We thank the reviewers for their appreciative and thoughtful feedback. Reviewer 1. "However, the authors fail to bring the result to their impact of the current state OT, or any novel stochastic optimization algorithm designed to compute it faster. We will further emphasize these aspects. " A measure with 0 mean. Reviewer 2. "If the paper could show the formula for that case [TV] that would be Figure 1: Large dimensions need more samples to approximate the moments of the unbalanced optimal transport plan. Reviewer 3. ""Figure 1 illustrates the convergence"... the convergence of what?" "Figure 2 is also difficult to understand.

We will highlight where future work can build upon these findings.

We thank R1 for their comments and will emphasize the broader implications of our work on model explainability. R2 asked to contrast using (i) influence functions to measure the importance of training points with (ii) existing These papers address a different problem setting from ours and their methods are correspondingly distinct. Despite their differences, these methods could be complementary, as R2 suggested. We will include this discussion and we thank R2 for pointing it out. R3 asked if our empirical findings hold for non-convex models.

Rivalry (SR), is interesting and novel. We will fix all writing issues and revise the title and notation. Such "local optima" are, e.g., low-entropy We will add the results to the Appendix. Note that local optima hinder learning even with "good" Sample complexity We will plot results in terms of sampled timesteps rather than episodes. F ormal analysis Our work contributes an extensive empirical validation of SR, we leave formal analysis for future work.

We thank all reviewers for their thoughtful feedback, which aided us in sharpening the presentation of our results. 's questions on bounds, we will present them more explicitly in the paper, as briefly described here. We refer R1 to corollary 2.1 Combining this upper bound with the lower bound above (right term in the max), Th2 is also tight w.r.t. 's questions: our contribution focuses solely on expressiveness aspects which draw the boundaries Note that the experiments in fig.1 We are glad for R2's implementation, but since we do not know the experiment details it is hard to Indeed Kaplan et al. employ hyper-parameters tunings (LR, initializations, batch size, etc) as

V AE references in our updated literature review, and welcome further suggestions.

We thank the reviewers for the thoughtful feedback in these difficult times caused by the global COVID-19 pandemic. QM9 is used for training, the model must be based on LCAO, and QDF achieved high extrapolation performance. We emphasize that even this LDA-like HK map achieved high extrapolation performance. We will address this in future work. Of course, QDF can be proposed without a comparison to GCN.

We thank reviewers for their thoughtful feedback. We outperform all the reviewers' additional references that "One model to learn them all" is We will add all mentioned references but we stress that they do not hurt our novelty claim nor our results. MIL-NCE by 2% in both UCF and HMDB, while enabling a task (ESC-50) that would not be possible with MIL-NCE. We agree that our novelty does not lie in the loss which is indeed not novel. We will clarify the impact of the deflation contribution in the paper.

We thank the reviewers for the thoughtful feedback in these difficult times caused by the global COVID-19 pandemic. QM9 is used for training, the model must be based on LCAO, and QDF achieved high extrapolation performance. We emphasize that even this LDA-like HK map achieved high extrapolation performance. We will address this in future work. Of course, QDF can be proposed without a comparison to GCN.

We thank reviewers for their thoughtful feedback. We outperform all the reviewers' additional references that "One model to learn them all" is We will add all mentioned references but we stress that they do not hurt our novelty claim nor our results. MIL-NCE by 2% in both UCF and HMDB, while enabling a task (ESC-50) that would not be possible with MIL-NCE. We agree that our novelty does not lie in the loss which is indeed not novel. We will clarify the impact of the deflation contribution in the paper.