  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.
