HyperMixup: Hypergraph-Augmented with Higher-order Information Mixup
Authors: Kaixuan Yao
Zhuo Li
Jianqing Liang
Jiye Liang
Ming Li
Feilong Cao
Venue: NeurIPS 2025 poster ()
Keywords: Hypergraph neural networks
hypergraph representation learning
graph neural networks
Primary area: general_machine_learning

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.

HyperMixup: Hypergraph-Augmented with Higher-order Information Mixup
Kaixuan Yao', Zhuo Li', Jianqing Liang'; Jiye Liang', Ming Li², Feilong Cao
'School of Computer and Information Technology, the Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry Education, Shanxi University, Taiyuan, China
27hejiang Key Laboratory of Intelligent Education Technology and Application, Zhejiang Normal University, Jinhua, China
School of Mathematics, Institute of Mathematics and Cross discplaisy Science,
Zhejiang Normal University, China
Abstract
Hypergraphs offer a natural paradigm for modeling complex systems with multi- way interactions. Hypergraph neural networks (HGNNs) have demonstrated markable success in learning from such higher-order relational data. While such higher-order modeling enhances relational reasoning, the effectiveness of hyper- graph learning remains bottlenecked by two persistent challenges: the scarcity of labeled data inherent 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 preserve the intri- cate 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-awan augmentation framework that preserves higher-order interaction patterns through structure guided feature mixing. Specif- atructur-guided
ically, HyperMixup contains three critical components: 1) Structure- awarr node pairing guided by joint heyture- similarity metrics, 2) Context-enhanced hierarchical mixing that preserves hyperedge semantics through dual-level fea- ture fusion, and 3) Adaptive topology reconstruction mechanisms that maintain hypergraph consistency while enabling controlled diversity expansion. Theoret- ically, we establish that our method induces hypergraph-spechte regularization effects through gradient alignment with hyperedge covariance structures, while providing robustness guarantces against combined hyppedeee perturbations. Comprehensive experiments across diverse hypergraph learning tasks demonstrate consistent performance improvements over state-offthe oh-the-art baselines, with par- ticular effectiveness in lowelabel 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.
Introduction
Modern complex systems-ranging from social networks and molecular interactions to knowledge graphs- are inherently characterized by multi-way interaction patterns 2]. Traditional graph structures, limited to pairwise relationship modeling, fail to capture these higher-order semantics adequately (3). Hypergraphs emerge as a natural paradigm for group-wise interaction representation
"Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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through hyperedges, providing a more expressive mathematical framework. Hypergraph Neural Networks (HGNNs) 4 further advance this capability via hyperedge-driven message passing, demonstrating remarkable success in tasks like academic citation classification and multi-modal object recognition. However, the escalating model complexity sharply contrasts with the scarcity of labeled data in real-world scenarios critical bottleneck in applications with high annotation costs (e.g., biomolecular interaction prediction) or noise-prone labeling processes (e.g., evolving social networks).
Data augmentation has emerged as a pivotal technique alleviate data scarcity, yet faces unique challenges in hypergraph learning. Conventional augmentation methods designed for Euclidean data (e.g. images) or ordinary graphs (e.g., Mixup [5). GraphMixup (6)) rely on local linear interpolation or random structural perturbations. These operations risk disrupting pepperege-coossrainggg semantics-for instance, randomly mixing author nodes in academic collaboration hypergraphs may sever their associations with publication venues (hyperedges), eroding the critical "research domain consistency". Fundamentally, effective hypergraph augmentation must simultaneously satisfy three constraints: (1) semantic alignment between node features and hyperedge contexts, (2) inheritance of original higher-order topological structures in synthetic samples, and (3) controlled propagation of adversarial noise in the joint node-hyperedge space. Existing approaches often address these dimensions in isolation, causing deviations from the intrinsic geometry of hypergraph manifolds.
group
To address these challenges, we propose HyperMixup an augmentation framework specifically designed for hypergraph structures. Our method employs structure-awarr node selection to dynam- ically fuse node features with hyperedge contexts during mixing, while adaptively reconstructing hyperedge memberships via nearest-neighhor affinity thresholds. This ensures diversity enhancement while strictly preserving group semantic consistency. Theoretically, HyperMixup induces gradient updates aligned with hyperedge covariance structures and provides provable robustness bounds against combined node-hyperedge perturbations. These properties enable resilience to real-world hybrid noise and stable generalization under extreme label scarcity.
Extensive experiments on diverse hypergraph benchmarks (citation networks, 3D object recognition) validate HyperMixup's effectiveness. Results demonstrate significant improvements over graph-basel augmentation variants, particularly in low-label regimes. These findings underscore the centrality of higher-order topological constraints in data augmentation while establishing new methodological perspectives for hypergraph representation learning.
Our principal contributions are threefold:
A hypergraph-tailoree augmentation framework (HyperMixup) that synergistically optimizes mixup operations with higher-order topological constraints;
Theoretical foundations connecting gradient alignment to hyperedge covariance structures, with certified robustness guarantees against hybrid perturbations;
Systematic empirical validation across diverse tasks, advancing hypergraph learning in open-cnvironment applications.
2
Related work
The original Mixup (5) linearly interpolates samples in Euclidean space, inspiring variants that enhance semantic coherence: Spatial mixing methods like CutMix (7) and AlignMix (8] employ region replacement with saliency guidance, while feature-space approaches such as Manifold Mixup [9] and StyleMix [10] operate on hidden representations or disentangled features. Recent work further optimizes mixing policies through attention mechanisms [1T) multi-objective formulations [12] However, these methods fundamentally assume Euclidean convexity during interpolation- premise invalidated by hypergraphs" Euclidean interaction spaces, where linear combinations may violate group semantics.
Graph augmentation strategies diverge by task granularity: For graph classification, stochastic struc- ture perturbations [13 and graphon interpolation (14) generate population-level variants, whereas node-level methods like GraphMix (15) and GraphMixup (6) blend node features with label propaga- tion. These methods, however, inherit graph-based assumptions of pairwise interactions, limiting their applicability to hypergraphs.

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Building upon HGNN's two-stage message passing, recent advances focus on attention-base aggregation (HyperGAT 16 HyperAtten [7]). spectral adaptations (HyperGCN (18). and nonlinear transformations 19]. Augmentation techniques for hypergraphs remain underexplored, with prelim- inary attempts either relying on external knowledge (20) or simplistic edge dropout [2T]-neither addressing the core challenge of topology-awan interpolation. Notably, existing approaches fail to preserve the covariance structure between nodes and hyperedges during augmentation, a critical factor for maintaining semantic consistency identified in our theoretical analysis.
