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Riemannian Stochastic Interpolants for Amorphous Particle Systems |
Soundness: 3: good
Presentation: 2: fair
Contribution: 3: good
Rating: 6: marginally above the acceptance threshold
Confidence: 2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked. |
The paper proposes to use Riemannian stochastic interpolants frameowork and group equivariant network for amorphous systems generation. The authors also adapt the architecture of graph neural network to leverage the full symmetry of the amorphous materials. Experiments on a classical glass model show the empirical performance of the proposed methods.
1. The paper is well-structured and esay to follow.
2. The paper leverages the symmetry and geometry structure of the amorphous materials, which is reasonable,
1. Limited experimental scope. The experiments appear to be restricted to two-dimensional and relatively small-scale datasets. Additional experiments on larger-scale and real-world datasets would strengthen the paper’s contributions. Please refer to Question 1 for further details.
2. Lack of efficiency analysis. I noticed that the authors use Eq. (8) to compute the expectation of physical quantities. To the best of my knowledge, such likelihood computations can be inefficient and inaccurate. Additional experimental results are needed to demonstrate that the proposed estimation process indeed converges reliably.
1. Since I am not an expert in amorphous materials, could you clarify whether there are any real-world datasets or tasks in this domain that are suitable for diffusion models? As mentioned in Weakness 1, experiments on large-scale datasets would help demonstrate the scalability of the proposed method and further strengthen the contribution of this work.
2. Could you elaborate on how you evaluate the average potential energy and heat? As mentioned in Weakness 2, does the simulation of Eq. (8) converge in practice?
3. How does the choice of numerical ODE solver affect the generation performance? |
Fully human-written |
|
Riemannian Stochastic Interpolants for Amorphous Particle Systems |
Soundness: 3: good
Presentation: 2: fair
Contribution: 1: poor
Rating: 2: reject
Confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked. |
The paper introduces an equivariant form of stochastic interpolants and applies it to amorphous materials. The main results are given on a toy problem with either 11 or 44 atoms with two different species.
- Figure 2 makes the equivariances quite convincing
- Competing methods have drawbacks (Riemannian DDPM, no likelihood; maximum-likelihood training of ODE, expensive)
- The reweighing is possible via the framework and it is shown to make a big improvement in performance.
- Figure 1, right side. The word "symmetrized" is written next to an image in which the symmetry is far from clear. What's going on there?
- There is a lot of time spent on what I would consider background information. Many of these symmetries are closely discussed in other works. I agree that a specific treatment of stochastic interpolants is technically new, but the details discussed here are somewhat minor.
- While the performance is obviously better with the author's treatment, the results are rather simple. Of course, everything gets more complex in amorphous state with periodic boundary conditions, but 44 atom with two species is not very many or complex. Is there any experimental data you can attempt to fit to?
- What is the citation issue on line 177?
- Can you consider any bigger systems or ones with more motivated datasets?
- Can you explain your main contribution more clearly? It seems like many of these modeling aspects existed already in extremely related frameworks. |
Fully human-written |
|
Riemannian Stochastic Interpolants for Amorphous Particle Systems |
Soundness: 3: good
Presentation: 3: good
Contribution: 1: poor
Rating: 2: reject
Confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. |
The paper presents a generative model for amorphous materials based on stochastic interpolants, taking symmetries and periodic boundary conditions into account. Mathematical details regarding the model design are included in detail. The method is evaluated on a small 2-d toy example simulating a single system at two scales (10 and 44 atoms respectively).
The paper is well written and while the mathematical details at time makes the paper a bit dense, it is quite readable.
The topic is timely and of great interest.
The method is described in sufficient detail, which makes it likely that results can be reproduced.
The focus on distributional/ensemble metrics is relevant and interesting.
The experimental validation is very limited. There is no real data example, e.g. with a 3-dimensional amorphous material.
While the method could be expected to generalize between different systems, the experiments only show a model trained for a single system.
The ability of the model to generalize should be clearly demonstrated.
Could you write M = R^3 / (LZ)^3 ?
