Lower Bounds on the Expressivity of Recurrent Neural Language Models
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911923806666752 |
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| author | Svete, Anej Nowak, Franz Sahabdeen, Anisha Mohamed Cotterell, Ryan |
| author_facet | Svete, Anej Nowak, Franz Sahabdeen, Anisha Mohamed Cotterell, Ryan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_19222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lower Bounds on the Expressivity of Recurrent Neural Language Models Svete, Anej Nowak, Franz Sahabdeen, Anisha Mohamed Cotterell, Ryan Computation and Language 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. |
| title | Lower Bounds on the Expressivity of Recurrent Neural Language Models |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2405.19222 |