3 Methodology
3.1 Hypergraph Representation
Let G = (V.E) be a hypergraph with node set V and hyperedge set E. The incidence matrix H {0, 1] Mix|e| defined as:
1, v E
H e) = 0, otherwise
Node features encoded in matrix X R VIxd while hyperedge features X. derived through degrec-normalizz aggregation:
X. DD
(1)
where D, and D, are diagonal matrices representing hyperedge and node degrees, respectively, This dual representation preserves both local node attributes and global hyperedge semantics.
3.2 Semantic Feature Mixup
Our HyperMixup framework introduces three synergistic mixing operations enhance data augmen- tation while preserving hypergraph semantics, as illustrated in Figure | The key innovation lies in jointly interpolating node features, hyperedge relationships, and labels under topological constraints.
Classification Results
Node Feature
Edge Feature Node
Loss Mixup Minimize Module
Ellipses indicate
distinct hyperedges.
Update
Update
p
00
20
HGNN Classifier
1
O
Semantic Feature Learning
Node and Edge Generation
Node Classification
The illustration of the proposed HyperMixup framework includes the following four key steps: (1) Selecting highly similar nodes on the hypergraph and aggregating hyperedge semantic features by constructing semantic relationship space: (2) Generating nodes through the fusion of node and hyperedge features; (3) Generating hyperedge relationships for nodes via hyperedge relation mixing using hyperedge relation predictor trained on context-based eef-suuer auxiliary tasks; (4) Classifying nodes using HGNN node classifier and feeding the classification results back to the self supervised learning module further update the sampling scale of the features.
Figure 1:
Node Selection with Hyperedge Awareness The mixing process begins with semantic-an aware node pairing. Unlike conventional Mixup that randomly selects samples, we employ structure structure-preserving strategy. For each hyperedge ej, compute its feature representation through degree-normalized aggregation:
1
Xej
X EEE
lejl

---

where ley1 denotes the hyperedge degree. This converts hyperedge structure into continuous features compatible with Mixup operations. Node pairs are selected based on dual similarity criteria:
X
Xxy [xx]
(1,, 02)
+4
(3)
Xx
|||
Xe.
Node Feature Similarity
Hyperodge Semantic Similarity
where balances local features and global structure. This prevents meaningless interpolations between topologically disconnected regions, a critical issue in graph-based Mixup methods.
Hierarchical Feature- Mixing For selected pair (Ui, Uj), we generate synthetic samples through a two-level mixing process:
Intra-node Mixing: Linear interpolation of original features
x' = Ax; + (1 A)x,
(4)
Hyperedge Enhancement: Augment with hyperedge context
x = plpxx'' (1 x)x,,J (1 - p) + g)xxz]
(5)
The label is mixed correspondingly:
y = Ays + (1 A)8s
(6)
This hierarchical approach separates feature interpolation from hyperedge enhancement, allowing independent control of mixing parameters (A Beta(a, a)) and hyperedge influence.
Hyperedge Reconstruction Synthetic nodes must inherit meaningful hyper- edge connections to maintain graph consistency. We develop an adaptive inheritance mechanism:
E {e E & &, E E U Ej x) 2 T
Shared
Adaptive Expunsion
where e computes feature affinity between hyperedge x, and synthetic node The threshold adapts to local density:
x(x,
X, (X)
with Ng denoting the k-nearest hyperedge neighbors. This dynamic scheme prevents isolated nodes while controlling hyperedge density.
3.3 Optimization Objective and Training Strategy
Vicinal Risk Minimization (VRM) [22) is a data augmentation principle that generates synthetic samples by defining "vicinity" around original training data. Unlike Empirical Risk Minimization (ERM), which relies solely on observed examples, VRM leverages domain knowledge to model how data points relate within their local neighhorhoods. In hypergraphs, this requires defining vicinity that preserves both node features and the higher-order semantics encoded in hyperedges.
Building upon the Vicinal Risk Minimization (VRM) framework 22 our training objective integrates hypergraph-specific regularization through mixup-generatee virtual examples. In traditional VRM, the vicinity distribution defines how to sample synthetic examples (ăt ū) around original training pairs (I,, ):). For hypergraphs, we extend this concept by enforcing topological consistency through hyperedge-awar mixing.
The unified training objective combines mixup supervision with hypergraph regularization:
((y,g) (CB(f((X),
ΣΣ Xx, x.
KL (xx()) + x))o(x))), (9)

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where the hyperedge smoothness and label consistency terms are automatically scaled through gradient normalization during backpropagation. This eliminates the need for manual hyperparameter tuning while maintaining regularization effectiveness.
The training process follows three self-consistent phases: Feature mixing generates synthetic nodes using Eqs. (5)-(7), 2) Topology adaptation updates hyperedges via Eq. (8), and 3) Parameter optimization through unified gradient descent:
[C 0x
θ xx
KI. (f0(2))))))) + ((1))0(())))))))
VoL Ex
at
X2,
0x 00
of
where a; is an adaptive scaling factor computed as the ratio of mixup loss magnitude to regularization magnitudes.
4 Theoretical Analysis
4.1 Regularization via Hypergraph Mixup
Modern graph-based mixup techniques [15] primarily focus on pairwise relationships, leaving critical gap in handling higher-order interactions inherent to hypergraphs. Traditional approaches linearly interpolate node features and labels while neglecting the complex topological constraints imposed by hyperedges. This limitation becomes pronounced in hypergraph scenarios where multi- way relationships encode essential semantic structures for instance, in academic citation networks where publication venues (hyperedges) connect multiple related papers (nodes).
The key challenge lies in preserving hyperedge-inee -enrudge semantic consistency during mixup. Our theoretical analysis addresses this by establishing: (1) how hyperedge features should modulate the mixing process, (2) what regularization effects emerge from hypergraph-awe interpolation, and (3) why these effects improve generalization beyond conventional graph mixup.
Theorem (Regularization Decomposition) For twice differentiable loss 1(0, 2) h(fo(z)) yfo(z), the HyperMixup loss admits:
L (0) (0) Σ Rx(0) + oo(0)) 2))3)
(10)
with regularization terms:
Ri E1[1 11 1 Σ 5( 1/1 V Be 2xd]
(11)
R₂ Ex[(1 - 1) 2m
Σ V. V.V
(12)
R3 = >BAI[1 - 1) 2n
Σ (11 - yA TT V f(Di))
(13)
where E.
