phonology (regular languages and functions) since almost every constraint-interaction formalism computes supra-regular patterns with ease, and many are either Turing complete or uncomputable. We will discuss our recent attempt to circumvent this gap, by directly embedding both (sub)regular constraints and transformations into the tensor calculus used by constraint-interaction models. We will use finite model theory to characterize objects like strings, trees, graphs, and even input-output pairs as relational structures. Logical statements meeting certain criteria over these models define various classes of constraints and transformations. The semantics of such statements can be compiled into tensors, using multilinear maps as function application for evaluation. We show how this works for varieties of First-order and Monadic Second-Order definable constraints and transformations, and compare to previous work on correspondence constraints using model theory.