@inproceedings{chiang-cholak-2022-overcoming,
    title = "Overcoming a Theoretical Limitation of Self-Attention",
    author = "Chiang, David  and
      Cholak, Peter",
    editor = "Muresan, Smaranda  and
      Nakov, Preslav  and
      Villavicencio, Aline",
    booktitle = "Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
    month = may,
    year = "2022",
    address = "Dublin, Ireland",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/fix-sig-urls/2022.acl-long.527/",
    doi = "10.18653/v1/2022.acl-long.527",
    pages = "7654--7664",
    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."
}