Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: Authors address the problem of temporal high-order interactions where more than two entities -- such as customers, commodities, and merchants -- correspond to one event. To tack the temporal drift of underlying node, authors propose the dynamic embeddings that follows a diffusion-based ODE model. Authors show that the proposed DMITRI model can capture the temporal dynamic well through both synthetic and real-world datasets. 
strength_and_weaknesses: * Strengths
- ODE is a reasonable way of representing the dynamics of embeddings.
- Authors use both synthetic and real-world datasets and show the proposed method can track the temporal patterns well.
- Empirical evaluations show that the proposed method outperforms the other baseline models.

* Weaknesses
- The manuscript can be further improved to present better. Crucial information -- such as the experimental task setup -- or explanation is often not very clear.
- The authors verify the end-to-end predictive power, but it would be great if the authors could analyze the insights from the dynamics of embeddings.
- For the dynamic embedding setting, it would be great to have some forecasting tasks for evaluations.
- It would be great if the authors evaluate on the other kinds of data, where the actual events are sparse like social interaction datasets. The provided datasets have the characteristics that graphs are generated from different forms of dataset, not naturally given such as social interactions or citations.
clarity,_quality,_novelty_and_reproducibility: ODE-based approach has been studied, but the authors extend it to multi-way interactions. Even though it is an interesting extension, the proposed method does not have a significant change beyond the related work.

Manuscript needs to be presented better. For example, ODE explanation has lots of repeated explanation, which distracts the main model description. 
summary_of_the_review: While the proposed method is incremental to existing work, authors translate the states over multi-dimensional space into a graph among multi-entities, apply the extended ODE, and show the good performance. The proposed method is worth being discussed in the community.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The authors propose the DMITRI framework to generate dynamic embeddings for multi-entity interactions with timestamps. A multi-entity interaction involves potentially many types of entities, e.g. traffic type, severity, latitude, and longitude, and consists of a timestamped observation for those entities, such as the number of traffic accidents under those conditions at different times. The DMITRI framework uses an ordinary differential equation (ODE) model to learn embedding trajectories for each entity of each type. The authors consider both a diffusion process across multi-partite graphs, representing interactions between different types, and a reaction process for the individual entities. They demonstrate improvements in predictive accuracy on 3 real datasets compared to a large number of existing methods.
strength_and_weaknesses: Strengths:
- Proposed DMITRI framework generates dynamic embeddings for entities in continuous, rather than discrete time, unlike most existing dynamic tensor factorization approaches.
- Use of neural ODEs to generate embeddings for multi-entity interactions appears to be novel.
- Comparisons to a wide range of competing methods yields impressive predictive accuracy on 3 real datasets.

Weaknesses:
- Minimal interpretations of the learned embedding trajectories. Beyond predicted observations, an additional output of DMITRI is the continuous-time embedding trajectories. The authors don't provide many interpretations of the trajectories, with only an example in Section 6.3.
- No empirical results on computation time. The authors state that their approach is limited to a small number of entities due to the multi-partite graph approach for the diffusion process. I would have liked to see some experiments (perhaps in the supplementary material) comparing wall clock time to competing methods.

Question:
1. On page 4, you state that there are $K(K+1)/2$ adjacency matrices $\mathbf{W}^{k,k'}$. Why $K(K+1)/2$ rather than $K(K-1)$? It appears that we can't have edges within the same type $k$, so no diagonal, and that there is no symmetry between $\mathbf{W}^{k,k'}$ and $\mathbf{W}^{k',k}$.

Typo:
- Page 6, second last paragraph: Unifrom\[0,5\] -> Uniform\[0,5\]
clarity,_quality,_novelty_and_reproducibility: - Clarity: High. I did have any problems understanding the paper.
- Quality: High. The proposed DMITRI framework appears technically sound along with the experiments.
- Novelty: High. I have not previously seen neural ODEs used to model multi-entity interactions. Additionally, continuous-time models in this area are rare yet potentially more powerful than discrete-time models.
- Reproducibility: Low. No code is provided, and the experiments use sampled subsets of larger data sets, e.g. 10K interactions from the Server Room data. Without knowing how the 10K interactions were selected, it would be difficult to reproduce results.
summary_of_the_review: I find this to be a novel and interesting contribution with strong empirical results for prediction accuracy, but also a few weaknesses in the experimental evaluation that prevent me from strongly recommending acceptance.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This paper targets modeling the temporal high-order interactions via neural diffusion-reaction processes. 
It proposes a Dynamical eMbedIngs of TempoRal hIgh-order interactions (DMITRI) framework. 
A multi-partite graph is built to encode the correlation between the entities. 
A graph diffusion process is constructed to co-evolve the embedding trajectories of the correlated entities and a neural network is used to capture the reaction process for each individual entity. 
strength_and_weaknesses: Strengths

(1) This paper provides sufficient details in both theoretical and experimental sections. Although the authors didn’t release their code, I think it’s not hard to implement their work.

