BHyGNN+: Unsupervised Representation Learning for Heterophilic Hypergraphs

Tianyi Ma; Yiyue Qian; Zehong Wang; Zheyuan Zhang; Chuxu Zhang; Yanfang Ye

cs.LGFeb 16, 2026

BHyGNN+: Unsupervised Representation Learning for Heterophilic Hypergraphs

Authors: Tianyi Ma, Yiyue Qian, Zehong Wang, Zheyuan Zhang, Chuxu Zhang, Yanfang Ye

Organizations: ♠University of Notre Dame · ♣Amazon GenAI · ♦University of Connecticut

Abstract

Hypergraph Neural Networks (HyGNNs) have demonstrated remarkable success in modeling higher-order relationships among entities. However, their performance often degrades on heterophilic hypergraphs, where nodes connected by the same hyperedge tend to have dissimilar semantic representations or belong to different classes. While several HyGNNs, including our prior work BHyGNN, have been proposed to address heterophily, their reliance on labeled data significantly limits their applicability in real-world scenarios where annotations are scarce or costly. To overcome this limitation, we introduce BHyGNN+, a self-supervised learning framework that extends BHyGNN for representation learning on heterophilic hypergraphs without requiring ground-truth labels. The core idea of BHyGNN+ is hypergraph duality, a structural transformation where the roles of nodes and hyperedges are interchanged. By contrasting augmented views of a hypergraph against its dual using cosine similarity, our framework captures essential structural patterns in a fully unsupervised manner. Notably, this duality-based formulation eliminates the need for negative samples, a common requirement in existing hypergraph contrastive learning methods that is often difficult to satisfy in practice. Extensive experiments on eleven benchmark datasets demonstrate that BHyGNN+ consistently outperforms state-of-the-art supervised and self-supervised baselines on both heterophilic and homophilic hypergraphs. Our results validate the effectiveness of leveraging hypergraph duality for self-supervised learning and establish a new paradigm for representation learning on challenging, unlabeled hypergraphs.

Figures & tables

Figure 1: The overall framework of BHyGNN+. Given a hypergraph ${\mathcal{H}}$ , we first obtain its dual ${\mathcal{H}}^{*}=\Tr({\mathcal{H}})$ . For each augmentation method $A_{i}\in{\mathcal{T}}$ , we generate the augmented hypergraph pair $\{\widetilde{H_{i}},\widetilde{H_{i}^{*}}\}$ . Each augmented hypergraph is then fed into the hypergraph encoder $f(\cdot)$ , a projection head $h(\cdot)$ , and a readout function to obtain hypergraph-level representations. We use cosine similarity, i.e., $\text{sim}(\cdot)$ , as the objective function to optimize the encoder.

		Senate		Synthetic		Congress		House		Walmart
Num. of Nodes		282	282	2,000	2,000	1,718	1,718	1,290	1,290	88,860	88,860
Num. of Edges		315	315	1,000	1,000	83,105	83,105	340	340	69,906	69,906
Average $h(v)$		0.50	0.50	0.28	0.28	0.55	0.55	0.51	0.51	0.53	0.53
Average $h(e)$		0.55	0.55	0.33	0.33	0.79	0.79	0.58	0.58	0.75	0.75
Noise std. $\sigma$		0.6	1.0	0.6	1.0	0.6	1.0	0.6	1.0	0.6	1.0
Supervised	MLP	62.24	50.35	50.00	37.48	79.45	65.91	77.12	64.07	62.23	44.69

Table 1: Performance comparison (Mean accuracy %) of baseline methods for node classification on heterophilic hypergraph datasets. OOM indicates an out-of-memory error. For each group, the bolded numbers indicate the best result and underlined numbers represent the runner-up performance within each group.

		Twitter		Citeseer		DBLP		Cora		Cora-CA		Pubmed
Num. of Nodes		2,936	2,936	3,312	3,312	41,302	41,302	2,708	2,708	2,708	2,708	19,717	19,717
Num. of Edges		35,502	35,502	1,070	1,079	22,363	22,363	1,072	1,072	1,579	1,579	7,963	7,963
Average $h(v)$		0.41	0.82	0.42	0.83	0.49	0.87	0.40	0.80	0.45	0.90	0.48	0.95
Average $h(e)$		0.45	0.90	0.42	0.83	0.47	0.93	0.44	0.88	0.43	0.86	0.44	0.88
Hypergraph Type		Het.	Homo.	Het.	Homo.	Het.	Homo.	Het.	Homo.	Het.	Homo.	Het.	Homo.
Supervised	MLP	67.38	67.38	68.05	68.05	83.76	83.76	68.45	68.45	69.45	69.45	84.45	84.45

Table 2: Performance comparison (Mean accuracy %) of baseline methods for node classification on homophilic hypergraph datasets. For each group, bolded numbers indicate the best result, and underlined numbers represent the runner-up performance within each group.

Table 3: Performance comparison in additional split settings.

Figure 2: Hyperparameter sensitivity analysis on (a) hidden dimensions and (b) augmentation ratio across various benchmark datasets.

Hypergraph Learning

Hypergraph learning models relationships among groups of entities to capture interactions that pairwise graphs cannot represent.

