# Unsupervised Multi-Scale Gromov-Wasserstein Hypergraph Alignment

arXiv: https://arxiv.org/abs/2608.29635 · HTML: https://mlsanity.com/paper/2608.29635/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [REGAL: Representation Learning-based Graph Alignment](https://mlsanity.com/paper/1802.06257/) (2018)
- [Clustering in graphs and hypergraphs with categorical edge labels](https://mlsanity.com/paper/1910.09943/) (2019)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [A Comparative Study of Graph Matching Algorithms in Computer Vision](https://mlsanity.com/paper/2207.00291/) (2022)
- [A Survey on Hypergraph Mining: Patterns, Tools, and Generators](https://mlsanity.com/paper/2401.08878/) (2024)
- [More Recent Advances in (Hyper)Graph Partitioning](https://mlsanity.com/paper/2205.13202/) (2022)
- [The Z-Gromov-Wasserstein Distance](https://mlsanity.com/paper/2408.08233/) (2024)
- [Deep Hypergraph Structure Learning](https://mlsanity.com/paper/2208.12547/) (2022)
- [A Flexible Tensor Block Coordinate Ascent Scheme for Hypergraph Matching](https://mlsanity.com/paper/1504.07907/) (2015)
- [Triangular Alignment (TAME): A Tensor-based Approach for Higher-order Network Alignment](https://mlsanity.com/paper/1510.06482/) (2015)
- [CURSOR: Scalable Mixed-Order Hypergraph Matching with CUR Decomposition](https://mlsanity.com/paper/2402.16594/) (2024)
- [ELRUHNA: Elimination Rule-basedHypergraph Alignment](https://mlsanity.com/paper/2506.09866/) (2025)

## Abstract (arXiv)

We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information, without node features, labels, seed matches, or side information. Direct higher-order formulations can represent hyperedge interactions faithfully, but they can be computationally demanding and cumbersome for non-uniform hypergraphs. Graph-reduction approaches introduce a different challenge: clique expansions keep the alignment problem on the original node set but collapse all hyperedge evidence into one pairwise graph, whereas bipartite expansions preserve incidence structure but enlarge the problem from nodes to nodes plus hyperedges. We introduce FALCON (Filtration-based hypergrAph aLignment via Cross-scale Optimal traNsport), an unsupervised optimal-transport framework for hypergraph alignment. Instead of representing each hypergraph by a single collapsed clique graph, FALCON constructs a filtration-induced sequence of clique-based co-occurrence dissimilarity matrices and jointly aligns all levels through one shared multi-scale Gromov--Wasserstein (GW) objective. The shared transport plan enforces a globally consistent node correspondence across filtration levels while avoiding the auxiliary hyperedge nodes introduced by bipartite expansion. Experiments on perturbation benchmarks derived from real-world hypergraphs show that FALCON is robust to structural noise and in almost all cases outperforms strong graph- and hypergraph-alignment baselines.