Dear Reviewers, we thank you for taking the time to provide valuable feedback. Below we address the main issues raised. Its performance depends on our ability to predict the distribution over future frames with low entropy. We will emphasize these aspects more in a revised version. RNNs to model dynamics in the latent space.

We thank all the reviewers for their insightful and encouraging comments. Per your suggestion, we will update the appendix by adding more explanations about the proof ideas. Similarly, we can extend convergence results in Theorem 4 in Appendix from FS to IFS. We expect that the approach developed in this paper will fuel this future investigation. We will update this into the revision.

We thank the reviewers for their careful consideration and constructive feedback. Below, please find our responses. Since no experimental evidence are provided... Please see our general response above. If'F' is available in closed form and the its gradients can be computed exactly.... Extension to the discrete setting: I do not understand how one would compute the multilinear extension efficiently. We will address this comment thoroughly in our revised version.

Clean and robust error on the test set under various adversarial attacks. Specifically, for example, 28. 25(47) stands for 28 .25 0 . We thank the reviewers for their constructive comments. The requested additional experiments are presented above. Gradient scattering is measured as the first-order gradient difference, i.e., The architecture of our MNIST models are the same as the ones in the challenge.

First of all, we thank the reviewers for their helpful comments and remarks. Moore-Penrose pseudo-inverse which explains why the complexity is only quadratic in K). Adaptative Neural Trees ([2]) and Deep Neural Decision Forests ([3]) are both built from decision trees. It is true that a standard regression tree with enough leaves can also approximate a smooth link function. We'll modify lines 228-230 as In that case, the distribution of x over regions is concentrated on one region.

We thank the reviewers for their helpful comments and remarks. Reviewer 3 suggests to assess'if the data augmentation scheme is actually helpful for a range of tasks' Also, when compared with other methods, we achieve better performance. Reviewer 1. Thank you for spotting the typos on lines 11, 58, 88 and Table 1. We will update the paper accordingly. 'Question: are the F1 scores here (T able 2) stratified at all by "extreme" vs not?' 'The proposed method regularizes fixed BERT embeddings to be heavy tailed, however most SOTA methods fine-tune Reviewer 3. Thank you for spotting the typos in Table 1.