Saturated Transformers are Constant-Depth Threshold Circuits
Published
2022-08-12
William Cooper Merrill
,
Ashish Sabharwal
,
Noah A. Smith
William Cooper Merrill
Allen Institute for AI
New York University
Ashish Sabharwal
Allen Institute for AI
Noah A. Smith
Allen Institute for AI
University of Washington
Abstract
Transformers have become a standard neural network architecture for many NLP problems, motivating theoretical analysis of their power in terms of formal languages. Recent work has shown that transformers with hard attention are quite limited in power (Hahn, 2020), as they can be simulated by constant-depth AND/OR circuits (Hao et al., 2022). However, hard attention is a strong assumption, which may complicate the relevance of these results in practice. In this work, we analyze the circuit complexity of transformers with saturated attention: a generalization of hard attention that more closely captures the attention patterns learnable in practical transformers. We first show that saturated transformers transcend the known limitations of hard-attention transformers. We then prove saturated transformers with floating-point values can be simulated by constant-depth threshold circuits, giving the class TC0 as an upper bound on the formal languages they recognize.
Article at MIT Press
Presented at EMNLP 2022