Peter Cholak


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Overcoming a Theoretical Limitation of Self-Attention
David Chiang | Peter Cholak
Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)

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.