On the Representational Capacity of Recurrent Neural Language Models

Franz Nowak, Anej Svete, Li Du, Ryan Cotterell

Submission Type: Regular Long Paper

Submission Track: Language Modeling and Analysis of Language Models

Submission Track 2: Linguistic Theories, Cognitive Modeling, and Psycholinguistics

Keywords: RNN, LM, Turing machine, formal languages, probabilistic, language model

Abstract:

This work investigates the computational expressivity of language models (LMs) based on recurrent neural networks (RNNs).
Siegelmann and Sontag (1992) famously showed that RNNs with rational weights and hidden states and unbounded computation time are Turing complete.
However, LMs define weightings over strings in addition to just (unweighted) language membership and the analysis of the computational power of RNN LMs (RLMs) should reflect this.
We extend the Turing completeness result to the probabilistic case, showing how a rationally weighted RLM with unbounded computation time can simulate any deterministic probabilistic Turing machine (PTM) with rationally weighted transitions.
Since, in practice, RLMs work in real-time, processing a symbol at every time step, we treat the above result as an upper bound on the expressivity of RLMs.
We also provide a lower bound by showing that under the restriction to real-time computation, such models can simulate deterministic real-time rational PTMs.

Submission Number: 5597