On the Practical Computational Power of Finite Precision RNNs for Language Recognition

Gail Weiss, Yoav Goldberg, Eran Yahav


Abstract
While Recurrent Neural Networks (RNNs) are famously known to be Turing complete, this relies on infinite precision in the states and unbounded computation time. We consider the case of RNNs with finite precision whose computation time is linear in the input length. Under these limitations, we show that different RNN variants have different computational power. In particular, we show that the LSTM and the Elman-RNN with ReLU activation are strictly stronger than the RNN with a squashing activation and the GRU. This is achieved because LSTMs and ReLU-RNNs can easily implement counting behavior. We show empirically that the LSTM does indeed learn to effectively use the counting mechanism.
Anthology ID:
P18-2117
Volume:
Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)
Month:
July
Year:
2018
Address:
Melbourne, Australia
Editors:
Iryna Gurevych, Yusuke Miyao
Venue:
ACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
740–745
Language:
URL:
https://aclanthology.org/P18-2117
DOI:
10.18653/v1/P18-2117
Bibkey:
Cite (ACL):
Gail Weiss, Yoav Goldberg, and Eran Yahav. 2018. On the Practical Computational Power of Finite Precision RNNs for Language Recognition. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 740–745, Melbourne, Australia. Association for Computational Linguistics.
Cite (Informal):
On the Practical Computational Power of Finite Precision RNNs for Language Recognition (Weiss et al., ACL 2018)
Copy Citation:
PDF:
https://aclanthology.org/P18-2117.pdf
Note:
 P18-2117.Notes.pdf
Presentation:
 P18-2117.Presentation.pdf
Video:
 https://aclanthology.org/P18-2117.mp4