  As more and more pre-trained language models adopt on-cloud deployment, the
privacy issues grow quickly, mainly for the exposure of plain-text user data
(e.g., search history, medical record, bank account). Privacy-preserving
inference of transformer models is on the demand of cloud service users. To
protect privacy, it is an attractive choice to compute only with ciphertext in
homomorphic encryption (HE). However, enabling pre-trained models inference on
ciphertext data is difficult due to the complex computations in transformer
blocks, which are not supported by current HE tools yet. In this work, we
introduce $\textit{THE-X}$, an approximation approach for transformers, which
enables privacy-preserving inference of pre-trained models developed by popular
frameworks. $\textit{THE-X}$ proposes a workflow to deal with complex
computation in transformer networks, including all the non-polynomial functions
like GELU, softmax, and LayerNorm. Experiments reveal our proposed
$\textit{THE-X}$ can enable transformer inference on encrypted data for
different downstream tasks, all with negligible performance drop but enjoying
the theory-guaranteed privacy-preserving advantage.
