%0 Conference Proceedings
%T Overcoming a Theoretical Limitation of Self-Attention
%A Chiang, David
%A Cholak, Peter
%S Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2022
%8 May
%I Association for Computational Linguistics
%C Dublin, Ireland
%F chiang-cholak-2022-overcoming
%X 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.
%R 10.18653/v1/2022.acl-long.527
%U https://aclanthology.org/2022.acl-long.527
%U https://doi.org/10.18653/v1/2022.acl-long.527
%P 7654-7664