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HyperFuse: Fast Self-Supervised Node Embeddings for Attributed Hypergraphs

Self-supervised hypergraph representation learning can produce informative node embeddings, but existing methods often require deep encoders trained for hundreds of epochs, making embedding generation costly even for hypergraphs with a few thousand nodes. This limits applications requiring embeddings for many or evolving hypergraphs. We present HyperFuse, a label-free pipeline for fast hypergraph representation learning. HyperFuse (i) computes structural node coordinates by maximizing a spectral relaxation of hypergraph modularity using Banerjee's hypergraph adjacency and a matrix-free operator with cost linear in node-hyperedge incidences; (ii) constructs multi-scale feature summaries and assigns bounded utility weights to hyperedges based on member stability under feature and membership masking; and (iii) trains a lightweight utility-weighted hypergraph encoder for 100 epochs using an invariance-decorrelation objective. We compare HyperFuse with TriCL, SE-HSSL, VilLain, and HypeBoy on nine public hypergraphs using six downstream classifiers and k-means clustering. On the eight datasets where all methods completed, HyperFuse required 8.7 s per dataset on average, achieving 13-179x geometric-mean speed-ups over the baselines. It achieved the highest average accuracy with five of six classifiers, while classification and clustering performance was not significantly different from TriCL and SE-HSSL. Compared with HypeBoy, HyperFuse was 13x faster and 2.1-4.1 percentage points more accurate across all classifiers. HyperFuse provides a practical approach for fast, repeated hypergraph embedding generation.

Megha P, Harshit Kumar, Srajan Agarwal +3

School of Data Science, Indian Institute of Science Education and Research Thiruvananthapuram, Thiruvananthapuram, 695551, Kerala, India. · Department of Mathematics and Statistics, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, West Bengal, India. · Institute of Computer Science, University of Rostock, Rostock, 18051, Germany. +1

Hypergraph Learning Hypergraph Neural Networks

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Aug 5, 2026

Towards Trustworthy Hypergraph Neural Networks under Label Noise

Hypergraph neural networks (HGNNs) have demonstrated remarkable capabilities in processing complex higher-order relationships. However, their performance is highly dependent on labeled data, making them vulnerable to label noise. Despite advances in learning with label noise (LLN) and graph learning with label noise (GLN), noisy-label learning on hypergraphs remains underexplored. In this paper, we present a systematic study of hypergraph node classification under label noise. First, we adapt representative LLN and GLN methods to hypergraphs and evaluate them under a unified benchmark, revealing the limitations of existing robust learning strategies for hypergraphs. Building on this, we propose a new hypergraph robust framework, HyperTrust, which first estimates hyperedge trustworthiness through a pretraining-based, entropy-aware strategy, and then incorporates the HyperedgeBoost module to enhance reliable supervision by connecting unlabeled nodes to trustworthy hyperedges, as well as the HyperedgePrune module to suppress noisy propagation by removing untrustworthy node-hyperedge incidences. Finally, two modules work collaboratively to adjust the hypergraph structure and generate final predictions. Extensive experiments and theoretical analysis demonstrate the effectiveness and robustness of HyperTrust on multiple hypergraph datasets under various noisy settings. Our work provides a unified benchmark and an effective solution for hypergraph learning with label noise and lays a foundation for future research in this direction.

Mengyao Zhou, Zhiheng Zhou, Xiao Han +1

Academy of Mathematics and Systems Science, Chinese Academy of Sciences and also with the University of Chinese Academy of Sciences, Beijing 100190, China · School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China · School of Artificial Intelligence, Beihang University, Beijing 100191,China

Graph Structure Learning Hypergraph Neural Networks Learning with Noisy Labels Hypergraph Learning

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Jul 27, 2026

Unsupervised Graph Representation Learning with Complementary View Alignment

Unsupervised graph representation learning aims to derive meaningful node embeddings by capturing both structural and attribute information without relying on labeled data. Existing methods, such as GAEs, have demonstrated effectiveness but typically rely on message-passing mechanisms that assume homophily, leading to performance degradation on heterophilous graphs, where connected nodes exhibit dissimilar features. This homophily bias results in the loss of critical high-frequency components that are essential for identifying heterophilous patterns. To address these challenges, we propose AlignGAE, a novel extension of MaskGAE that preserves the full frequency spectrum through complementary view alignment. Our framework introduces a dual-encoder architecture that separately processes structural and attribute information, incorporates node positional encoding to approximate Neighborhood Identity Distribution (NID), and employs dual reconstruction tasks for both edges and node attributes. We further propose theoretically grounded NID alignment strategies that ensure semantic consistency across views while preserving their distinct characteristics. Through comprehensive spectral analysis, we demonstrate that AlignGAE achieves optimal representation properties when the alignment loss converges. Extensive experiments across 12 benchmark datasets validate our approach, showing that AlignGAE outperforms state-of-the-art methods by up to 18.7% on heterophilous graphs in node classification, while maintaining competitive performance on homophilous graphs. Our results establish a new paradigm for frequency-aware graph representation learning.

Zengyi Wo, Shiyu Zhang, Qiyao Peng +2

Nanjing University, Nanjing, China · Tianjin University, Tianjin, China

Graph Neural Networks Graph Representation Learning Graph SSL

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Abstract

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