Variational autoencoders (VAEs) are powerful tools for learning latent representations of data used in a wide range of applications. In practice, VAEs usually require multiple training rounds to choose the amount of information the latent variable should retain. This trade-off between the reconstruction error (distortion) and the KL divergence (rate) is typically parameterized by a hyperparameter $\beta$. In this paper, we introduce Multi-Rate VAE (MR-VAE), a computationally efficient framework for learning optimal parameters corresponding to various $\beta$ in a single training run. The key idea is to explicitly formulate a response function that maps $\beta$ to the optimal parameters using hypernetworks. MR-VAEs construct a compact response hypernetwork where the pre-activations are conditionally gated based on $\beta$. We justify the proposed architecture by analyzing linear VAEs and showing that it can represent response functions exactly for linear VAEs. With the learned hypernetwork, MR-VAEs can construct the rate-distortion curve without additional training and can be deployed with significantly less hyperparameter tuning. Empirically, our approach is competitive and often exceeds the performance of multiple $\beta$-VAEs training with minimal computation and memory overheads.

本文提出了一种称为多速率 VAE（MR-VAE）的计算有效的框架，其可以在单次训练运行中学习与各种 $\beta$ 相应的最佳参数，通过使用超网络显式地公式让 $\beta$ 映射到最佳参数，并且 MR-VAE 可以构建速率-失真曲线，无需额外训练，并且可以在较少的超参数调整下部署。

多速率VAE：只训练一次，即可得到完整的速率失真曲线