Kati8/ICLR_2023_2025 huggingface dataset:
authors: Andreas Mazur
authors: Fabian Hinder
authors: Barbara Hammer
reviews: 
Comments: This paper proposes unifying the intrinsic spatial convolution on manifolds from Bronstein et al 2021 with the spatial convolution and patch operators in Monti et al 2017. The authors show that there is an implicit prior by connecting the two formulations and propose a class of intrinsic CNNs with different priors.
Strengths: The authors describe previous work (Masci et al 2015, Boscaini et al 2016, Monti et al 2017) in detail and provide a good background of the different patch operators.
Weaknesses: -My primary concern with this paper is that it’s not clear to me why it is called a prior and how using a different prior helps. It simply seems like different instances of the patch operator, akin to the Gaussian in Masci et al. 2015. 

-If the Dirac prior is the most expressive, why should one consider other priors? The results don’t seem to show much difference between the other priors.

-Are the shot descriptors orientation invariant? Does a global gauge exist?

-Why was a gauge-equivariant method such as [1] not considered? It seems very relevant to the proposed method and has the advantage that the output transforms accordingly with the gauge transformations.

References:
[1] De Haan, P., Weiler, M., Cohen, T., & Welling, M. (2020, October). Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs. In International Conference on Learning Representations.
Recommendation: 3: reject, not good enough
Reviewer 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.
Soundness/correctness: 2 fair
Clarity: 3 good
reviews: 
Comments: The paper builds a connection between a practical implementation of mesh CNN (Monti et al., 2017) to Intrinsic Mesh CNN (Bronstein et al., 2021). By defining a template, Intrinsic Mesh CNN reduces to the mesh CNN defined by Monti et al. with a Dirac prior. The paper later experiments with different choices of priors and show that Dirac prior leads to better results.
Strengths: - The paper connects a practical model with the theoretical framework of Intrinsic convolution on meshes.
- The intuition behind the idea is straightforward and easy to understand.
- The paper proves that a partial order exists for comparing these priors.
- The paper shows some quantitative results to compare the difference between different priors.
Weaknesses: - Although by defining priors the paper builds a connection between theory and practice, the resulted model is not that useful. In particular, the Dirac prior, which corresponds to Monti et al., 2017, is still the best solution at least in the experiments in the paper.
- Indeed, instead of decoupling $w_t(\cdot)$ (the  into $w(\cdot)$ (the prior) and $t(\cdot)$ (the template) and learning the template, one may simply treat $w_t(\cdot)$ as the learnable parameter. If we are allowed to discretize $w_t(\cdot)$ with sufficient amount of parameters, parametering $w_t$ is flexible enough. Making a (not quite accurate) analogy to regular Euclidean CNNs: it seems to me what the paper presents is to pre-convolve some handcrafted $H$ with the original convolutional kernel $K$, with $H$ being something very restrictive in the sense of both capacity and optimization. It therefore does not surprise me too much that the Dirac prior (equivalent to directly parametering $w_t$) is better than all other variants.
- Continuing the point above, I believe there is no reason not to learn the priors at the same time. And doing this may lead to some additional benefits in optimization.
- The presentation seems a bit messy in the experiment section. Many descriptions can be simplified: for instance, I do not think one needs to write down the exact formula of cross entropy (I guess it is well known by the majority of the audience).
- The benchmark seems to be quite toy. I feel that if the paper includes empirical results on the tasks presented by MeshCNN, it will be much more convincing.

[1] Hanocka, Rana, et al. "Meshcnn: a network with an edge." ACM Transactions on Graphics (ToG) 38.4 (2019): 1-12.
Recommendation: 3: reject, not good enough
Reviewer 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.
Soundness/correctness: 3 good
Clarity: 2 fair