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.

翻译：变分自编码器最初由Kingma与Welling（2014）提出时，被解释为一种执行近似贝叶斯推理的概率生成模型。β-VAE（Higgins等，2017）的提出打破了这一解释，通过引入允许实践者在隐表示的信息内容（"比特率"）与重构数据失真之间进行权衡的目标函数（Alemi等，2018），将VAE推广至生成建模以外的应用领域（如表征学习、聚类或有损数据压缩）。本文在分层VAE（即具有多层隐变量的VAE）背景下重新审视这种率/失真权衡。我们识别出一类通用的推理模型，其可将信息率分解为各层的独立贡献，从而实现对各层的独立调节。我们推导下游任务性能作为各层信息率函数的理论界，并通过大规模实验验证理论发现。研究结果为实践者针对特定应用场景选择信息率空间中的最优区域提供了指导。