On Friday, April 12, visiting faculty Jon Rawski was invited to give a talk at the Computional Linguistics at Yale (CLAY) talk series, where he presented joint work with Zhouyi Sun, 2nd year grad student in our department.
Title: Tensor Product Representations of Regular Languages and Transformations
Abstract:
A crowning achievement of connectionist modeling in linguistics embedded symbolic structures using tensors as an intermediary to neural computation, relying on fixed “role decompositions” like substrings, subtrees, etc. At the same time, work in descriptive complexity has created a flexible unified ontology for finite structures, and tight links between regular languages and transformations which represent an upper bound for linguistic computation. I 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 formal languages and transformations. The semantics of such statements can be compiled into tensors, using multilinear maps as function application for evaluation. I show how this works for varieties of First-order and Monadic Second-Order definable languages and transformations.