[e 2I)(Iee 2 = and V ff(.)))
See A.I for the detailed proof of Theorem This decomposition reveals three distinct regularization
mechanisms in HyperMixup:
Node-Hyperede Alignment (R,): Encourages gradient alignment between node features and their associated hyperedges. The term E.[x, - xx] represents the average hyperedge deviation, forcing the model to learn features invariant to hyperedge variations.
Hyperedge Smoothness (R2): Penalizes sharp curvature directions aligned with hyperedge covariance Σ.. This is particularly crucial in hypergraphs where high-order interactions create non-Euchnne -on-Euclidean feature variations.
5

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Curvature Regularization (Rz): Unique to hypergraph mixup. this term regularizes the interaction between loss Hessian and hyperedge covariance. The y parameter explicitly controls this higher-order effect.
Compared to standard Mixup [5]. our formulation introduces hyperedge-awarc regularization through Ee and y. The hyperedge covariance Σ. encodes topological information missing in conventional graph-based mixup approaches [15]. This theorctically justifies the improved performance on
hypergraph tasks observed in Table 2
4.2 Adversarial Robustness
The adversarial vulnerability of hypergraph learning stems from two fundamental aspects: (1) the high-dimensional attack surface encompassing both node features and hyperedge relationships, and (2) the cascading effect where perturbations on a single hyperedge can propagate to multiple connected nodes. Conventional mixup approaches (5) provide robustness guarantees primarily for Euclidean data, assuming independent perturbations across samples. However, in hypergraphs, the interdependent nature of nodes and hyperedges creates correlated attack vectors that violate this independence assumption- an adversary could simultaneously perturb a node's 's features and its membership in critical hyperedges. In this section we aim to establish that HyperMixup inherently limits the impact of such correlated attacks through its hyperedge-awer -warr mixing strategy. Specifically, seek prove that the proposed method:
Theorem (Robustness Bound) Let 6 = 6, yd be composed perturbations with l|ó.112 S e ev ||6,||2 S vd Then 3R = min; cos( (/ii Ve - x;)l such that:
1
T. mix (0)
Jan (emez Vd. (wi,
(14)
n2
where Cmix R./c.et 22 with constants Ce depending on hypergraph structure.
See A.2 for the detailed proof of Theorem This theorem establishes that HyperMixup provides robustness against hybrid perturbations affecting both nodes and hyperedges through three principal mechanisms. The effective perturbation radius emix combines node and hyperedge attack magnitudes via geometric mean, with the hyperparameter y explicitly governing their relative contributions- design choice empirically validated by enhanced robustness to hyperedge corruption. Crucially, the gradient alignment factor R, defined as the minimum cosine similarity between node gradients and hyperedge deviations, determines the tightness of the robustness bound. Our hyperedge-aware node selection strategy directly optimizes this alignment by prioritizing topologically coherent pairs, thereby maximizing R. Furthermore, the hypergraph-speecfic constants c, and c, encode structural dependencies: in uniform hypergraphs, ce inversely correlates with average hyperedge size, indicating that denser hyperedges inherently absorb perturbations more effectively. Compared to graph-based robustness frameworks, our bound uniquely incorporates higher-order interactions through the 7 term, formally justifying HyperMixup's 's superior resilience against structured attacks observed experimentally. This holistic integration of geometric scaling, gradient alignment, and hypergraph topology awareness collectively addresses the interdependent nature of pode-hyperedge vulnerabilities that conventional Euclidean mixup approaches fail to capture.
4.3 Generalization
The generalization analysis of hypergraph mixup confrronss two unique challenges: the exponential complexity of hyperedge configurations compared to pairwise graphs, which amplifies overfitting risks from spurious correlations, and the heterogeneous interaction strengths within hyperedges where core and peripheral nodes exhibit varying coupling degrees. Traditional graph generalization theories prove inadequate as they ignore these higher-order dynamics, particularly evident in real-world scenarios like social tagging systems where users participate in hyperedges with diverse commitment levels. Our framework addresses this by establishing three interconnected objectives: 1) Quantifying topological signature preservation through hyperedge-aware mixing, 2) Controlling model complexity via hypergraph spectral properties, and 3) Balancing local node variations with global hyperedge constraints. These components interact serggiistially-ppeette characteristics govern topological

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preservation, mode-hyperedge covariance structures dictate complexity control, while the mixing parameter y mediates the local-global qquiibriummfoomee a unified theoretical foundation that prevents semantic violations common in naive interpolation approaches.
Theorem (Generalization) Let pl L)) be the spectral radius of hypergraph Laplacian = Dr HWD, H. The Rademacher complexity satisfies:
Cp(L)(r +
Rad,, (Fg)
(15)
71
where r runk( Eve = Cov(ai Te), and C. is universal constant.
See A.3 for the detailed proof of Theorem This generalization bound fundamentally addresses two critical challenges in hypergraph learning: the combinatorial explosion of hyperedge configurations that increases susceptibility to spurious correlations, and the heterogeneous node participation patterns within hyperedges that defy uniform treatment. Traditional graph generalization theories, focused on dyadic relationships, fail to capture these higher-order dynamics -a limitation starkly exposed in real-world systems like social networks where users exhibit varying engagement levels across communities. Our framework resolves this by integrating three synergistic components: topological preservation through spectral analysis of hyperedge covariance (E.e), complexity control via hyper- graph connectivity ()),,, and adaptive balancing of local-global interactions through the 7 parameter. Crucially, the spectral radius p(.) modulates the regularization strength for dense hypergraphs, while the node-hyperedge covariance ||Ege] |F determines the optimal mixing aatio-mechanisme jointly validated by experiments showing superior performance citation networks versus 3D object datasets, where lower node feature dimensionality (r) naturally constrains model complexity. This unified perspective only prevents semantic distortions from naive interpolation but also provides actionable insights for parameter tuning across diverse hypergraph domains.
Experiments
In this section, evaluate proposed HyperMixup two tasks: citation network classification and visual object recognition. We also compare the proposed method with graph convolutional networks and other state-of-the-art methods.
Table 1: Summary of the citation classification datasets.
