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.

可变自动编码器(VAE)最初是受激励的(Kingma&Well， 2014)作为概率生成模型，其中执行近似 贝叶斯推理。$\beta$-VAE(Higgins等人，2017)的提议破裂 这种解释将VAE推广到了更广泛的应用领域 生成性建模(例如，表示学习、聚类或有损数据 压缩)通过引入一个目标函数，允许实践者 在潜在的信息内容(比特率)之间进行权衡 重建数据的表示和失真(Alemi等人，2018年)。 在本文中，我们在以下背景下重新考虑这一速率/失真权衡 层次VAE，即具有一层以上潜变量的VAE。我们 确定一类一般的推理模型，可以对其进行拆分 转化为来自每一层的贡献，然后可以独立调整。我们 将下游任务的性能作为函数导出理论界限 并验证我们的理论发现 大规模的实验。我们的结果为实践者提供了指导 速率空间中的哪个区域是给定应用的目标。