Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper proposes the notion of disentangled equivariance for systems of interactive systems, as well as a framework that disentangles the effects of underlying global field from the local system dynamics that are equivariant to transformations in SE(3). They are also able to learn a neural field to predict underlying field effects. 
strength_and_weaknesses: Strengths:

1. This work proposes a novel notion of disentangled equivariance, and proposes a framework to successfully disentangle global field effects from local system interactions that are equivariant to translations and rotations.
2. They are able to predict global field effects that are latent by observing the system dynamics using neural fields.

Weaknesses:

1. The paper need more work to explain the motivation and their method. Most of the explanation for base concepts is referred to in related papers. 
2. The experimental setup is not clear. Again, an explanation of datasets and learning problem should have been provided, either in the main paper or if not, in the supplementary.
3. The relationship between the notion of approximate equivariance and disentangled equivariance is unclear from their description. In section 3.3, they mention that the difference lies in the fact that approximate equivariance tries to combine global field and local field effects. But it seems from their model description in section 3.1 that they are doing the same thing (especially from eqs. 5-7). Hence, the novelty of their notion of disentangled equivariance is unclear.
4. The experiments are also conducted on fairly limited settings (in two dimensional systems) and in scenarios where the underlying global fields remain fixed throughout the interaction. This makes it difficult to assess the impact of this work.
5. The results are also difficult to interpret and require more details about what is the ideal result and how the method compares to the baselines. For eg., in Figure 7, it is unclear what the figures represent and why the predicted and ground-truth fields look so different.

Other things that could improve the paper:

1. A more detailed description of their experimental setup, and datasets used in the supplementary would be helpful to making the method and its impact more clear.
2. Deeper explanation of the model architecture by using the supplementary material would also be helpful.
clarity,_quality,_novelty_and_reproducibility: See strength and weakness section.
summary_of_the_review: See strength and weakness section.
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The authors' response address many of my concerns and questions. I will raise the score.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This work introduces Aether, a new method that disentangles local object interactions from global field effects in interacting dynamic systems. The new approach leverages the neural field and VAE model to infer from the dynamics along. Then combining neural fields with equivariant graph networks learns dynamic systems.  A set of examples are used to demonstrate the methods compared with several baseline methods. 
strength_and_weaknesses: - Strength

1. The paper is well-written and organized so that it is easy to follow.
2. Background section provides many necessary details and information
3. The overall idea of disentangling local and global is very interesting  

- Weakness

1. The novelty is not clear to show. 
2. Lack of high-level intuition why the proposed method works better, specifically disentanglement property 

clarity,_quality,_novelty_and_reproducibility: clarity is high, except the core method 
quality is good, easy to understand
novelty is not clear, may need improvement 
reproducibility, is not sure. The domain knowledge of dynamic systems is needed and no code is provided. 

summary_of_the_review: Overall, the paper is good to show the idea with solid experiments. However, the core idea is not very clear to show. As I mentioned in the weakness, 

1. what's the core difference between aether and previous SOTA work？ 
2. what's the major contribution that makes entanglement to disentanglement? 
3. What's high-level intuition? 
4. The method is VAE-based disentanglement. Any previous related works? 
5. What's the current limitation, except the domain limitation?
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper considers the task of discovering the underlying force field of the interacting dynamical systems. In particular, this paper focus on the setting where the observed trajectories of particles are driven by the interacting forces between the particles as well as a global force field. The entanglement of global and local effects makes recently popularized equivariant networks inapplicable, since they fail to capture global information. To address this issue, this work proposes to disentangle local object interactions from external global field effects. Specifically, a neural field is used to approximate the latent field and the interactions between particles are modeled with equivariant graph networks operating in local coordinate frames. Experiments show that the proposed approach accurately discovers the underlying fields in several interesting application.
strength_and_weaknesses: Strength:

While previous works focus on the discovery of the interacting force between particles from the observable trajectory of particles, this work takes a step further by considering the existence of an underlying global force field. This generalized setting cannot be captured by the equivariant networks as they fail to capture global information. By incorporating an additional neural field, the authors design a new model, Aether, which in principle is able to automatically learn the interacting force and global force separately, which hence disentangles these two forces.

