BHyGNN+ contrasts a hypergraph with its dual for self-supervised learning, beating supervised and self-supervised baselines on 11 benchmarks without negative samples

It proposes BHyGNN+, a contrastive self-supervised framework centered on hypergraph duality that aligns augmented views of a hypergraph and its dual via cosine similarity, using no ground-truth labels during training. The earlier BHyGNN was supervised and relied on downstream class labels to learn propagation actions and node representations; BHyGNN+ replaces the downstream task loss with a contrastive loss so the same broadcast/receive propagation machinery can be trained without labels. The paper derives the full objective, summing the contrastive loss with the variational loss, and states that at inference the original hypergraph is fed to the encoder and then to a classifier; experiments use a 20%/20%/60% split, ten runs of 500 epochs, and report mean with standard deviation.

The duality-based contrastive formulation removes the need for negative samples, relying only on positive contrastive pairs. Existing hypergraph contrastive methods such as HyperGCL, TriCL, HyGCL-ADT, and HypeBoy depend on negative samples, whose high-quality construction is hard on large hypergraphs; BHyGNN+ sidesteps this by contrasting a hypergraph with its dual. The method section states the objective maximizes cosine similarity between dual and corresponding hypergraph representations, and the introduction lists eliminating the negative-sample requirement as a main contribution.

Across eleven benchmark datasets, BHyGNN+ outperforms supervised and self-supervised baselines on both heterophilic and homophilic hypergraphs. The evaluation spans heterophilic hypergraphs (Senate, Congress, House, Walmart, and a synthetic dataset) and homophilic ones (Twitter, Citeseer, DBLP, Cora, Cora-CA, Pubmed), and additionally augments homophilic datasets to simulate heterophily, going beyond a single-setting evaluation. Accuracy is the metric under a 20%/20%/60% split with ten runs reporting mean and standard deviation; for example, on Senate at noise σ=0.6 BHyGNN+ reaches 68.13 versus 67.87 for BHyGNN and 66.89 for HyperGCL, and on Walmart at σ=1.0 it reaches 68.51 versus 66.85 for BHyGNN.

The advantage is larger when training samples are scarce, and performance stays stable across hidden dimensions and augmentation ratios. Under a 10%/10%/80% split, BHyGNN+ reaches 93.16 on Congress versus 90.23 for BHyGNN, while under a 50%/25%/25% split the gap between self-supervised and supervised baselines becomes marginal. The paper reports two additional split settings and a sensitivity analysis over hidden dimensions {64,128,256,512,1024} and augmentation ratios {0.1,0.2,0.3,0.4}, noting that most datasets perform best at an augmentation ratio of 0.2.

The result targets hypergraph data where hyperedges capture higher-order relations, and fits settings where labels are unavailable during training but a small amount of annotation is available for node classification at inference; the evaluation centers on node-classification accuracy, and the paper states that at inference the original hypergraph is fed to the trained encoder and then to a classifier. For readers aiming to cut annotation cost while handling heterophilic higher-order relations, the combination of duality-based contrasting and variational propagation offers a directly reusable training recipe; the paper also notes it could be extended to hyperedge-level or hypergraph-level tasks.

The paper lists investigating the theoretical foundations as future work, so why duality-based contrasting works in heterophilic settings remains an empirical observation; the augmentation strategies are designed specifically for heterophilic structure, and their best ratio is not uniform across datasets (most peak at 0.2 and decline slightly beyond that). In addition, the heterophilic benchmark datasets contain no node features, and the paper follows prior practice by synthesizing features from a label-dependent Gaussian distribution, which affects how far the results transfer to settings with real features. The current framework focuses on node-level tasks, so performance on hyperedge-level and hypergraph-level tasks remains to be verified.