All reviewers found this work interesting and addressing an important issue in GAN training. The authors did a great job in presenting their analyses and experiments. Please take the reviewers' comments into account in your next revision (particularly some presentation advices). The authors are encouraged to cite the following work for a similar "non-leaking" DA: https://arxiv.org/abs/2006.05338 We did not bring this out during discussion nor used this for or against the authors.)

Weaknesses: My central concern for this paper is the misalignment between the motivation and methodology. As motivation, the authors argue that self-supervised CV and **NLP** "algorithms are not effective for tabular data." The proposed model, though, is effectively the binary masked language model whose variants pervade self-supervised NLP research (e.g. Granted, instead of masking words, the proposed models are masking tabular values, but this is performing a very similar pretext task. In fact, there is concurrent work that learns tabular representations using a BERT model [1].

This paper proposes a new reconstruction loss for unsupervised training of representations. This loss extends auto-encoders via a pretext task that uses the marginal distribution of features. The reviewers were unanimous in their decision to accept this paper.

This is not obvious since recent work has applied Hamiltonian/Lagrangian to general latent spaces as opposed to rigid body systems.

This paper makes it possible to learn Lagrangian dynamics from images and use them for energy-based control. This represents an important and significant advance for this fledgling new research subfield of physics-aware prediction, which might very well go on to prove important and significant in the coming years. I believe the reviewers are all in agreement on this point. However, by entering this new territory for physics-aware prediction, this paper has also exposed itself to interest from a broader community of readers and NeurIPS attendees who are familiar with the progress in image-based *intuitive physics* modeling and control methods over the last 5 years or so (R2 and R4 point to some such approaches). A lot of the difficulty in arriving at a reviewer consensus for this paper can be put down to the fact that its positioning is somewhat myopic and ignores this broader context, perhaps because the authors themselves might not be familiar with these approaches.

The paper discusses how to solve semi-supervised learning with multi-layer graphs. For single-layer graphs, this is achieved by label regression regularized by Laplacian matrix. For multi-layer, the paper argues that it should use a power mean Laplacian instead of the plain additive sum of Laplacians in each layer. This generalizes prior work including using the harmonic means. Some theoretical discussions follow under the assumptions from Multilayer Stochastic Block Model (MSBM), showing that specificity and robustness trade-offs can be achieved by adjusting the power parameter.

This paper makes a contribution toward the theory of semi-supervised learning for graph classification, as well as an efficient algorithm for computing the proposed classifier. This is an interesting problem and the reviewers agree the contribution is at least incremental. I suggest the authors carefully revise the paper to address reviewer concerns to get the maximum impact.

It seems trivial to extend the Triplet Mutual Information [1] and its code [2]. The contribution of the proposed method is not clear. Please explain the difference between your work and [1] about Triplet Mutual Information. For the comparison, how were the parameters of other methods tuned? 4. Deformable template matching is an existing technology. Please explain the difference between your work and [3, 4] separately.

The reviewers found the usage of the deformable templates here interesting and this work will be useful to a large part of the NeurIPS community.

Weaknesses: The paper has many weak points unfortunately. They are presented below as separate categories. Intro/Motivation: The paper focuses too much on "not using momentum encoder", "not using memory bank". All these are largely irrelevant points. Firstly, until one shows one gets no benefit from momentum encoder, it is best not to claim that "not having momentum" is a contribution / a positive aspect of the model.