Title: HyperMixup: Hypergraph-Augmented with Higher-order Information Mixup
Venue: NeurIPS 2025
Accepted: yes
Keywords: Hypergraph neural networks

hypergraph representation learning

graph neural networks
Abstract: Hypergraphs offer a natural paradigm for modeling complex systems with multi-way interactions. Hypergraph neural networks (HGNNs) have demonstrated remarkable success in learning from such higher-order relational data. While such higher-order modeling enhances relational reasoning, the effectiveness of hypergraph learning remains bottlenecked by two persistent challenges: the scarcity of labeled data inherent to complex systems, and the vulnerability to structural noise in real-world interaction patterns. Traditional data augmentation methods, though successful in Euclidean and graph-structured domains, struggle to preserve the intricate balance between node features and hyperedge semantics, often disrupting the very group-wise interactions that define hypergraph value. To bridge this gap, we present HyperMixup, a hypergraph-aware augmentation framework that preserves higher-order interaction patterns through structure-guided feature mixing. Specifically, HyperMixup contains three critical components: 1) Structure-aware node pairing guided by joint feature-hyperedge similarity metrics, 2) Context-enhanced hierarchical mixing that preserves hyperedge semantics through dual-level feature fusion, and 3) Adaptive topology reconstruction mechanisms that maintain hypergraph consistency while enabling controlled diversity expansion. Theoretically, we establish that our method induces hypergraph-specific regularization effects through gradient alignment with hyperedge covariance structures, while providing robustness guarantees against combined node-hyperedge perturbations. Comprehensive experiments across diverse hypergraph learning tasks demonstrate consistent performance improvements over state-of-the-art baselines, with particular effectiveness in low-label regimes. The proposed framework advances hypergraph representation learning by unifying data augmentation with higher-order topological constraints, offering both practical utility and theoretical insights for relational machine learning.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents HyperMixup, a data-augmentation framework for hypergraph neural networks that preserves higher-order semantic relationships. It begins by pairing nodes in a structure-aware manner, using a combination of feature similarity and hyperedge affinity to guide the selection. A context-enhanced hierarchical mixing process then blends node features first and hyperedge attributes second, ensuring both local and global information is incorporated into each synthetic sample. Finally, hyperedges are adaptively reconstructed using a local affinity threshold, maintaining semantic coherence in the augmented graph. The paper also presents comprehensive theoretical analyses, including regularization interpretations, robustness bounds against joint node–edge perturbations, and a Rademacher complexity bound for generalization.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n- **Clear Motivation:** Addresses a genuine gap in hypergraph augmentation by preserving multi‑way semantics.  \n- **Topology‑Preserving Augmentation:** Mixup operations respect hyperedge structures, avoiding the semantic drift common in graph‑level Mixup.  \n- **Method Design:** A well‑thought‑out three‑stage pipeline that blends node and hyperedge information.  \n- **Theoretical Rigor:** Non‑trivial derivations connect Mixup to covariance regularization, and the paper provides robustness and generalization bounds.  \n\n### Weaknesses\n\n- **Missing Baseline Comparisons:** Although hypergraph‑specific baselines are scarce, the paper should compare at least against graph‑based Mixup techniques (e.g., Mixup [1]) to demonstrate its added value.  \n- **No Standard Error Reporting:** The experiments are not repeated across multiple runs, and standard deviations are not reported. As a result, it is not possible to confidently claim that the proposed method outperforms others, since the impact of random seed variation and different dataset splits on performance remains unknown.\n- **Scalability Concerns:** Covariance‑based regularizers scale cubically with hyperedge size, yet there is no runtime or memory profiling on larger graphs.  \n- **Limited Ablation Study:** Only module‑level ablations are performed; finer‑grained studies (e.g., mixing only node features) are missing.  \n\n### Minor Issues\n\n- **Missing Reference:** Section 3.1 lacks citations for the definition of the incidence matrix, only one possible version is presented without justification, and for the formulation of the hyperedge features.\n\n---\n\n### References\n\n[1] Hongyi Zhang, Moustapha Cisse, Yann N. Dauphin, and David Lopez-Paz. “mixup: Beyond Empirical Risk Minimization.” *International Conference on Learning Representations* (ICLR), 2018.\n\nQUESTIONS:\n- How does HyperMixup scale in terms of runtime and memory on hypergraphs with large hyperedges (e.g., thousands of nodes)?  \n- Can HyperMixup be extended to hyperedge prediction tasks?  \n- Have you considered techniques to accelerate the covariance regularization step? For instance, using low-rank approximations or randomized sketching methods to reduce the computational complexity of estimating and manipulating the covariance matrix.\n- Can HyperMixup be adapted to dynamic or evolving hypergraphs, and how would such extensions impact the theoretical guarantees?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nA novel and well-motivated data augmentation framework (termed HyperMixup) specifically designed for hypergraph neural networks. It effectively addresses the critical challenges of label scarcity and structural noise vulnerability in hypergraph learning, which are inadequately handled by existing Euclidean or graph-based augmentation methods. The work is further strengthened by rigorous theoretical analysis, demonstrating how HyperMixup induces hypergraph-specific regularization via gradient alignment with hyperedge covariance and provides robustness guarantees against hybrid perturbations. Comprehensive experiments across citation networks and multi-modal datasets show consistent performance gains over strong baselines. The paper makes a significant contribution by unifying data augmentation with hypergraph topological constraints.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nS1. This work tackles two critical challenges in hypergraph learning simultaneously: label scarcity and structural noise vulnerability - a well-motivated gap not addressed by existing Euclidean/graph augmentation methods. They also identify the core limitation of prior work: naive interpolation disrupts hyperedge semantics essential for higher-order reasoning.\n\nS2. This work provides rigorous theoretical guarantees: it formally establishes topology-aware regularization through gradient alignment with hyperedge structures, certifies robustness against combined node-hyperedge perturbations, and derives generalization bounds tied to hypergraph spectral properties. This unified analysis bridges hypergraph geometry with data augmentation.\n\nS3. Consistent SOTA gains across citation (+0.8–1.5%) and 3D recognition (+0.3–1.39%) tasks, with exceptional low-label robustness. Full code/data/hyperparameter disclosure satisfies NeurIPS reproducibility standards.\n\nWeaknesses:\n\nThe method faces scalability limitations due to cubic-complexity hyperedge covariance computations, assumes static hypergraphs (limiting dynamic applications), and simplifies hyperedge representation via mean aggregation.\n\nQUESTIONS:\nQ1. Would augmenting mean aggregation (e.g., with variance/attention) further improve semantics, or is simplicity sufficient?\n\nQ2. Have you explored non-linear label mixing beyond Eq. 6？\n\nQ3. For structural noise robustness (Sec. 5.2), could you test adversarial hyperedge perturbations?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes HyperMixup, a data augmentation framework for hypergraph neural networks designed to address data scarcity and structural noise. The method introduces three components: structure-aware node pairing, hierarchical feature mixing, and adaptive topology reconstruction. The authors provide theoretical analyses for regularization, robustness, and generalization.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n- The paper is presented with a good structure that covers methodology, theoretical analysis, and empirical experiments.\n\nWeaknesses: \n- Flawed Motivation: The paper's key motivation, namely that existing graph augmentation methods are unsuitable for hypergraphs, is debatable. Many prominent spectral-based hypergraph neural networks are mathematically equivalent to applying Graph Neural Networks (GNNs) on a simple graph derived from a clique expansion of the hypergraph. These spectral-based hypergraph neural networks include the baselines used in the paper such as HGNN and HGNN+. The hypergraph convolution operators used in these models, namely $D_{v}^{-1/2}HWD_{e}^{-1}H^{T}D_{v}^{-1/2}$ and $D_{v}^{-1}HWD_{e}^{-1}H^{T}$, mathematically obey the definition for a graph adjacency matrix produced from the given hypergraph using clique expansion. Given this equivalence, any standard graph-domain augmentation methods, such as [1,2,3], could be directly applied to the clique-expanded graph as a preprocessing step before feeding it to methods such as HGNN and HGNN+.\n- Unjustified Computational Cost for Marginal Gains: The performance improvements reported in Table 2 are limited. Compared to the strongest baselines, the accuracy gain is around 1% on four out of the five datasets (Cora, Pubmed, ModelNet40, NTU2012) and even shows a performance decrease on CiteSeer. Given these marginal and statistically unsubstantiated gains, it is critical for the authors to demonstrate that their method does not introduce an unreasonable computational burden. However, the proposed loss function (Eq. 9) includes a \"hyperedge smoothness\" regularizer that requires iterating over all hyperedges and their constituent nodes during each training step, suggesting a significant increase in complexity. The authors concede this point in their conclusion, noting that the \"computational overhead of hyperedge covariance alignment scales cubically with hyperedge size\". The paper provides no runtime analysis or comparison to baselines, making it impossible to assess the trade-off. Therefore, the method's practical value is questionable, as it likely introduces significant computational cost for limited performance improvement.