Overcoming a Theoretical Limitation of Self-Attention

David Chiang, Peter Cholak


Abstract
Although transformers are remarkably effective for many tasks, there are some surprisingly easy-looking regular languages that they struggle with. Hahn shows that for languages where acceptance depends on a single input symbol, a transformer’s classification decisions get closer and closer to random guessing (that is, a cross-entropy of 1) as input strings get longer and longer. We examine this limitation using two languages: PARITY, the language of bit strings with an odd number of 1s, and FIRST, the language of bit strings starting with a 1. We demonstrate three ways of overcoming the limitation implied by Hahn’s lemma. First, we settle an open question by constructing a transformer that recognizes PARITY with perfect accuracy, and similarly for FIRST. Second, we use layer normalization to bring the cross-entropy of both models arbitrarily close to zero. Third, when transformers need to focus on a single position, as for FIRST, we find that they can fail to generalize to longer strings; we offer a simple remedy to this problem that also improves length generalization in machine translation.
Anthology ID:
2022.acl-long.527
Volume:
Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
Month:
May
Year:
2022
Address:
Dublin, Ireland
Venue:
ACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
7654–7664
Language:
URL:
https://aclanthology.org/2022.acl-long.527
DOI:
10.18653/v1/2022.acl-long.527
Bibkey:
Cite (ACL):
David Chiang and Peter Cholak. 2022. Overcoming a Theoretical Limitation of Self-Attention. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 7654–7664, Dublin, Ireland. Association for Computational Linguistics.
Cite (Informal):
Overcoming a Theoretical Limitation of Self-Attention (Chiang & Cholak, ACL 2022)
Copy Citation:
PDF:
https://aclanthology.org/2022.acl-long.527.pdf
Code
 ndnlp/parity