In the literature, various reversible deep neural networks (DNN) models have been proposed to reduce memory consumption or improve data-throughput in the training process. However, almost all existing reversible DNNs either are constrained to have special structures or are constructed by modifying the original DNN architectures considerably to enable reversibility. In this work, we propose exact bit-level reversible transformers without changing the architectures in the inference procedure. The basic idea is to first treat each transformer block as the Euler integration approximation for solving an ordinary differential equation (ODE) and then incorporate the technique of bidirectional integration approximation (BDIA) (see [26]) for BDIA-based diffusion inversion) into the neural architecture together with activation quantization to make it exactly bit-level reversible, referred to as BDIA-transformer. In the training process, we let a hyper-parameter $\gamma$ in BDIA-transformer randomly take one of the two values $\{0.5, -0.5\}$ per transformer block for averaging two consecutive integration approximations, which regularizes the models for improving the validation accuracy. Light-weight side information per transformer block is required to be stored in the forward process to account for binary quantization loss to enable exact bit-level reversibility. In the inference procedure, the expectation $\mathbb{E}(\gamma)=0$ is taken to make the resulting architectures of BDIA-transformer be identical to transformers up to activation quantization. Empirical study indicates that BDIA-transformers outperform their original counterparts notably due to the regularization effect of the $\gamma$ parameter.

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