On Efficiently Representing Regular Languages as RNNs

TL;DR

This paper generalizes previous work to show that RNNs can efficiently represent a broader class of language models, including those modeled by pushdown automata with bounded stacks, offering new insights into their inductive biases.

Contribution

It extends the theoretical understanding of RNNs' capabilities, demonstrating their efficiency in representing complex language models beyond hierarchical structures.

Findings

RNNs can represent language models modeled by pushdown automata with bounded stacks.

The construction applies to a larger class of language models than previously shown.

This broadens the understanding of RNNs' inductive biases in language modeling.

Abstract

Recent work by Hewitt et al. (2020) provides an interpretation of the empirical success of recurrent neural networks (RNNs) as language models (LMs). It shows that RNNs can efficiently represent bounded hierarchical structures that are prevalent in human language. This suggests that RNNs' success might be linked to their ability to model hierarchy. However, a closer inspection of Hewitt et al.'s (2020) construction shows that it is not inherently limited to hierarchical structures. This poses a natural question: What other classes of LMs can RNNs efficiently represent? To this end, we generalize Hewitt et al.'s (2020) construction and show that RNNs can efficiently represent a larger class of LMs than previously claimed -- specifically, those that can be represented by a pushdown automaton with a bounded stack and a specific stack update function. Altogether, the efficiency of representing this diverse class of LMs with RNN LMs suggests novel interpretations of their inductive bias.