Paper:
Generative networks are promising models for specifying visual transformations. Unfortunately, certification of generative models is challenging as one needs to capture sufficient non-convexity so to produce precise bounds on the output. Existing verification methods either fail to scale to generative networks or do not capture enough non-convexity. In this work, we present a new verifier, called APPROXLINE, that can certify non-trivial properties of generative networks. APPROXLINE performs both deterministic and probabilistic abstract interpretation and captures infinite sets of outputs of generative networks. We show that APPROXLINE can verify interesting interpolations in the network's latent space.

Review:
summary:
The paper proposes a method to efficiently verify that generative models are consistent with respect to some known (latent) attribute. The authors defines attribute consistency by 1) mapping pairs of input (x1, x2) with matching attribute to a latent space using an encoder n_E(x) and 2) measuring how correctly an auxiliary classifier will classify the known attribute using (decoded) linear interpolations between the two latent encodings. Importantly, the proposed method gives guaranteed bounds on this consistency score, as opposed to simply evaluating the classifier on a fixed set uniformly sampled points between x1 and x2. In experiments the authors use their method to test for attribute independence as well as consistency under left-right flipping of an image using two different autoencoder models (VAE and CycleAE) obtaining tighter bounds on the ‘attribute consistency’ score than competing methods.  
Decision & supporting arguments:
Conceptually I found the paper very appealing, and it tackles an important problem in generative modelling. However I have some concerns with respect to the paper in its current state:
1) It is not clear to me why the attribute consistency score, a key component in the paper, is a good measure of consistency in generative models. Notably, I miss motivation for why linear interpolations between encoded inputs should necessarily keep the attribute stable.
2) Although I found the experiments interesting, I did not find the experimental section completely comprehensive. There is no discussion or experiments probing the dependency on the quality of the auxiliary classifier or the encoder/decoder model used. 
3) I did not find the description of the proposed method to be reasonably self-contained. Especially section 3 which describes the proposed method is challenging to follow. The background material in section 2 reads very much like a set of definitions. Since ICLR has a quite broad audience, I think the paper should be written in a more pedagogical way, with for instance clarifying examples. An example of a sentence that is incredibly hard to parse is on page 4, describing domain lifting: “Any deterministic abstract domain can be directly interpreted as a probabilistic abstract domain, where the concretization of an element is given as the set of probability measures whose support is a subset of the set produced by the deterministic concretization.” I think making this paper more pedagogical requires major rewriting.
Due to the above reasons I currently score the paper as a ‘weak reject’.
Further detailed questions/comments:
Consistency Score
Q1: What is the motivation behind the definition of the consistency attribute score. Especially, why is an attribute considered consistent if it is stable to linear interpolations in the latent space? 
Experiment Results:
Q2.1: Did you perform any experiments on how the L1 score of the auxiliary classifier affects the consistency score? I would also like to see some quantitative numbers on the auxiliary classifier.
Q2.2: Why is the L1 score used for training the classifier instead of bernoulli which seems more natural for binary attributes?
Q2.3: Similarly, I would like to see some numbers on the quality of the encoder/decodes. Simply inspecting the interpolations in figure 3) the reconstructions seem quite blurry, likely due to the relatively small models used. Is it prohibitively expensive to run the proposed method on bigger models (e.g. ResNet based encoder/decoders or Unet-style models)?
Q2.4: I believe it would be more informative to show the actual confidence intervals in figure 2b) instead of only the width of the confidence intervals?
Readability:
Q3: I found it quite challenging to understand how the proposed is implemented in practice - My suggestion is that the authors add a pseudo-code / algorithm to section 3 clarifying exactly how the bounds reported in the experimental section are calculated.