Wasserstein Hypergraph Neural Network
Iulia Duta, Pietro Li\`o
TL;DR
This paper introduces Wasserstein Hypergraph Neural Network, which uses optimal transport-based pooling to better capture higher-order relationships in hypergraphs, improving node classification performance.
Contribution
It proposes a novel Wasserstein pooling method for hypergraph neural networks that preserves geometric distribution properties, advancing beyond traditional set-based aggregation techniques.
Findings
Achieves top performance on multiple real-world datasets
Significantly improves node classification accuracy
Demonstrates the effectiveness of Wasserstein pooling in hypergraph learning
Abstract
The ability to model relational information using machine learning has driven advancements across various domains, from medicine to social science. While graph representation learning has become mainstream over the past decade, representing higher-order relationships through hypergraphs is rapidly gaining momentum. In the last few years, numerous hypergraph neural networks have emerged, most of them falling under a two-stage, set-based framework. The messages are sent from nodes to edges and then from edges to nodes. However, most of the advancement still takes inspiration from the graph counterpart, often simplifying the aggregations to basic pooling operations. In this paper we are introducing Wasserstein Hypergraph Neural Network, a model that treats the nodes and hyperedge neighbourhood as distributions and aggregate the information using Sliced Wasserstein Pooling. Unlike…
Peer Reviews
Decision·Submitted to ICLR 2026
* Paper is well-written. I learned a bunch, as perhaps apparent from the above summary. It provides both good mathematical understanding (step-by-step walkthrough), as well as demonstration figures in main paper and Appendix. * The paper utilizes different grounds-up concepts, which is "refreshing" in LLM era. * Good experimental results
## main weakness The main weakness is in the clarity of the method. Not in terms of the write-up/motivation/high-level description (I think those are clear), but in terms of actually implementing or replicating this method. The math/algorithm section has loose ends, and personally, while I appreciate this work, I am unable to implement it from reading this paper alone. Great papers, on the other hand, I am able to implement them by reading only those papers. Let's try to improve this paper from
The key strengths are two-fold: - The key idea is simple, intuitive, and solid. Existing set pooling functions may struggle to capture the full geometry of set-structured inputs, and using a more expressive pooling function to improve HNNs is a natural approach. - The approach is also somewhat original to hypergraph learning. Intuitively, node feature distribution within each hyperedge could be distinct and informative for hypergraph learning.
I have five primary concerns: - [limited novelty]: The key technical innovation is adapting Sliced Wasserstein Pooling (SWP), an existing module published in 2021, for HNNs. While the adaptation makes sense and seems to be performant, without a new technical innovation, the paper does not meet the standards of a top-tier conference. - [thin content]: The experiments and analyses are thin. The authors used only 7 benchmark datasets with 8 (old) baseline HNNs. The method is evaluated only based on
1. Although the paper addresses a traditional GNN problem, it takes a very interesting perspective. Instead of using conventional aggregators like mean or sum, the authors represent the nodes within a hyperedge as a distribution. This approach better captures the internal structure and higher-order relationships of hyperedges. 2. The writing of the paper is very logical and well-structured. Although it involves some theoretical concepts, the explanations are clear and easy to follow. 3. This pap
The main drawback of the paper is the lack of complexity analysis and runtime comparisons. Since the optimal transport algorithm is generally not cheap computationally, this raises some concerns about the efficiency of the proposed method.
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Taxonomy
TopicsAdvanced Graph Neural Networks · Graph Theory and Algorithms · Machine Learning in Healthcare