BHyGNN+: Unsupervised Representation Learning for Heterophilic Hypergraphs

TL;DR

BHyGNN+ addresses representation learning on heterophilic hypergraphs under label scarcity by employing hypergraph duality to create a self-supervised, negative-sample-free contrastive framework. It pairs augmented hypergraphs with their duals and optimizes a cosine-based global contrast between their representations, while preserving a variational objective for propagation actions. The method extends the supervised BHyGNN with a dual-view SSL objective and four novel augmentations, achieving state-of-the-art results across 11 datasets, including both heterophilic and homophilic hypergraphs. This work introduces a new paradigm for unsupervised hypergraph learning that leverages dual structures to capture complementary higher-order relationships, with practical impact for scalable, annotation-light relational learning.

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 (2)

• Figure 1: The overall framework of BHyGNN+. Given a hypergraph ${\mathcal{H}}$, we first obtain its dual ${\mathcal{H}}^* = \mathop{\mathrm{Tr}}\nolimits({\mathcal{H}})$. 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.
• Figure 2: Hyperparameter sensitivity analysis on (a) hidden dimensions and (b) augmentation ratio across various benchmark datasets.

Theorems & Definitions (4)

• Definition 2.1
• Definition 2.2
• Definition 2.3
• Definition 2.4