text: This paper presents an alternative approach to constructing variational lower bounds on data log likelihood in deep, directed generative models with latent variables. Specifically, the authors propose using approximate posteriors shared across groups of examples, rather than posteriors which treat examples independently. The group-wise posteriors allow amortization of the information cost KL(group posterior || prior) across all examples in the group, which the authors liken to the "KL annealing" tricks that are sometimes used to avoid posterior collapse when training models with strong decoders p(x|z) using current techniques for approximate variational inference in deep nets. The presentation of the core idea is solid, though it did take two read-throughs before the equations really clicked for me. I think the paper could be improved by spending more time on a detailed description of the model for the Omniglot experiments (as illustrated in Figure 3). E.g., explicitly describing how group-wise and per-example posteriors are composed in this model, using Equations and pseudo-code for the main training loop, would have saved me some time. For readers less familiar with amortized variational inference in deep nets, the benefit would be larger. I appreciate that the authors developed extensions of the core method to more complex group structures, though I didn't find the related experiments particularly convincing. Overall, I like this paper and think the underlying group-wise posterior construction trick is worth exploring further. Of course, the elephant in the room is how to determine the groups across which the posteriors can be shared and their information costs amortized.