LSTM Networks Can Perform Dynamic Counting

Mirac Suzgun, Yonatan Belinkov, Stuart Shieber, Sebastian Gehrmann

Abstract
In this paper, we systematically assess the ability of standard recurrent networks to perform dynamic counting and to encode hierarchical representations. All the neural models in our experiments are designed to be small-sized networks both to prevent them from memorizing the training sets and to visualize and interpret their behaviour at test time. Our results demonstrate that the Long Short-Term Memory (LSTM) networks can learn to recognize the well-balanced parenthesis language (Dyck-1) and the shuffles of multiple Dyck-1 languages, each defined over different parenthesis-pairs, by emulating simple real-time k-counter machines. To the best of our knowledge, this work is the first study to introduce the shuffle languages to analyze the computational power of neural networks. We also show that a single-layer LSTM with only one hidden unit is practically sufficient for recognizing the Dyck-1 language. However, none of our recurrent networks was able to yield a good performance on the Dyck-2 language learning task, which requires a model to have a stack-like mechanism for recognition.
Anthology ID:
W19-3905
Volume:
Proceedings of the Workshop on Deep Learning and Formal Languages: Building Bridges
Month:
August
Year:
2019
Address:
Florence
Editors:
Jason Eisner, Matthias Gallé, Jeffrey Heinz, Ariadna Quattoni, Guillaume Rabusseau
Venue:
ACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
44–54
Language:
URL:
https://aclanthology.org/W19-3905
DOI:
10.18653/v1/W19-3905
Bibkey:
Cite (ACL):
Mirac Suzgun, Yonatan Belinkov, Stuart Shieber, and Sebastian Gehrmann. 2019. LSTM Networks Can Perform Dynamic Counting. In Proceedings of the Workshop on Deep Learning and Formal Languages: Building Bridges, pages 44–54, Florence. Association for Computational Linguistics.
Cite (Informal):
LSTM Networks Can Perform Dynamic Counting (Suzgun et al., ACL 2019)
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PDF:
https://preview.aclanthology.org/nschneid-patch-5/W19-3905.pdf
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