Self-Attention Networks Can Process Bounded Hierarchical Languages

Shunyu Yao, Binghui Peng, Christos Papadimitriou, Karthik Narasimhan


Abstract
Despite their impressive performance in NLP, self-attention networks were recently proved to be limited for processing formal languages with hierarchical structure, such as Dyck-k, the language consisting of well-nested parentheses of k types. This suggested that natural language can be approximated well with models that are too weak for formal languages, or that the role of hierarchy and recursion in natural language might be limited. We qualify this implication by proving that self-attention networks can process Dyck-(k, D), the subset of Dyck-k with depth bounded by D, which arguably better captures the bounded hierarchical structure of natural language. Specifically, we construct a hard-attention network with D+1 layers and O(log k) memory size (per token per layer) that recognizes Dyck-(k, D), and a soft-attention network with two layers and O(log k) memory size that generates Dyck-(k, D). Experiments show that self-attention networks trained on Dyck-(k, D) generalize to longer inputs with near-perfect accuracy, and also verify the theoretical memory advantage of self-attention networks over recurrent networks.
Anthology ID:
2021.acl-long.292
Volume:
Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)
Month:
August
Year:
2021
Address:
Online
Editors:
Chengqing Zong, Fei Xia, Wenjie Li, Roberto Navigli
Venues:
ACL | IJCNLP
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
3770–3785
Language:
URL:
https://aclanthology.org/2021.acl-long.292
DOI:
10.18653/v1/2021.acl-long.292
Bibkey:
Cite (ACL):
Shunyu Yao, Binghui Peng, Christos Papadimitriou, and Karthik Narasimhan. 2021. Self-Attention Networks Can Process Bounded Hierarchical Languages. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 3770–3785, Online. Association for Computational Linguistics.
Cite (Informal):
Self-Attention Networks Can Process Bounded Hierarchical Languages (Yao et al., ACL-IJCNLP 2021)
Copy Citation:
PDF:
https://aclanthology.org/2021.acl-long.292.pdf
Video:
 https://aclanthology.org/2021.acl-long.292.mp4
Code
 princeton-nlp/dyck-transformer
Data
WikiText-103WikiText-2