Are you sure that Eq. (1) is not a metric on the quotient space M? Perhaps you meant to say it is not a true metric on R^d.
The potential energy as defined in Eq. (2) assumes no self-interaction across the periodic boundaries, right?
What do you mean by "For instance, the modulo operator defines a fundamental invariance for probability densities on M, as any density that is not modulo-invariant would assign infinite mass (...)"? Do you mean p(X) = p(X+kL) for all k in Z^d? I am not sure I understand this, since if X is in M, then X (in R^d) and X+kL (in R^d) is literally the same point in M, so this is already built into the domain, p: M->R.
Line 131. Is the ⨂ notation necessary here? Could you not just write (X + u) % L? I think that is fairly standard and perhaps more readable. Same goes for line 139. Perhaps you prefer the chosen notation because it makes it explicit that operations are on all N atoms?
What is the practical significance of Eq. (4)? Also, if b should be in R^{N|S|+Nd} that seems to not align with the definition of b in appendix A, lemma 10: b=1_N ⨂ c where c is in R^d.
Could the logarithmic map (Definition 2) be written more compactly as (A-B+L/2) % L - L/2 ?
On the flat torus, where the differential of the exponential map is the identity, doesn’t Eq. (9) recover the exact trajectories rather than only the time-marginals?
I am confused about the notation in Proposition 8. The velocity field is defined as \hat v: [0,1] x C -> TC. So is are the coordinates not already defined on M, and thereby by definition \hat v(t, (s,X)) = \hat v(t, (s,X+kL)) ?
What is the relation to generative models based on kinetic Langevin diffusion? Could you compare to this line of work?
Can you demonstrate the capability of the model to generalize beyond the training data? |
Fully human-written |
|
Riemannian Stochastic Interpolants for Amorphous Particle Systems |
Soundness: 3: good
Presentation: 3: good
Contribution: 1: poor
Rating: 4: marginally below the acceptance threshold
Confidence: 2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked. |
The authors tackle the problem of sampling equilibrium configurations of glass-forming materials. They do so by combining the Riemannian Stochastic Interpolants and equivariant flow matching for the groups of interest (permutations, translations and symmetries). They substantiate their claims empirically and improve on baselines where available.
- The paper is well-presented.
- The developed theoretical framework is arguably simple, but rigorous and thorough. The proofs seem sound and are well written.
- The paper formalises and proves some intuitive claims (e.g., Prop. 9) – something often overlooked.
- The empirical evidence clearly shows improvement on existing baselines on the provided experiment. Not being an expert in the field of the application, I cannot exactly judge of its quality, however; but the overall method seems to produce much more stable configurations by about a magnitude. Moreover, it looks sound.
- The empirical evidence seems very thorough on the provided dataset.
- The novelty is arguably very low. This paper mostly applies equivariant architectures to Riemannian Flow Matching. In particular, the considered GNN is made Lipschitz-bounded and equivariant, which, as mentioned in the paper, has already been done numerous times. (Perhaps not all at once?)
- Similarly, the theoretical framework does not seem particularly insightful; it mostly formalises results that intuitively seem self-evident. While it is good to prove these, it does not add anything new. At least, this is in my current understanding of the theorems.
- The experiments are convincing, but arguably most of the improvement comes from the equivariance of the architecture.
Overall, this seems to be a good paper, but I mostly doubt that ICLR is the right venue: the interesting part for a Machine Learning conference is really the experiments section. Moreover, and because of that, I am not expert on this particular sub-field, so I do apologise in advance for not being knowledgeable enough on this. So:
- Have I missed out on some particular novelty in the paper?
- Are the experiments more related to ML than I have understood? Are there perhaps any conclusions to be made about Riemannian Flow Matching/Stochastic Interpolants?
- Have you tried out your method on different data/larger scales, and do you see similar improvements?
- Could you point out the main differences between your method and Equivariant Flow Matching?
I am happy to engage in the discussion period well to hopefully deepen my understanding and better my assessment of this work. |
Fully human-written |