(2) The experimental results seem quite encouraging compared with the current baselines.

Weaknesses

(1) I suggest the authors reorganize this paper carefully. The author should emphasize their contributions concisely and accurately. In the current version, both the abstract and the introduction are filled with too many details and make me hard to capture what are the key contributions that the authors would like to present. It would be even better if the author could add a figure to demonstrate the architecture of the proposed framework. 

(2) Could the authors discuss the correlations and differences with the work of [1]? It seems to have quite similar ideas with this paper, both the motivations and the methodologies. The authors should at least take it as a baseline. 

[1] Li, Shibo, Robert Kirby, and Shandian Zhe. "Decomposing Temporal High-Order Interactions via Latent ODEs." In International Conference on Machine Learning, pp. 12797-12812. PMLR, 2022.

(3) The authors mention in the conclusion the proposed method is limited to a small number of entities. I suggest the authors provide some discussions about the algorithm complexity. Although the authors plan to develop graph cut algorithms to improve the scalability, I wonder how effective this algorithm can be.

(4) Typos: The last line of page 1, “these” should be “this”.
clarity,_quality,_novelty_and_reproducibility: The authors provide quite enough detail about their work. It would be better if the abstract and the introduction can be refined.
Considering the work of [1], I’m not sure about the novelty of this paper.
summary_of_the_review: Considering [1], I’m not sure about the theoretical contributions and the results are SOTA.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This paper proposes a neural diffusion-reaction process model, which can take into account the timestamps and model the temporal embedding of participants behind high-order interactions, compared with existing related tensor factorization methods.

- To that end, they build the model upon the ODE framework that can handle continuously observed timestamps.
- They build a multi-partite graph on observed interactions, and learn a graph diffusion process to allow the dynamic embeddings of correlated participants to co-evolve over time.
- A separate neural net is used to construct a reaction process to capture individual difference.
- The final interaction result is captured using a Gaussian observation model, of which the mean is a function of the dynamic embedding.
strength_and_weaknesses: Strength :

The paper targets an interesting question, and the method looks solid.

Weaknesses :

To me, the technical part of Sec. 3 is not that easy to digest. For instance, it is necessary to thoroughly explain why to construct the diffusion and reaction processes in this way, for someone else to take it up.

For the results in Table 1, it is entirely unclear that what does the RMSE error reflect? On pp.9, you only mention use remaining for test. But, I cannot find what are you predicting in the test set!
clarity,_quality,_novelty_and_reproducibility: Clarity: 
The technical parts in Sec.3 about the diffusion reaction processes, are not that easy to digest, to me.
THe final experimental protocol is not entirely clear.

Quality: 
Overall, the method looks solid.

Novelty:
The studied method seems to be novel in its motivated context.
summary_of_the_review: This paper develops a new model to capture timestamps and to model dynamic embedding of entities behind high-order interaction time series, which cannot be well captured using existing tensor factorization solutions.

To me, the method looks interesting and solid, but somewhat novel in the motivated context.

In addition, the final experiment is not entirely clear to me.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: In this paper, the authors considered a time-varying tensor decomposition scenario and proposed an ODE-based method called DMITRI to capture the dynamics of latent embeddings. The proposed method considers the high-order interactions among different entities over time and leverages a diffusion-reaction process to model the evolution of the embeddings. Experiments demonstrate the usefulness of the proposed method.

Strengths:
(1) The proposed method is reasonable, and its derivation is detailed and clear.

Weaknesses:
(1) The novelty of the proposed method is limited. Many temporal tensor factorization methods have been proposed. Additionally, in the continuous-time cases, point process (PP)-based factorization methods should also be discussed and considered as baselines. Actually, for recent years, there are some ODE/SDE-based sequential models embedding evolutionary entities. The differences and the connections between them and the proposed method are not clarified. 
(2) The experiments are insufficient. As aforementioned, some PP-based methods and SDE-based sequential models should be considered.
justification_for_why_not_higher_score: See the weaknesses discussed above.
Decision: Reject