Lower Bounds on the Expressivity of Recurrent Neural Language Models

Code

• github.com/rycolab/nondeterministic-rnns
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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' representational capacity is a lively area of research. However, investigation into the representational capacity of neural LMs has predominantly focused on their ability to 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 language models (LMs), which are definitionally distributions over strings. We take a fresh look at the representational capacity of RNN LMs by connecting them to probabilistic FSAs and demonstrate that RNN LMs with linearly bounded precision can express arbitrary regular LMs.

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