Nimbus: Secure and Efficient Two-Party Inference for Transformers

TL;DR

This work presents a new two-party inference framework $\mathsf{Nimbus}$ for Transformer models and proposes an approach of low-degree polynomial approximation for GELU and Softmax, which improves the performance of the SOTA polynomial approximation.

Abstract

Transformer models have gained significant attention due to their power in machine learning tasks. Their extensive deployment has raised concerns about the potential leakage of sensitive information during inference. However, when being applied to Transformers, existing approaches based on secure two-party computation (2PC) bring about efficiency limitations in two folds: (1) resource-intensive matrix multiplications in linear layers, and (2) complex non-linear activation functions like $\mathsf{GELU}$ and $\mathsf{Softmax}$. This work presents a new two-party inference framework $\mathsf{Nimbus}$ for Transformer models. For the linear layer, we propose a new 2PC paradigm along with an encoding approach to securely compute matrix multiplications based on an outer-product insight, which achieves $2.9\times \sim 12.5\times$ performance improvements compared to the state-of-the-art (SOTA) protocol. For the non-linear layer, through a new observation of utilizing the input distribution, we propose an approach of low-degree polynomial approximation for $\mathsf{GELU}$ and $\mathsf{Softmax}$, which improves the performance of the SOTA polynomial approximation by $2.9\times \sim 4.0\times$, where the average accuracy loss of our approach is 0.08\% compared to the non-2PC inference without privacy. Compared with the SOTA two-party inference, $\mathsf{Nimbus}$ improves the end-to-end performance of \bert{} inference by $2.7\times \sim 4.7\times$ across different network settings.

Figures (12)

• Figure 1: An example of the window encoding of the matrix multiplication using $N = 16$ and $\ell = 5$.
• Figure 2: Two rows represent the client and server operations, respectively. The inefficient parts that are accelerated are marked by dashed boundaries. The input communication is shifted as a one-time setup, and the output ciphertexts are compact. The expensive NTT/INTT operations at the online stage are also reduced.
• Figure 3: Illustration of our matrix multiplication. Left: Functionality of the matrix multiplication using row-wise encoding. Middle: Computing the first row of the output through the scalar-poly product. Right: Packing two ciphertexts using aright shift for less number of output ciphertext.
• Figure 4: The input distribution of non-linear functions. The y-axis indicates the occurrence counts.
• Figure 5: The L2-Norm of output error between oracle non-linear functions and approximations.