Thank you for your response and help towards improving the paper.
["might be better to claim it as "training generative models with constraints""]
Thank you for your suggestion. We will make sure to clarify it in the paper.
["considering training-time approaches only, there are still a bunch of work closely related…, I even feel the proposed approach in this paper can be seen as a special case of [1]. "]
Thank you for pointing out this related work. We are happy to discuss it in our related works section. It is unclear, however, how applicable it is to our setting. The approach in [1] rests upon the framework of posterior regularization [4], which requires that we design feature functions encoding the constraint. Such feature functions need to *factorize* over the tokens of the sentence (see section 2.5 in [4]). That might be doable for very simple constraints such as those considered in [1], but not in general.
Setting aside that issue, the approach in [1] minimizes an extra KL-divergence between the autoregressive distribution and a log-linear variational distribution. For the constraints considered, computing such KL-divergence is intractable. Even approximating the KL-divergence is hard, due to the computational hardness of sampling the constraint ([1] sample from the autoregressive distribution and threshold using the feature function, which does not sample from the correct distribution). There is also no notion of perturbations; these are simply samples from the distribution. We would also argue that log-linear models defined by a set of linear constraints as variational distributions have been in use since posterior regularization was first introduced. [1] is simply an instantiation of such a framework. In our case, however, our distributional approximation is novel: it is a first-order approximation of the true autoregressive distribution. Consequently, we are **exactly computing the probability of the constraint being satisfied w.r.t. our proposed approximate distribution**.
["Missing discussion and citation"]
We are happy to cite any and all related work. We were of course aware of neurologic and other inference time approaches, but felt they might be orthogonal to approach proposed here. Having discussed it with the reviewers, however, we will happily include a discussion with such works. Moreover, our work tends to focus on developing methodology for *general* constraints. And despite our best efforts, due to the massive number of works, it can be easy to miss methods geared towards very specific tasks from other communities. We greatly appreciate the reviewer bringing these to our attention.
["Claims"]
Having said all of the above, fundamentally, the issue at hand seems to be the reviewer's disagreement with our overarching claim. We are happy to relax our claim to something along the lines of "Unlike previous works that are only able to approximately handle simple constraints under relaxations of autoregressive distributions, our approach injects non-trivial constraints, that don't easily factorize, as part of the training process, computing the probability of the constraint exactly w.r.t an approximate distribution".
Thanks again for engaging with us, and we hope this convinces the reviewer to push their scores towards an accept.
[References]:
[4] Posterior Regularization for Structured Latent Variable Models (JMLR 2010)