Paper:
We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on several well-known datasets, including M3, M4 and TOURISM competition datasets containing time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS for all the datasets, improving forecast accuracy by 11% over a statistical benchmark and by 3% over last year's winner of the M4 competition, a domain-adjusted hand-crafted hybrid between neural network and statistical time series models. The first configuration of our model does not employ any time-series-specific components and its performance on heterogeneous datasets strongly suggests that, contrarily to received wisdom, deep learning primitives such as residual blocks are by themselves sufficient to solve a wide range of forecasting problems. Finally, we demonstrate how the proposed architecture can be augmented to provide outputs that are interpretable without considerable loss in accuracy.

Review:
This goal of this paper is to present a strong empirical result showing that a "pure" machine learning based method can outperform all known methods on some of the most challenging time series forecasting benchmarks (TOURISM, M3 and especially M4). Since I am not from the field of forecasting, I can not be sure of this, but from my understanding these benchmark datasets are indeed challenging and the cited references back up the claims of the paper related to these datasets being important in the field. 
On the most challenging dataset (M4), the best known performing method combines RNNs with a traditional smoothing algorithm. The model proposed in this paper outperforms it without being combined with any classical approach, though it does utilize ensembling.
The experimental setup is sound in my opinion, and the result appears to be of high potential significance.
However, despite trying to go through Section 3 multiple times, the exact model architecture is not clear to me. Due to this reason, my current decision is a weak rejection since the model is a central contribution of the paper. I will be happy to increase my score if the authors can make the model description crystal clear.
Even though my expertise is deep neural network architectures, I find it hard to follow the descriptions in Sec. 3. I faced the most difficulty understanding section 3.1, which obviously made the rest of subsections even harder to follow. Here are my main points of confusion:
- One big issue is that the paper uses an illustration (Fig. 1) to explain the architecture instead of equations, but then uses symbols in the main text that do not appear on Fig. 1 at all such as g_theta. Is the "FC Stack (4 layers)" g_theta? 
- Where are (uppercase) phi functions? I could infer that these are the "FC" blocks but they should be labeled.
- The Figure has the symbols g^b_theta and g^f_theta that do not appear in the text description. What exactly do they do? And is the theta that parameterizes each of them the same theta that parameterizes g_theta? How is this possible if g_theta is the "FC Stack (4 layers)"?
- The description in second and third paragraph of Section 3.1 is very confusing and unclear. It should be replaced or augmented with equations using clearly defined symbols that match Figure 1.
- More confusion stems from the use of the term "parameters" in (I believe) a different context than is used in neural networks, where "parameters" refers to connection weights. But here parameters are outputs of some functions, so either they are not connection weights or this is a fast-weight style architecture where outputs are weights [1], in which this should be made clear.
- Design of the doubly residual architecture in Section 3.2 makes sense to me at a high level, but I feel it is still very hard to clearly understand and implement it. Again, use of equations to clearly define the computation would be very helpful.
[1] Schmidhuber, Jürgen. "Learning to control fast-weight memories: An alternative to dynamic recurrent networks." Neural Computation 4.1 (1992): 131-139.
--- Update after rebuttal ---
I am happy to see the paper greatly improved by the authors in their updates. My concerns related to the presentation of the model have been addressed, and I find the architecture much easier to understand. I also appreciate the detailed supplementary material that is likely to help readers interested in the area. Related to the areas I work in, I noticed the following missing references:
Densenets: Lang, K.J. and Witbrock, M.J., 1988, June. Learning to tell two spirals apart. In Proceedings of the 1988 connectionist models summer school (No. 1989, pp. 52-59).
Metalearning: Schmidhuber, J., 1987. Evolutionary principles in self-referential learning, or on learning how to learn: the meta-meta-... hook (Doctoral dissertation, Technische Universität München).
While improving papers is generally the objective of the rebuttal phase, I suggest that the authors to not take this as an opportunity to submit unpolished papers in the first phase. That said, I have increased my rating to reflect my satisfaction with the current version of the paper.