Naturality-Guided Hyperedge Disentanglement for Message Passing Hypergraph Neural Network
Graph Neural Network;Hypergraph;Category Theory;Categorcial Deep Learning;Disentangled Representation Learning
Yes
No ethics review needed.
Please see the weakness.
1. The authors have identified an interesting issue in hypergraph representations and the solution that guidance for disentanglement hyperedge is pretty novel. 
2. The experiments are comprehensive, including 8 clinical datasets, 8 benchmark datasets, and a synthetic dataset. 
3. This paper is well-organized and easy to follow.
This paper presents a hyperedge disentangling method, called Natural-HNN, that captures the inherent hyperedge types or the interaction context of hyperedge, based on the naturality condition in category theory.
1. I am  a little bit concern with the overfitting issue, as it contains $k$ MLP for each layer. Does the parameters shared across layers?
2. How does the heterophilic level for the clinial datasets look like? From the model design, it may works well for heterophilic hypergraphs. Can you also report performance for heterophilic hypergraphs, e.g. Congress, Senate, and Walmart in EDHNN [1]?

[1] Equivariant Hypergraph Diffusion Neural Operators. ICLR'23
Yes
No ethics review needed.
- What is the motivation behind this work?
- Could this method be applied to standard hypergraph datasets (as presented in previous work), and could you provide results for those datasets as well?
- This paper addresses the novel and important problem of hyperedge disentangling
- The authors applied their method on a hypergraph of genetic pathway which is an interesting application.
This paper presents Natural-HNN, a hyperedge disentangling method designed to identify hyperedge types or interaction contexts within hypergraphs. Natural-HNN incorporates a message-passing layer that leverages node-to-hyperedge interactions, allowing it to capture the underlying structure of hyperedges more effectively. The authors validate their approach on a hypergraph of genetic pathways, showing that Natural-HNN outperforms established baseline methods.
- The proposed method lacks novelty.
- The primary issue addressed by this paper—namely, that convolution-based methods cannot perform interaction context-dependent message passing—could be resolved by considering the bipartite representation of a hypergraph and applying a simple message-passing mechanism on it.
- The example provided in Figure 1 is confusing, and none of the datasets are related to it. It would be more compelling if Figure 1 were related to the genetic pathways experiment.
- The authors assert that a drawback of sheaf-based methods is that "there is no guidance that helps the transformation to be related to interaction context." However, they do not explain why this is a drawback or why such guidance is important.
- The introduction is verbose, and portions of it could be more appropriately placed in the related works section.
- Section 3 and Figure 2 are positioned too closely, making the text difficult to follow.
- In Section 5, the authors state, "there is no benchmark dataset verified to contain useful interaction context that is related to the task." If this is the case, the motivation for the proposed method is unclear.
- The model performance shown in Table 1 does not significantly surpass the other baselines.
- Although the authors claim to have an effective hyperedge disentangling method, they need to demonstrate that they have addressed the disentanglement problem in their experiments.
Yes
No ethics review needed.
[1] applies the proposed method to the edge-dependent node classification task, where node labels are determined by the hyperedge context. This makes it clear and intuitive why modelling the hyperedge context is beneficial for enhancing model performance. However, in this paper, the authors apply their method to a more general node classification setting, which raises questions about the importance of modelling interaction context. It would be helpful if the authors included a dedicated section discussing why capturing interaction context is crucial for improving model performance.

Minor: It seems that the link to the code provided in the paper does not work. Could the authors please double-check the accessibility of the code?

[1] Choe, Minyoung, et al. "Classification of edge-dependent labels of nodes in hypergraphs." Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2023.
The paper is clearly presented and easy to follow, with the proposed model demonstrating superior empirical performance compared to existing baseline methods.
The paper introduces Natural-HNN, a hypergraph neural network (HNN) designed to effectively capture the context of interactions within hyperedges. In experiments, it outperforms baseline models in cancer subtype classification.
This paper overlooks an important related work [1], which also discusses the idea that different hyperedges provide distinct contextual information to different nodes. In the introduction, the authors highlight one of their key contributions, stating, "To the best of our knowledge, we are the first to propose a hyperedge disentanglement-based method that is systematically designed to capture the context of multiway interaction." Therefore, it is crucial to clarify the differences and advantages of the proposed method compared to the approach presented in [1].

[1] Choe, Minyoung, et al. "Classification of edge-dependent labels of nodes in hypergraphs." Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2023.
Reflecting the interaction context of each hyperedge is important for real world problems. We propose a simple but effective hyperedge disentangling model that can reflect inherent heterogenity (hyperedge type) even in homogeneous data
@inproceedings{
anonymous2024naturalityguided,
title={Naturality-Guided Hyperedge Disentanglement for Message Passing Hypergraph Neural Network},
author={Anonymous},
booktitle={Submitted to The Thirteenth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=bhD0EQWNut},
note={under review}
}
Hypergraph data structure has been widely used to store information or meaning derived from group interactions, meaning that each hyperedge inherently contains the context of their interactions. For example, a set of genes or a genetic pathway can be represented as a hyperedge to express the interaction of multiple genes that collaboratively perform a biological function (i.e., interaction context). However, most existing hypergraph neural networks cannot reflect the interaction context of each hyperedge due to their limited capability in capturing important or relevant factors therein. In this paper, we propose a \textbf{simple but effective} hyperedge disentangling method, \textbf{Natural-HNN}, that captures inherent hyperedge types or the interaction context of an hyperedge. We devised a novel guidance for hyperedge disentanglement based on the naturality condition in the category theory. In our experiments, we applied our model to hypergraphs of genetic pathways for the cancer subtype classification task, and showed that our model outperforms baselines by capturing the functional semantic similarity of genetic pathways.
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Graph Neural Network Hypergraph Category Theory Categorcial Deep Learning Disentangled Representation Learning
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learning on graphs and other geometries & topologies
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Naturality-Guided Hyperedge Disentanglement for Message Passing Hypergraph Neural Network
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