Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper proposes a new time-aware GNN networks called Zigzag Filtration Curve based Supra-Hodge Convolution Networks(ZFC-SHCN). Specifically, the networks composes 1) the simplicial neural networks with an efficient zigzag persistence curve and 2) a new temporal multiplex graph representation module. In practice, the experimental results on several synthetic and real world datasets demonstrate the effectiveness and efficiency of the proposed ZFC-SHCN.
strengths_and_weaknesses: Strengths

+ The paper is well-written and well-organized.
+ The idea, amplifying the power of SNNs with a time-conditioned topological knowledge representation in a form of zigzag persistence, is interesting and novel. 
+ The experimental results show ZFC-SHCN outperforms other baselines.
+ Codes are provided.

Weaknesses

+ It worth noting that the gains from ZFC convolution and Supra-Hodge convolution in Tabel 4 are not significant as expected, It would be fairer if the authors could provide more comparison experiments. E.g.  Replacing ZFC with zigzag persistence image
(ZPI) to show the gain from ZFC, replacing Supra-Hodge convolution with $GCN_{temp}$ to show the gain from Supra-Hodge convolution, etc. Or theoretical analysis of the differences is given.
questions: Same as weaknesses.
limitations: N/A
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper addresses the problem of  capturing information other than pairwise relations in GNN. A time-conditioned topological knowledge representation is proposed, and related theoretical properties are presented. The topic is very interesting and influential.
strengths_and_weaknesses: Strengths
- good idea.
- there is theoretical stability guarantees.

Weaknesses
- the complexity should be discussed.
- it is not very convincing that the expression is enough for various of tasks.
questions: The complexity should be discussed and some other type of tasks should be done.
limitations: No suggestions.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: In this paper, the authors propose a method for predicting time series of graphs with the addition of the concept of TDA. There is no discussion of graph construction methods here, but rather the general setting of the existence of time-varying graphs. The proposed method is basically a conventional graph convolution -recurrent neural network with an additional mechanism to consider topological information. The zigzag filtration curve and supra-Hodge convolution are used as topological information. The authors also prove the stability of ZFC and demonstrate its effectiveness in comparison to conventional methods in their experiments.
strengths_and_weaknesses: Strength
-  The authors provide a framework for time series prediction of graphs that includes topological information that has not been previously taken into account.
-  Introduced zigzag filtration as topological information
- The authors have organized the mathematical background of the algorithm before introducing the algorithm.
- The authors have tested the effectiveness of this method compared to many conventional methods from multiple perspectives on multiple data sets

Weakness
- Although the authors have compared the proposed method with conventional methods that do not include topology information, they have not examined whether the proposed method is appropriate as a method that takes topology information into account.
- There are doubts about some of the experimental setups.

Overall, the prediction of graph time series is a very important issue, including from a practical viewpoint, and it is worthwhile to have provided an effective framework for this problem with the addition of TDA-based information. Since I have some doubts, I would like to make a final decision based on the answers to the following questions.
questions: 1. The proposed method introduces zigzag filtration features and supra-Hodge convolution features in addition to the conventional graph convolution features. Although the overall framework has been evaluated, it is not clear which features have what effect on each of them. Since it is not possible to determine whether all of the elements are necessary, I wonder if a comparison with a system that excludes any of the information would make the observation possible. Are such comparisons being made?

2. Features using Zigzag filtration Creation is a natural concept, but I am sure there are other possibilities. Are there any comparisons with other methods? Of course, since the effectiveness of this system as a whole has been demonstrated, it is only a proposal as a first step, and if improvements using other TDA methods is a future issue, that is fine.

3. The experimental results, especially in Table 3, show that the proposed method seems to create different models for different evaluation indicators for a single problem. The same model should be used to compare different indicators in the evaluation. If you want to show that each indicator can be set appropriately, you should compare them separately.

limitations: The authors have clearly defined the application, clearly described the performance, and adequately addressed the limitation of their work.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The authors propose the Zigzag Filtration Curve based Supra-Hodge Convolution Networks (ZFC-SHCN) which is able to learn time-aware persistent topological features and simplicial geometry of graphs. The theoretical stability of the zigzag filtration curve is studied in the paper. Experiment results show that ZFC-SHCN achieves the best performance of forecasting with less computational requirements.

strengths_and_weaknesses: Strengths:
- The proposed novel framework connects the dynamical behavior of complex systems and persistence homology analysis.
- The authors claim that this paper is the first work that brings the concepts of simplicial convolution to time-aware learning.
- The experiments on varying datasets including covid case and traffic flow show the superiority of the proposed method in terms of the prediction tasks. ZFC-SHCN is also faster compared with runner-ups.

Weakness:
- I recommend adding some references in the introduction section to support the statements. 
- I suggest the authors to check these related paper of time series prediction:
https://ieeexplore.ieee.org/abstract/document/8430866
https://openreview.net/forum?id=d2TT6gK9qZn
- The writing quality of this paper needs to be improved, please see below some questions that need to be clarified in the paper main body.
- The contribution is clear as stated in the introduction section. However, the connection among/inside section 3 and 4 (and the subsections) is not very clear.
- Are the tasks to predict the further covid cases, traffic flow etc. as both time series and node attribute of graph?
- How are the graphs or the simplicial complexes constructed on each dataset? In the appendix it says the graph represents the border connection, but it is unclear about other datasets.
- How is the simplex constructed in the experiment section? Does it only consider nodes and edges, or also involve actual higher-order information like a 2-simplex, 3-simplex or more? If not, where does the higher-order information appear in the graph structure?
- Is the embedding dimension mentioned in line 281 the same as the dimension of feature of each node (d_e) or something else? Is it predefined or computed following any rules? The number here looks rather small, any reason for such a choice?
questions: Please see weakness.
limitations:  Limitations and potential negative societal impact have been addressed.
review_title: null

Meta-review: metareview: Their new ideas are highly appreciated by the authors. The authors' enthusiastic revision of the paper is also good.
It is also nice that the benefits are clear and the advantages are clearly presented both theoretically and experimentally.
confidence: Certain
Decision: Accept