Overcoming a Theoretical Limitation of Self-Attention
David Chiang, Peter A. Cholak · Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2022
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 become less and less confident (that is, with crossentropy approaching 1 bit per string) as input strings get longer and longer.We examine this limitation using two languages: PAR-ITY, 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 suggested 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.