The paper introduces a new perspective for explaining instability in GANs training by analyzing the continuous dynamics of the training algorithm. They first show that these dynamics should converge in the vicinity of the Nash equilibrium and then make the hypothesis that instability is due to the discretization of this dynamics. They show that using higher order ODE time integrators for solving the dynamics help stabilizing the training. The paper is clear, the reviewers agree that this brings a new perspective for analyzing and training GANs and that this is a significant contribution to this topic. The theoretical findings are backed up by a nice empirical evaluation and analysis.

Summary: The paper proposes to use GANs in the LLP setting, where only the proportions are known per bag of covariates (say images), the goal is to create a classifier on the covariate level. Similar to the previous work in semi-supervised learning with GANs, the discriminator in this case classifies between the current classes and a new class for fake samples. Here, the loss function like the normal GANs uses two term, one for the supervision for the matching of the label proportion, the other for the adversarial training. The authors then proceed to analyse this loss function. Originality: I have not previously seen the use of GANs in the LLP setting or the use of the lower bound approximation that allows for SGD on individuals.

All three reviewers agreed that the idea of using adversarial learning for learning from label proportions is novel and interesting. For the final version, we would recommend the proposed method to be validated on: 1) structured and non-random bag assignment setting (e.g.

The authors prove that the probabilities they obatin are equivalent to the probabilities yielded by the Random Walker algorithm. The authors state that this result has been shown in the original Random Walker work, yet is little known, and their proof is different and more self-contained, not relying on potential theory. Excitingly, their way of proof yields a novel interpretation of the Random Walker / Probabilistic Watershed probabilities in terms of the triangle equation on effective resistances between graph nodes. Last but not least the authors relate their theory to the Power Watershed, again yielding an exciting new insight, namely that for parameters beta 2 and alpha towards infinity, the latter computes marginals over all seed-separating *maximum* spanning forests (i.e.

Brings new insights to old algorithms accept.

Overall I think this paper raises an interesting perspective to understanding adversarial generative models. I think this paper has some value by raising the question and offering some interesting experimental results. The theory is quite standard, the authors first cite a relationship between differential privacy and RO stability, then cite that RO stability bounds the generalization gap. The short coming is that the theory only analyzes the discriminator, which do not seem much different compared to previous work analyzing classifiers. It would be much more interesting and novel to see an analysis of the joint learning process of generator and discriminator.

All the reviewers liked the link between privacy and generative adversarial networks. The authors could also successfully answer the main concerns of the reviewers in their rebuttal.

Is there any comparison with the baselines in terms of the number of network parameters? What is the performance of baselines with the same number of parameters as GAM? This seems to be a fairer comparison.

This paper proposed a novel graph learning method for graph-based semi-supervised learning. Besides the model of the classifier (the classification model in the paper), another model of the graph is considered (the agreement model in the paper), and the contribution to the loss of each edge is determined by the model of the graph. Although there are still concerns about the novelty in the end, we all agree that the proposed method is simple, well-explained and can still achieve good performance. This may have impacts to practitioners using semi-supervised learning in their projects, and as a result, I recommend an acceptance. Please survey this direction and include your survey in the final version.

Summary and Contributions: This paper introduces a new class of algorithms for local graph clustering, based on Lp objectives (for p 2) rather than the standard L2 (used in reference works like Anderson-Chang-Lang), or L_infinity (which corresponds to minimum cut). The authors make a clear point that the p 2 regime corresponds to the primal objective which optimizes in the space of flows, whose dual problem corresponds to optimizing an Lq norm (1 q 2) in the space of cuts. For the purpose of this paper, they stick to the cut problem, since it is more naturally connected to the algorithm described here. Essentially, the presented algorithm is a generalization of ACL for Lq norms. It performs a sequence of steps, in each step, it picks a node with excess residual and performs "push" operation.