Weakness:

1. The global field is assumed to be independent of the observed objectives, but this seems to be a strong assumption, e.g. when the blackhole is considered as the source of the global field, its position and velocity are also affected by the planets around it. Therefore, this assumption may not hold, especially in a large time interval.
2. While authors do consider the setting of dynamic field, it is clear how the interacting force can be disentangled from this time-varying dynamic field. In the worst case scenario, all forces can be described by a dynamic field.
clarity,_quality,_novelty_and_reproducibility: Clarity: This paper is well-written overall. I do have a question about section 3.3. How is it related to section 3.1?

Novelty: I think this is a nice paper as it is studying the force field discovery in a more practical setting.
summary_of_the_review: This is nice paper that studies the force field discovery in a more practical setting. A question I have for the authors is that in the more interesting dynamic field setting, why can we expect the dynamic force and the interacting forces to be disentangled using this approach? Intuitively, this is not possible without further assumptions.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: Please provide a brief summary of the paper and its contributions.
The authors proposed a disentanglement approach to local object interactions from external global ﬁeld effects, which depend on absolute positions and orientations. 
The contribution of this paper is as follows: 
* They introduced the idea of entangled equivariance that intertwines global and local effects, and proposed a new architecture that disentangles equivariant local object interactions from global ﬁeld effects. 
* They introduced neural ﬁelds to discover global latent ﬁelds in interacting dynamical systems, and infer them by observing the dynamics alone. 
* They proposed an approximately equivariant graph network that extends local coordinate frame graph networks by introducing an auxiliary origin node.
* They conducted experiments on a number of ﬁeld settings, and observed that explicitly modeling ﬁelds was mandatory for effective future forecasting, while their unsupervised discovery provided model explainability.

strength_and_weaknesses: Strength: 
* The ideas of the above three contributions are interesting and may have a novelty.
* Overall, the paper was well-written and I can understand most of the ideas.
* The experimental results clearly show the superiority of the proposed approach.

Weakness:
* Although the presentation was overall clear, some points in methods and experimental results were unclear to me (described as the specific comments).

Specific comments
* About the name of the proposed method: Aether. The existence of Aether in modern physics may be denied, but what is the standpoint of the authors? I want to know the motivation and the opinion from the viewpoint of physics. 
* In section 3.3, the author said that “Finally, in practice, we integrate G-LoCS in Aether” but in the experiments I did not find the integration. Where is this?
* First sentence in Section 5.2: InD (Bock…
* Fig 6: I understand “the learned ﬁeld is a function of positions and orientations”, but how did the author define C4 in the inD experiment? I did not understand how we should see Fig 6. The definition of the orientations here and qualitative explanations may be required.
* Section 5.4: In the ablation experiments, I did not understand why the oracle simulations accumulated errors. 

clarity,_quality,_novelty_and_reproducibility: The presentation was clear in total but I found the above unclear points. The quality was also good in total because of the above contributions and strengths. The experiments may not be reproduced at this stage (they said that their source code, data, and models will be shared upon publication).
summary_of_the_review: Based on the comment above, I consider that the strength of this paper outperformed the weakness, but I had some concerns at this stage, so I cannot give a higher rating.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: This paper has received four expert reviews and was a borderline case. The paper was discussed first asynchronously over openreview and finally a meeting was held between the AC and two of the reviewers, which had initially given borderline ratings. The discussion of the paper again brought several issues to light:

- The experiments and tasks are extremely simple, and far from the SOTA.
- Generalization experiments are missing, for instance increasing the number of objects / particles between training and testing. This is important as this is one part which is captured by an equivariant model with pairwise terms in a GNN only, and the additional global field could hurt this capacity.
- It is unclear how estimating the field is done ensuring that disentangling is done during training. The problem is that a part of the model (the field) seems to have been learned from data which corresponds to the full problem, including the equivariant part. 
- There is no comparison with the SOTA on models which could solve this problem, in particular what the authors call "Approximate equivariance". The papers contains a full related work paragraph on them, but it is not clear why the proposed method cannot be compared to this body of work.

After the meeting the AC interacted with the authors regarding learning the non-equivariant (global) field from the full data only. This discussion confirmed that the authors were (1) not aware of this quite important technical problem and, had not addressed it. This confirms a major weakness of the paper, as learning the global (non-equivariant) field alone from full data (even if it considered as "given") is an option, and the signal processing and ML community has been dealing with similar issues for a long time, for instance through alternating optimization schemes.

A consensus had already emerged before, and together with the other shortcomings of the paper, this lead to a clear decision of rejection.
justification_for_why_not_higher_score: This was a very clear case.
justification_for_why_not_lower_score: -
Decision: Reject