"we plan to derive an extension of this work to PU learning in which the proportion of positives in the dataset will

Thank you very much for the thorough reviews. We respond to each comments below. Time-centric refers to the optimal strategy. Then why try the other strategy? It seems that we used a misleading phrasing here and we owe an apology.

This is indeed an omission, but it is not terribly complicated and we will add it to the paper.

In this paper, authors study the graph convolution networks. Especially, the authors propose a new filter to approximate the true Fourier transformation, in the same spirit of Chebyshev filters and others. The proposed filter is based on the ARMA filter of Eq. (6). This equation is computationally heavy, so the proposed feedback-looped filter approximates the equation as in Eq.(7). Then the actual implementation of Graph Neural Network is formulated as in Eq.(12).

This work initially received mixed reviews, but after the author feedback cleared up a misunderstanding, most reviewers are now recommending acceptance. Nevertheless, I think R2 (who has not raised their score) has some valid concerns, which I want to account for in my decision. I have decided to recommend acceptance. The experimental section of this work is fairly comprehensive, and adequately demonstrates that the proposed architecture is effective. However, it is important to point out that the majority of experiments was conducted using ground-truth mel-spectrogram conditioning, which does not match the usual practical setting of TTS systems, where the spectrograms are themselves generated by a model (and thus imperfect).

After feedback and reviewer discussion, this paper received final ratings of 6, 7 and 7. Although the novelty of the proposed model is relatively minor in the context of previous work proposing Adaptive Computation Time (Graves 2016), the reviewers were impressed by the empirical performance and praised the detailed ablation studies (including the additional experiments with single-headed attention in the author feedback, which was important in reaching the final consensus view of reviewers to accept this paper). We encourage the authors to follow the suggestion of R1 (cut down space devoted to standard captioning components in Secs 3.2.1,

The abstract claims to remove the small step size requirements of prior work. However, to attain a good convergence rate (Corollary 1) the main theorems (Theorems 1 and 2) need a small step size, similar to previous works. In fact Safran and Shamir (2020) show that convergence is only possible for step size O(1/n) . Please modify the claims accordingly. However, the dependence on \mu has worsened.

Weaknesses: (W1): As such the high-level outline of the proof strategy follows previous procedures for drift analysis in (Yu et al. 2017) and MDP analysis in (Neu et al. 2012 and Rosenberg et al. 2019). Lemma B.2 is very similar to Lemma 4 in Neu et al. 2012 and Lemma B.2 in Rosenberg et al. 2019. Lemma 5.2 mirrors Lemma 8 in Yu et al. 2017. Technical lemmas for stochastic analysis are also from the previous paper: (Lemma B.6 and B.7 are Lemma 5 and 9 in Yu et al. 2017). The main lemma, Lemma 5.3, has the same goal as Lemma 7 in Yu et al. 2017, which is to show Q_t satisfies the drift condition stated in Lemma 5 in Yu et al. 2017. Lemma 5.6 is also exact as Lemma 3 in Yu et al. 2017.

All of the reviewers found the proposed technique original and the theory interesting. The reviewers initially had concerns regarding the structure of the paper, relevance of some of the experiments, and comparison with perceptual loss. These concerns are alleviated given the author feedback. Assuming that the authors will integrate the author feedback into the paper and incorporate all of reviewers' feedback, I recommend acceptance as a poster.

The paper introduces a new family of randomized Newton methods, based on a prototypical Hessian sketching scheme to reduce the memory and arithmetic costs. Clearly, the idea of using a randomized sketch for the Hessian is not new. However, the paper extends the known results in a variety of ways: The proposed method gets linear convergence rate 1) under the relative smoothness and the relative convexity assumptions (and the method is still scale-invariant). These results also include the known results for the Newton method as a special case. The related work is adequately cited, the similar approaches from the existing literature and their weaknesses are discussed in a short but concise discussion in the paper.