\n- Insufficient Experiments: The experimental evaluation omits key relevant baselines, specifically, hypergraph-specific augmentation methods [4, 5], which are directly comparable in terms of both the scope and objectives. Additionally, as highlighted in Weakness 1, many of the baselines used in Table 2 (e.g., clique-expansion-based methods: HGNN, HGNN+, and GNNs: GCN, GAT, GraphSAGE, GraphConv) can benefit from existing graph-domain augmentation techniques [1, 2, 3]. The paper fails to apply or discuss such enhancements for these baselines, potentially underrepresenting their true capabilities.\n\n[1] Ling H, Jiang Z, Liu M, et al., “Graph mixup with soft alignments,” International Conference on Machine Learning, 2023.\n\n[2] Han X, Jiang Z, Liu N, et al., “G-mixup: Graph data augmentation for graph classification,” International Conference on Machine Learning, 2022.\n\n[3] Zhao W, Wu Q, Yang C, et al., “GeoMix: Towards Geometry-Aware Data Augmentation,” ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2024.\n\n[4] Wang J, Wang J, Jin D, et al., “Hypergraph Collaborative Filtering With Adaptive Augmentation of Graph Data for Recommendation,” IEEE Transactions on Knowledge and Data Engineering, 2025.\n\n[5] Wei T, You Y, Chen T, et al., “Augmentations in hypergraph contrastive learning: Fabricated and generative,” Advances in Neural Information Processing Systems, 2022.\n\nQUESTIONS:\n- Can the authors provide a detailed complexity analysis and empirical run-time results (e.g., training time and peak memory) of the full pipeline in comparison with baselines in Table 2 across datasets of varying scale? \n- Can the authors directly compare the proposed method with established graph-based augmentations [1,2,3] by applying them to a standard graph neural networks (like GCN and GAT) and a clique-expansion-based hypergraph neural networks (like HGNN and HGNN+)? \n- Can the authors benchmark the proposed approach against existing hypergraph augmentation techniques [4,5] by integrating them into hypergraph learning models, such as HGNN, HGNN+, HyperGCN, and Hyper-Atten?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 1, "ORIGINALITY": 2, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents HyperMixup, a novel hypergraph-aware augmentation framework that effectively addresses data scarcity and structural noise in hypergraph neural networks. The method innovatively integrates structure-guided node pairing, hierarchical feature mixing with hyperedge context, and adaptive topology reconstruction to preserve higher-order semantics during data augmentation. Theoretically, it establishes regularization effects through hyperedge covariance alignment, provides robustness guarantees against joint node-hyperedge perturbations, and derives generalization bounds via hypergraph spectral analysis. Comprehensive experiments on citation networks and multi-modal datasets demonstrate consistent improvements over state-of-the-art baselines, particularly in low-label regimes. The work makes a valuable contribution by unifying data augmentation with hypergraph topological constraints, offering both practical efficacy and theoretical grounding for relational learning.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: This work Directly addresses the critical yet underexplored challenge of data augmentation for hypergraphs, where traditional Euclidean/graph methods fail to preserve higher-order semantics.  Establishes three foundational theorems linking gradient alignment to hyperedge covariance (Thm 1), certifies robustness against hybrid perturbations (Thm 2), and derives generalization bounds via hypergraph spectral analysis (Thm 3)—significantly advancing the theoretical understanding of hypergraph regularization. Demonstrates consistent SOTA-beating results across 5 diverse benchmarks (citation/3D object datasets), with notable gains (+0.8–1.5%) in low-label regimes.\n\nWeaknesses: The $O(|\\mathcal{E}|^2)$ complexity of hyperedge covariance computation could challenge web-scale applications (e.g., social networks). Evaluations omit temporal/dynamic hypergraphs (e.g., evolving collaborations).\n\nQUESTIONS:\nHow might you approximate hyperedge covariance computation ($\\Sigma_e$) to reduce $O(|\\mathcal{E}|^2)$ complexity for web-scale hypergraphs \n\nCould HyperMixup handle evolving hypergraphs? \n\nIs there a correlation between optimal $q$/$γ$ and hypergraph properties (e.g., spectral radius $\\rho(L)$ or node-hyperedge covariance $|\\Sigma_{ve}|_F$)?\n\nLIMITATIONS:\nNA", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-02"}