Open access
Date
2023-12Type
- Conference Paper
ETH Bibliography
yes
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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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000650677Publication status
publishedExternal links
Book title
Proceedings of the 2023 Conference on Empirical Methods in Natural Language ProcessingPages / Article No.
Publisher
Association for Computational LinguisticsEvent
Organisational unit
09682 - Cotterell, Ryan / Cotterell, Ryan
02219 - ETH AI Center / ETH AI Center
Related publications and datasets
Is supplemented by: https://github.com/rycolab/rnn-turing-completeness
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ETH Bibliography
yes
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