This weekend, visiting Professor Jon Rawski gave invited talks at the CUNY Computational Linguistics Lecture Series, and the Workshop on Theoretical Phonology (WTPh) in Montreal.
Transductive Linguistics Redux
In 1991, Manaster-Ramer argued that linguistic well-formedness with its well-developed mathematics (formal languages) should be replaced by transductions (mappings between finite structures), but lamented the lack of mathematical work. Thirty years later we are ready to answer this challenge. I will overview recent developments connecting the theory of transductions to linguistics and computer science. I will give known upper and lower bounds on the weak and strong generative capacity of morphological and phonological phenomena. I will show how these bounds give a solid basis for comparing linguistic frameworks. I will then present new theoretical bounds on the capacity of large language models, connecting various transformer variants to classes of first-order finite-state transductions.
Rethinking Poverty of the Stimulus
This talk reimagines the “poverty of the stimulus” in language acquisition and linguistic theory. I will explain deficiencies and confusions in PovStim and in “grammar induction” more generally. I will argue for a move from acquisition as induction to abduction, focused around a core inference problem of “richness of the hypothesis space”. I will give a mathematical characterization of hypothesis generation, shifting the focus from grammars to classes of grammars, organized around particular intrinsic properties. The search for grammars becomes a constraint-satisfaction problem (not in the OT sense) guided by tractability, learnability, and other covering criteria, in line with current results and perspectives in psychology, linguistics, and computer science. I will discuss these and some recent work inferring grammars from data.