Lower Bounds on the Expressivity of Recurrent Neural Language Models

• URL: http://arxiv.org/abs/2405.19222v2
• Date: Tue, 18 Jun 2024 15:42:32 GMT
• Title: Lower Bounds on the Expressivity of Recurrent Neural Language Models
• Authors: Anej Svete, Franz Nowak, Anisha Mohamed Sahabdeen, Ryan Cotterell,
• Abstract summary: Investigation into the representational capacity of neural LMs has predominantly focused on their ability to emphrecognize formal languages. We take a fresh look at the representational capacity of RNN LMs by connecting them to emphprobabilistic FSAs and demonstrate that RNN LMs with linearly bounded precision can express arbitrary regular LMs.
• Score: 47.537525313391164
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The recent successes and spread of large neural language models (LMs) call for a thorough understanding of their computational ability. Describing their computational abilities through LMs' \emph{representational capacity} is a lively area of research. However, investigation into the representational capacity of neural LMs has predominantly focused on their ability to \emph{recognize} formal languages. For example, recurrent neural networks (RNNs) with Heaviside activations are tightly linked to regular languages, i.e., languages defined by finite-state automata (FSAs). Such results, however, fall short of describing the capabilities of RNN \emph{language models} (LMs), which are definitionally \emph{distributions} over strings. We take a fresh look at the representational capacity of RNN LMs by connecting them to \emph{probabilistic} FSAs and demonstrate that RNN LMs with linearly bounded precision can express arbitrary regular LMs.

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