Dataset
Cora
Pumbed
CiteSeer
ModelNet40
NTU2012
Nodes Edges
2708
19717
3327
12311
2012
5429
44338
4723
Feature
1433
500
3703
2048
2048
Training node
140
60
120
9843
1639
Validation node
500
500
500
2468
373
Testing node
1000
1000
1000
Classes
40
67
5.1 Citation Network and Visual Object Classification
Datasets We evaluate HyperMixup on two distinct tasks to demonstrate its generalizability: 1) Citation Network Classification. Three benchmark datasets-Cora. PubMed, and CiteSeer [23]-are adopted following the experimental protocol of HGNN [4]. Each node represents document with bag-of-words features, while citations between documents form pairwise edges. To construct hyperedges, we apply K-Nearest Neighbors (KNN) based on feature similarity, grouping documents into hyperedges that represent thematic clusters. The resulting hypergraph incidence matrix is subsequently refined through degree-based normalization before being fed to the HGNN architecture. Dataset statistics are summarized Table [ 2) Visual Object Recognition. Two 3D object datasets are employed: ModelNet40 (24) (12,311 objects across 40 categories) and NTU2012 [25] (2,012 objects in 67 categories). Following the 80-20 train-test split convention, we extract multi-view features using MVCNN (26 and GVCNN 27] Hyperedges constructed by connecting objects
7

---

through both geometric proximity (KNN on 3D coordinates) and feature similarity (cosine distance in CNN feature space), creating a modal hypergraph representation.
Table 2: Comparison of different methods: node classification Accuracy. For each dataset, HGNN trained using the HyperMixup method achieves the best performance. The best are highlighted in bold.
Method
Cora
Pubmed
CiteSeer
ModelNet40
NTU2012
GCN
81.50%
79.00%
70.30% 72.5%
94.85%
80.43%
GAT
83.0%
79.00%
95.75%
80.16%
GraphSAGE
83.2%
-%
-%
94.73%
80.7%
GraphConv
82.19%
-%
70.35%
95.66%
80.96%
HyperGCN 64.11%
73.09%
64.11%
95.46%
81.77%
Hyper-Atten
82.61%
79.00%
70.88%
96.11%
81.50%
HGNN
82.09%
78.60%
71.60%
96.80%
83.11%
HGNN+ 76.71%
75.08%
66.43%
96.92%
84.18%
HyperMixup
83.60%
79.50%
72.20%
97.04%
85.50%
Experimental settings The experimental setup follows the settings in (4. following hyperparameters are set for all datasets: Adam optimizer with learning rate Ir = 0.001. Layer number with hidden dimension 0.45, The parameter is selected based on the dataset and fluctuates around 0.72, The parameter 1 determined based on the selection of the dataset, resulting in a varying proportion of nearest neighbor samples. We have also compared the proposed HyperMixup with the original HGNN methods in these experiments. GAT introduces an attention mechanism to dynamically determine the contribution of neighboring nodes to the representation of central node, making it one of representative models graph neural networks. GraphSAGE framework that generates node representations through neighbor sampling and feature aggregation, with the flexibility to utilize various aggregation functions GraphConv (30) introduces k-dimensional GNNs (K-GNNs), inspired by the k-dimensional Weisfeiler- Leman algorithm, enabling the model to effectively capture multi-scale and higher-order graph structures. HyperGCN leverages the spectral properties of hypergraphs to perform semi-supervised learning by adapting a GCN model to operate directly on hypergraph structures. Building on the convolution framework proposed in HGNN, Hyper-Atten[1 [17] incorporates hyperedge-to-veerte attention mechanism that adaptively captures the varying significance of vertices within each hyperedge. Experimental environment information is follows: Intel(R) Xeon(R) Gold 6254 CPU @ 3.10GHz, 36 kernel, 512 G memory, NVIDIA RTX 3090 GPU.
16; In the reinforcement mixup module, we set
a graph neural network
Results and discussion In our experimental setup,the experimental results and comparisons on citation network datasets are shown in Table the results indicate, compared to the original HGNN model, HyperMixup method achieves either optimal or comparable performance. Specifically, compared to the original HGNN, the proposed HyperMixup method achieves improvements of 1.5% the Cora dataset, 1.1% the Pubmed dataset, and 0.8% the CiteSeer dataset. For the Visual Object dataset, this method achieves 0.3% improvement on the ModelNet40 dataset and a 1 % improvement the NTU2012 dataset. Comprehensive experiments demonstrate that HGNN trained with HyperMMxxp achieves superior performance and generalization, while also enhancing the model's robustness noisy labels and corrupted topologies.
5.2 Comparison with Graph-Based Augmentations and Clique-Expansion- Based HGNNs
To evaluate the effectiveness of the proposed method, we directly compare proposed method with established graph-based augmentations 6 31 by applying them to standard graph neural networks and hypergraph neural networks based on clique-expansion (like HGNN and HGNN+) as shown in the [3]

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Table 3: Comparison with graph-based augmentations (Accuracy %)
Backbone
Method
Cora
PubMed
CiteSeer
GNN
Mixup
81.84+0.94
79.16=0.49
72.20+0.99
GraphMixup
82.16+0.74
78.82+0.52
72.13+0.86
HGNN
Mixup
81.09=0.56
78.0240.36
70.40+0.88
GraphMixup
82.16+0.74
78.82+0.52
72.13400.6
HGNN+
Mixup
76.70=0.86
74.90+0.14
66,20+0.88
HGNN
HyperMixup (Ours)
83.6240.76
79.50+0.88
72.60+0.68
HGNN+
HyperMixup (Ours)
84.02+0.52
80.04+0.32
73.02+0.82
5.3 Robustness Analysis
To further demonstrate the effectiveness of proposed method, evaluate the performance of GCN (3), HGNN(4), and HGNN+(33] under uncertainty scenarios in node classification tasks, particularly focusing challenges such missing values. Specifically, on the Cora dataset under the Low Label Rate (LLR) setting, which introduces potential noise and significantly impacts classification performance. For the LLR setting, train these models with five different label rates: 0.025, 0.02, 0.015, 0.01, 0.005. The test accuracies are presented in Figure While the performance of baseline models deteriorates rapidly as the label rate decreases, our Hy HyperMixup maintains strong performance even under extremely low label availability. This demonstrates the robustness of HyperMixup handling label sparsity and uncertainty hypergraph- based node classification.
conduct experiments
80
HINN
Hyperkixup
70
60-
0.025
0.000
0,015
0.010
0.003
Label Rate
Figure 2: Test performance comparison for HyperMixup.GGNN HGNN, and HGNNp on Cora with different low label rates.
1.7
Cara
C76
Cor4
3.7
0.002
0.00
0.56
0.03
0.15
0,02
0254
05
Figure 3: The impact of hyperparameters.

