Theoretical Limitations of Self-Attention in Neural Sequence Models

Michael Hahn


Abstract
Transformers are emerging as the new workhorse of NLP, showing great success across tasks. Unlike LSTMs, transformers process input sequences entirely through self-attention. Previous work has suggested that the computational capabilities of self-attention to process hierarchical structures are limited. In this work, we mathematically investigate the computational power of self-attention to model formal languages. Across both soft and hard attention, we show strong theoretical limitations of the computational abilities of self-attention, finding that it cannot model periodic finite-state languages, nor hierarchical structure, unless the number of layers or heads increases with input length. These limitations seem surprising given the practical success of self-attention and the prominent role assigned to hierarchical structure in linguistics, suggesting that natural language can be approximated well with models that are too weak for the formal languages typically assumed in theoretical linguistics.
Anthology ID:
2020.tacl-1.11
Volume:
Transactions of the Association for Computational Linguistics, Volume 8
Month:
Year:
2020
Address:
Cambridge, MA
Editors:
Mark Johnson, Brian Roark, Ani Nenkova
Venue:
TACL
SIG:
Publisher:
MIT Press
Note:
Pages:
156–171
Language:
URL:
https://aclanthology.org/2020.tacl-1.11
DOI:
10.1162/tacl_a_00306
Bibkey:
Cite (ACL):
Michael Hahn. 2020. Theoretical Limitations of Self-Attention in Neural Sequence Models. Transactions of the Association for Computational Linguistics, 8:156–171.
Cite (Informal):
Theoretical Limitations of Self-Attention in Neural Sequence Models (Hahn, TACL 2020)
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PDF:
https://aclanthology.org/2020.tacl-1.11.pdf