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.

A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes (including EDM, DDIM, and DPM-Solver) by optimizing certain coefficients via improved integration approximation (IIA). We propose to minimize, for each time step, a mean squared error (MSE) function with respect to the selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps, which in principle provides a more accurate integration approximation in predicting the next diffusion state. The proposed IIA technique does not require any change of a pre-trained model, and only introduces a very small computational overhead for solving a number of quadratic optimization problems. Extensive experiments show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-Solver than the original counterparts when the neural function evaluation (NFE) is small (i.e., less than 25).