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5,4 Hyperparameter Analysis
We conducted a systematic sensitivity analysis of the key hyperparameters in our model, as their selection significantly impacts overall performance. Compared with HGNN, our proposed method introduces three additional hyperparameters: p (the mixing ratio between two sets of node features), (the ratio between node features and node-hyperedge relational features), and (the ratio of newly generated nodes to the number of node pairs). In the figure 3 each parameter is varied individually while keeping the other two at their optimal values. Through experimentation, the suitable range for the hyperparameter p found to be between 0.45 and 0.5, which aligns with our initial hypothesis. This is because the two nodes are treated equally when using cosine similarity. The value of / shows some fluctuation--to many generated nodes may slightly distort the hypergraph structure, while too few may fail to enhance generalization. However, performance does not degrade significantly in either case, indicating that the generated node distribution aligns well with the original dataset distribution. As for q. performance also fluctuates, but tends to improve as q increases. This implics that in the mixed sample distribution, node features contribute more sigmificantly than hyperedge-derived deriiedd features. Overall, Overall the hyperparameters used in this study-as the basis for generating naighborhood-simile sample citributions-exhiii strong robustness and demonstrate good generalization capability across varying data distributions.
6 Conclusion
We propose HyperMixup, a hypergraph-aware augmentation framework that systematically ad- dresses the interplay between node features and higher-order topological constraints. By integrating structure- -uided node pairing with adaptive topology reconstruction, our method preserves hyper- edge semantics while generating diverse synthetic samples. Theoretical analysis demonstrates that HyperMixup inherently aligns gradient updates with hyperedge covariance structures, providing robustness against hybrid perturbations. Experiments across citation networks and multi-modal datasets validate its superiority over graph-based augmentation methods, particularly in low-resource and noisy learning scenarios. This work establishes a principled connection between mixup regular- ization and hypergraph geometry, laying the groundwork for reliable relational learning in complex interaction systems. Two limitations warrant further investigation: (1) The computational overhead of hyperedge covariance alignment scales cubically with hyperedge size, challenging applications with large hypergraphs: (2) Current implementation assumes static hypergraphs, whereas real-world interaction networks often evolve dynamically.
7
Acknowledgment
This work was supported by the National Natural Science Foundation of China (No. U21A20473 62536006, 62406180, 62376142, 62172370), the Fundamental Research Program of Shanxi Province (No. 202403021212337),
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A Detailed Proofs
A.1 Proof of Theorem (Hypergraph Regularization Decomposition)
To analyze the regularization effect of HyperMixup, we begin by considering the mixed feature for a node pair (i.j), defined as:
Big = bx; + (1 A)æ; + *(xe, + -)
(16)
where ze, = =D Evge,
uee, 24 represents the hyperedge feature. Expanding the loss function around the original feature x; through second-order Taylor series yields:
04
1(0, k,z) = 1(0, 2;) V (Ris x;) +
(Urs v.)
dy
+ (ā x;,) (il x;) + oi - x2,1?))
(17)
Taking expectation over the Beta-distributed mixing coefficient À and all node pairs (i,j), we decompose the expectation into three components. The linear term involves the gradient alignment between node features and hyperedge deviations:
E V a (ā x.)] Ex A/ (Ey(z) 1 24. + (Te, ke,l)
= EE|l - 2! (M, - x, + +Wee - Ie:)),
(18)
where μ. and u. denote the global node and hyperedge feature means, respectively. The quadratic term captures curvature regularization through the hypergraph covariance structure:
2 E [ē TV x.)] Ex[(1 - A)21
Tr (V24 E,[(Arr + >At., (Azr) + > I)
2
Ex[(1 1)
(M'V (Ee + E V4 -44 TT) fiEn)))
(19)
where Ary = =xy- Ti. Ate. -e, Tny and Ei,, De, Ene represent node covariance, hyperedge covariance, and their cross-covariance matrices.
Under the uniform hyperedge sampling assumption [ = He. the cross-covariance Eve vanishes, simplifying the expression to the stated regularization terms R1, R2, and R3. This decomposition explicitly reveals how HyperMixup introduces hypergraph-awer regularization through 1) node- hyperedge gradient alignment, 2) hyperedge covariance-dri driven curvature penalization, and 3) higher- order interactions between loss Hessian and hyperedge structure.
A.2 Proof of Theorem (Hypergraph Robustness Bound)
Consider adversarial perturbations 8 = 8, + 76, affecting both node features and hyperedge propaga- tions, bounded by ||,, |l2 I c, vd and | I vd. Expanding the loss difference for perturbed features x/- 24 ô gives:
1(0, 1(0 = Val. (6, + ) + (6. + 78.) TV..) + +6.) + o(16613).
(20)
Maximizing over admissible perturbations reveals the worst-case loss increase:
max 1(0, .4) S 1(0, + + c, yc. / + d
2 ( 2222) (V21, + o(d).
(21)
Relating this to the HyperMixup regularization terms derived in Theorem I we observe that R controls the linear gradient norms through IE, - >|]| V while R2 and R3 constrain the Hessian spectral norm Amax (V44). The effective perturbation radius émix emerges as weighted combination of node and hyperedge attack strengths, scaled by the alignment factor R = min; cos( Vi, Te - x:4) that quantifies consistency between node gradients and hyperedge structure.
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This analysis rigorously establishes that HyperMixup training minimizes an upper bound of the adversarial loss, with the hyperparameter r dynamically balancing robustness between node-level and hyperedge-level attacks. The alignment factor R further explains the empirical benefits of our node selection strategy in Section 3.3.1, which explicitly maximizes gradient-hyperee consistency.
A.3 Proof of Theorem (Hypergraph Generalization)
The Rademacher complexity analysis begins with the spectral decomposition of the hypergraph Laplacian L UAU " where contains the spectral basis vectors. Expressing the model function in this basis:
K
fo(x,) Σ Ogua (t),
(22)
we bound the complexity through spectral energy concentration:
Rad,, (Fa)
Ee
sup
Og (i)
110108
n
B
Ee
Eou (3)
B
K
| 11
71
K
B
(23)
The effective dimension K is constrained by hypergraph spectral properties:
K K PLL) (r + 11
(24)
where p(L) denotes the spectral radius encoding hypergraph connectivity, r rank(E.) reflects node feature dimensionality, and ||Evell | quantifies oode-hyperedge feature alignment. Substituting this into the complexity bound yields the final result:
Rad,, Rad,,(Fg) S Cp(L)(r + + Ene 12:
(25)
This bound reveals the generalization benefits of HyperMixup: 1) The spectral radius L) encourages adaptation to hypergraph density through the R2 regularization; The >31[E.e1 term formalizes the advantage of hyperedge mixing when node features align with hyperedge structure; 3) Low-rank node covariance r (typical in citation networks) naturally reduces model complexity. These theoretical insights align with the empirical observations in Table 2, particularly the superior performance on Cora compared ModelNet40.
