Variational Autoencoders (VAEs) were originally motivated (Kingma & Welling, 2014) as probabilistic generative models in which one performs approximate Bayesian inference. The proposal of $\beta$-VAEs (Higgins et al., 2017) breaks this interpretation and generalizes VAEs to application domains beyond generative modeling (e.g., representation learning, clustering, or lossy data compression) by introducing an objective function that allows practitioners to trade off between the information content ("bit rate") of the latent representation and the distortion of reconstructed data (Alemi et al., 2018). In this paper, we reconsider this rate/distortion trade-off in the context of hierarchical VAEs, i.e., VAEs with more than one layer of latent variables. We identify a general class of inference models for which one can split the rate into contributions from each layer, which can then be tuned independently. We derive theoretical bounds on the performance of downstream tasks as functions of the individual layers' rates and verify our theoretical findings in large-scale experiments. Our results provide guidance for practitioners on which region in rate-space to target for a given application.

此论文研究了层次化变分自编码器中速率/失真权衡的问题，并提出了一个通用类别的推理模型，可以将解码速度分成各层的贡献，从而可以独立调节。我们根据下游任务的理论性能作为各个层速率的函数推导了理论界限，并在大规模实验中验证了我们的理论发现，这为从事者在一个给定应用程序中目标速率空间提供了指导。

分层变分自编码器中潜变量之间的交易信息