Permutation Equivariance of Transformers and Its Applications

Abstract

Revolutionizing the field of deep learning Transformer-based models have achieved remarkable performance in many tasks. Recent research has recognized these models are robust to shuffling but are limited to inter-token permutation in the forward propagation. In this work we propose our definition of permutation equivariance a broader concept covering both inter- and intra- token permutation in the forward and backward propagation of neural networks. We rigorously proved that such permutation equivariance property can be satisfied on most vanilla Transformer-based models with almost no adaptation. We examine the property over a range of state-of-the-art models including ViT Bert GPT and others with experimental validations. Further as a proof-of-concept we explore how real-world applications including privacy-enhancing split learning and model authorization could exploit the permutation equivariance property which implicates wider intriguing application scenarios. The code is available at https://github.com/Doby-Xu/ST