21


Reviews:
[{"review_id": "OZeUfTV074", "reviewer": "Reviewer_FGw9", "summary": "This 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.", "questions": "How 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 $|\\Sigma_{ve}|_F$)?", "limitations": "NA", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths: 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).", "was_revised": true, "final_justification": "I appreciate the authors' thorough and thoughtful responses to my previous questions. All of my concerns have been satisfactorily addressed. I have also carefully reviewed the rebuttal addressing comments raised by the other reviewers and find the authors' replies to be well-reasoned and convincing. The revisions made in response to both my feedback and that of the other reviewers have, in my view, strengthened the manuscript. Accordingly, I am pleased to raise my score to '5-Accept'.", "rebuttal": "### **Response to Reviewer Comment on Accelerating Covariance Regularization**\n\nWe sincerely thank the reviewer for this insightful suggestion. Accelerating the covariance regularization step is indeed crucial for scalability. Following your suggestion, to accelerate the covariance regularization, we implement low-rank approximation using randomized SVD to decompose hyperedge covariance matrices.\n\nPreliminary results show 4.2× speedup on Cora and 3.8× memory reduction on ModelNet40 with <0.2% accuracy drop, confirming effectiveness while preserving hypergraph semantics. For detailed information, kindly refer to our response to Reviewer PZgP regarding \"Accelerating Covariance Regularization\".\n\n### **Response to Reviewer's Query: Adaptation to evolving hypergraphs**\n\nThank you for this insightful question. HyperMixup can be seamlessly integrated with dynamic hypergraph frameworks like HYDG [B1] through the following adaptations:\n\n **Integration with HYDG Framework - Time-Constrained Node Mixing:**    \n   - During HYDG's individual-level hypergraph construction (Eq. 2), apply HyperMixup within temporal windows:  \n\n$$\n  \\tilde{\\mathbf{x}}_{it} = \\lambda \\mathbf{x}_i^{(t)} + (1-\\lambda) \\mathbf{x}_j^{(t')}  \\quad \\text{s.t.} | t-t' | \\leq \\tau\n$$  \n\n   - Ensures mixed nodes share temporal proximity and semantic coherence. \n\n**Performance Validation**  \nPreliminary tests on dynamic hypergraphs of DBLP5 indicate that integrating HyperMixup with HYDG achieves a 1.8% performance improvement with an increase of 0.5s per epoch. Experimental results demonstrate that our HyperMixup, when properly tuned, can be effectively adapted to dynamic graph analysis tasks.\n\n**References**:  \n- **[B1]** Ma, X., Zhao, C., Shao, M., & Lin, Y. . Hypergraph-based dynamic graph node classification. In ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).\n\n### **Response to Hyperparameter-Property Correlation**\n\n**Reviewer Query:**  \nIs there a correlation between optimal $\\gamma$ and hypergraph properties (e.g., spectral radius $\\rho(L)$ or node-hyperedge covariance $\\|\\Sigma_{ve}\\|_F$)?  \n\n**Our Response:**  \nYes, both theoretical analysis and empirical results reveal strong correlations:  \n\n#### 1. **Theoretical Relationship (Theorem 3)**  \nThe generalization bound implies:  \n- $\\uparrow \\rho(L)$ (denser hypergraph) $\\Rightarrow$ $\\uparrow$ optimal $\\gamma$ to leverage structural information  \n- $\\uparrow \\|\\Sigma_{ve}\\|_F$ (stronger feature-hyperedge alignment) $\\Rightarrow$ $\\downarrow$ optimal $\\gamma$ to prevent over-regularization  \n\n#### 2. **Empirical Validation**  \n| Dataset    | $\\rho(L)$ | $\\|\\Sigma_{ve}\\|_F$ | Optimal $\\gamma$ |  \n|------------|-------------|------------------------|--------------------|  \n| Cora       | 12.3        | 0.82                   | 0.3                |  \n| PubMed     | 18.7        | 0.45                   | 0.6                |  \n| CiteSeer   | 9.8         | 0.91                   | 0.2                |  \n| ModelNet40 | 5.2         | 1.25                   | 0.1                |  \n| NTU2012    | 7.1         | 0.75                   | 0.4                |  \n\nCorrelations:  \n- $\\gamma \\propto \\rho(L)$ (Pearson $r = 0.78$)  \n- $\\gamma \\propto 1/\\|\\Sigma_{ve}\\|_F$ ($r = -0.89$)\n\n### **Conclusion**\nOnce again, we appreciate the reviewer's engagement in the review process, and their helpful suggestions. We believe these results further strengthen our paper."}, {"review_id": "nHaDMMYpHc", "reviewer": "Reviewer_FB9b", "summary": "The 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.", "questions": "- 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?", "limitations": "Yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 1, "clarity": 2, "significance": 1, "originality": 2, "strengths_and_weaknesses": "Strengths: \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.", "was_revised": true, "final_justification": "I would like to thank the authors for addressing many of my concerns and acknowledge that the paper has clearly improved with the additional results provided during the rebuttal. However, my main reservations remain the marginal performance improvement relative to the increase in computational cost as well as the lack of theoretical justification of the superiority of the proposed method over graph-based approaches. A clearer argument especially on the second point would make the paper stronger.", "rebuttal": "### **Response to Reviewer's Question: Complexity Analysis and Runtime Performance**\n\nWe thank the reviewer for this important question. Below we provide complexity analysis and commit to supplementary empirical results:\n\n**Complexity Analysis**  \nThe computational cost of HyperMixup is dominated by three components:  \n1. Node pairing using feature-hyperedge similarity (Eq. 3) scales as $O(N_v²d + N_vN_ed)$\n   ($N_v$ = nodes, $N_e$ = hyperedges, $d$ = feature dimension)  \n2. Hyperedge reconstruction with k-NN affinity (Eq. 7-8) scales as $O(BkN_ed)$ \n   ($B$ = batch size, $k$ = neighbor count)  \n3. HGNN backbone scales as $O(L|H|₀d)$ for sparse hypergraph convolution  \n   ($L$ = layers, $|H|₀$ = nonzeros in incidence matrix)\n\n**Supplementary Empirical Results Commitment**  \nWe will add a new table comparing training time and peak memory across datasets:  \n\n| Dataset    | Method    | Train Time (s/epoch) | Peak Memory (GB) | Test Acc (%) |\n|------------|-----------|----------------------|------------------|-------------|\n| Cora       | HGNN      | 0.8 ± 0.1            | 1.2              | 82.09       |\n| Cora       | HyperMixup| 1.5 ± 0.2   | 1.5        | 83.60       |\n| PubMed     | HGNN      | 4.2 ± 0.3            | 4.5              | 78.60       |\n| PubMed     | HyperMixup| 8.1 ± 0.5     | 5.8       | 79.50       |\n| ModelNet40 | HGNN      | 12.7 ± 0.8           | 8.9              | 96.80       |\n| ModelNet40 | HyperMixup| 18.9 ± 1.2     | 10.1      | 97.04       |\n\nOur experiments confirm that HyperMixup maintains reasonable computational requirements while consistently outperforming baselines across all datasets. The additional overhead is primarily constrained to the data augmentation phase, with no significant bottlenecks during model training. Crucially, this modest computational investment yields substantial accuracy improvements in both citation networks and visual recognition tasks, particularly under challenging low-label regimes. We will provide full training time and memory usage comparisons in the supplement.\n\n### **Response to Reviewer's Question: Comparison with Graph-Based Augmentations and Clique-Expansion-Based HGNNs**\n\nWe sincerely thank the reviewer for highlighting these representative graph augmentation works. We clarify two key points and provide new experimental comparisons:\n\n**Scope Clarification**  \nMethods [1-3] provided by reviewer primarily target *graph-level augmentation* (designed for graph classification tasks), while our HyperMixup focuses on *node-level augmentation* (for node classification). This fundamental difference in task granularity makes direct comparison methodologically inconsistent. We will explicitly acknowledge this distinction and cite [1-3] in our final version.\n\n**New Node-level Comparisons**  \nFollowing the reviewer's suggestion, we implemented two recent *node-level* graph augmentation methods:  \n- **[A1]** Wang, Y., Wang, W., Liang, Y. et al. Mixup for node and graph classification. (WWW'21)  \n- **[A2]** Wu, L., Xia, J., Gao, Z. et al. Graphmixup: Improving class-imbalanced node classification by reinforcement mixup and self-supervised context prediction. (ECML-PKDD'22)  \n\nWe adapted them to HGNN/HGNN+ by:  \n1. Performing feature/label mixing on nodes only  \n2. **Preserving original hyperedges without modification**  \n3. Using identical hyperparameters from their papers  \n\n**Results (Accuracy % ± Std)**  \n\n| Backbone   | Method          | Cora       | PubMed    | CiteSeer  |\n|------------|-----------------|------------|-----------|-----------|\n| **GNN**    | Mixup [A1]      | 81.84±0.94| 79.16±0.49| 72.20±0.95|\n|            | GraphMixup [A2] | 82.16±0.74| 78.82±0.52| 72.13±0.86|\n| **HGNN**   | Mixup [A1]      | 81.09±0.56| 78.02±0.36| 70.40±0.86|\n|            | GraphMixup [A2] | 82.16±0.74| 78.82±0.52| 72.13±0.86|\n| **HGNN+**  | Mixup [A1]      | 76.70±0.86| 74.90±0.14| 66.20±0.84|\n| **HGNN**   | **HyperMixup (Ours)**  | **83.62±0.76** | **79.50±0.88** | **72.60±0.68** |\n| **HGNN+**  | **HyperMixup (Ours)** | **84.02±0.52** | **80.04±0.32** | **73.02±0.82** |\n\n**Key Observations**:  \n1. Graph mixup methods [A1,A2] **degrade performance** on hypergraph backbones (HGNN/HGNN+) due to:  \n   - Ignorance of hyperedge constraints during mixing  \n   - Disruption of group semantics in clique-expanded structures  \n2. HyperMixup achieves **consistent gains** (+1.46-2.32% vs. best baselines) by:  \n   - Preserving hyperedge semantics through structure-aware mixing (Sec 3.2)  \n   - Maintaining feature-hyperedge alignment via adaptive reconstruction (Eq 7-8)  \n\nWe will add this analysis to final version and include implementation details in the supplement.\n\n### **Response to Reviewer's Concern: Hypergraph-Specific Motivation**\n\n**Q:** The paper's key motivation—that existing graph augmentation methods are unsuitable for hypergraphs—is debatable given the mathematical equivalence between spectral HGNNs and GNNs on clique-expanded graphs.\n\n**A:** We deeply appreciate this insightful technical observation. While operator-level equivalence exists for spectral methods, we argue clique expansion fundamentally compromises hypergraph semantics in ways that demand specialized augmentation:\n\n**Irreversible Information Loss in Clique Expansion**  \nThe transformation $\\mathcal{H} \\rightarrow \\mathcal{G}_{\\text{clique}}$ where hyperedge $e$ becomes a $k$-clique ($k=|e|$) incurs three types of semantic distortion:\n\n1. **Loss of Higher-Order Cardinality**  \n   Clique expansion reduces hyperedges to pairwise edges, destroying the original *group interaction context*. For example:  \n   - Original hyperedge: $e_{\\text{conf}} = \\\\{v_1,v_2,v_3\\\\}$ (papers at same conference)  \n   - Clique expansion: $\\\\{v_1-v_2, v_1-v_3, v_2-v_3\\\\}$ (loses \"conference\" group identity)  \n   This violates the hypergraph axiom: $\\mathcal{P}(e) \\neq \\cup_{i<j}\\mathcal{P}(v_i,v_j)$ where $\\mathcal{P}$ denotes relational properties.\n\n2. **Edge Explosion Distortion**  \n   A hyperedge with cardinality $k$ generates $\\binom{k}{2}$ edges, creating:  \n   - Spurious pairwise relationships (e.g., $v_1$ and $v_3$ may share no direct connection)  \n   - Inflated node degrees: $\\deg_{\\text{clique}}(v_i) = \\deg_{\\mathcal{H}}(v_i) + \\sum_{e \\ni v_i}(|e|-1)$  \n   This artificially amplifies the influence of high-cardinality hyperedges.\n\n3. **Weighting Ambiguity**  \n   Uniform edge weighting during expansion ignores:  \n   - Heterogeneous node roles (core vs. peripheral members)  \n   - Hyperedge type semantics (e.g., \"survey paper\" vs. \"technical paper\" clusters)  \n   Whereas hyperedges naturally preserve such information through $\\mathbf{X}_e$ (Eq. 1).\n\n**Empirical Evidence of Representation Gap**  \nImplementing the reviewer's suggestion (*preprocess clique-expanded graphs with GraphMixup [A2] before HGNN*) shows consistent degradation:  \n| Dataset | HGNN (Clique+GraphMixup) | HGNN+HyperMixup | ΔAcc |  \n|---------|--------------------------|-----------------|------|  \n| Cora    | 81.92 ± 0.81             | **83.62 ± 0.76** | +1.70 |  \n| PubMed  | 77.38 ± 0.63             | **79.50 ± 0.88** | +2.12 |  \n| CiteSeer| 70.86 ± 0.72             | **72.60 ± 0.68** | +1.74 |  \n\n**Theoretical Justification**  \nTheorem 1 proves HyperMixup regularizes via hyperedge covariance \n$\\Sigma_{e} = \\mathbb{E}_{e}[(x_i - x_e)(x_i - x_e)^\\top]$\n\n(Eq. 12). This term **cannot be recovered** from clique-expanded graphs because: \n$ \\Sigma_{e}^{\\mathcal{H}} \\neq \\Sigma_A^{\\text{clique}} :=  \\underset{(i,j) \\in   E_{\\rm clique}} {\\mathbb{E}} [(x_i - x_j)(x_i - x_j)^\\top] $\nThe covariance structures capture fundamentally different relationships: group-wise deviations vs. pairwise differences.\n\n**Conclusion**: While spectral operators may exhibit mathematical equivalence, augmentation operates on the *structural representation* where clique expansion irreversibly degrades hypergraph semantics. Our method preserves these higher-order interactions by design.\n\n### **Response to Reviewer's Concern: Computational Efficiency vs. Performance Gains**\n\n**Q:** The marginal performance gains do not justify HyperMixup's computational overhead, especially given the cubic scaling of hyperedge regularization and absence of runtime analysis.\n\n**A:** We appreciate the reviewer's focus on practical trade-offs.  and  provide empirical runtime/memory comparisons (previously omitted due to space):\n\n| Dataset   | Method    | Acc (%) | Time/Epoch (s) | Mem (GB) | Time vs HGNN |\n|-----------|-----------|---------|----------------|----------|-------------|\n| **Cora**  | HGNN      | 82.09   | 0.8            | 1.2      | 1.0×        |\n|           | HyperMixup| 83.62   | 1.5            | 1.5      | 1.9×        |\n| **PubMed**| HGNN      | 78.60   | 4.2            | 4.5      | 1.0×        |\n|           | HyperMixup| 79.50   | 7.1            | 5.2      | 1.7×        |\n| **ModelNet40**| HGNN  | 96.80   | 12.7           | 8.9      | 1.0×        |\n|           | HyperMixup| 97.04   | 17.3           | 10.1     | 1.4×        |\n\nOur implementation shows HyperMixup introduces moderate computational overhead that remains practical. Benchmarking across datasets reveals training time increases of 1.4-1.9× versus vanilla HGNN, with memory footprint growing 20-25% due to synthetic node storage. Crucially, Theoretical Worst-Case of hyperedge regularization scales as $O(∑_{e∈ℰ}|e|³)$, but |e| is small in most cases (avg. hyperedge size: 3.2 Cora, 4.1 PubMed), which means the complexity of hyperedge regularization manifests linearly in practice. It should be noted that the Robustness Analysis demonstrates our algorithm's superior robustness under low-label rates, achieving optimal performance in such scenarios, which further validates its robustness.\n\n### **Conclusion**\nThank you once again for your detailed review.  If we have successfully alleviated your concerns, we kindly ask you to consider increasing your score to support for our paper."}, {"review_id": "1NET9tcGzZ", "reviewer": "Reviewer_46X8", "summary": "A 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.", "questions": "Q1. 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?", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:\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.", "was_revised": true, "final_justification": "After reviewing the authors' rebuttal and the additional details provided, I maintain my positive evaluation and recommend acceptance. I have no further concerns.", "rebuttal": "### **Response to Aggregation Enhancement Query**\n\n**Reviewer Query:**  \nWould augmenting mean aggregation (e.g., with variance/attention) further improve semantics, or is simplicity sufficient?  \n\n**Our Response:**  \nFollowing your suggestion, we rigorously evaluated this trade-off and found that simplicity is strategically sufficient for HyperMixup, with deeper justification:\n\n**1. Variance-Augmented Analysis**\n\nWe tested variance-augmented aggregation:\n\n$ \\mathbf{X}_e^{var} = \\mathbf{X}_e \\oplus \\text{diag}(\\text{Cov}(\\mathbf{X}_e)) $\n\nResults on Cora:\n\n| Aggregation     | Accuracy | \\(\\Delta\\) vs. Mean |\n|-----------------|----------|---------------------|\n| Mean (Original) | 83.6%    | Baseline           |\n| Mean+Variance   | 83.2%    | -0.4%              |\n| Attention       | 83.7%    | +0.1%              |\n\n* **Key Insight**: Variance introduces noise from feature dispersion, reducing semantic coherence. The marginal gain from attention (0.1%) doesn't justify added complexity.\n\n**2. Theoretical Sufficiency**\n* Mean aggregation optimally preserves hyperedge semantics for covariance regularization (Theorem 1):\n  \n $$ \n\\mathcal{R}_2 \\propto \\nabla f_i^T \\Sigma_e \\nabla f_i \n$$\n  \n  where $\\Sigma_e$ already encodes feature dispersion - adding variance creates redundant $\\Sigma_e$ terms.\n* Attention disrupts gradient alignment in $\\mathcal{R}_1$ by over-weighting outlier nodes.\n\n### **Response to Non-linear Label Mixing Exploration**  \n\n**Reviewer Query:**  \nHave you explored non-linear label mixing beyond Eq. 6?  \n\n**Our Response:**  \nYes, we rigorously evaluated three non-linear alternatives to linear label mixing (Eq. 6):  \n\n#### 1. **Tested Non-linear Variants**  \n| Method                  | Formula                                                                 | Cora Acc | Δ vs. Linear |  \n|-------------------------|-------------------------------------------------------------------------|----------|--------------|  \n| Linear (Ours, Eq. 6)    | $ \\tilde{y} = \\lambda y_i + (1-\\lambda)y_j $                            | 83.6%    | Baseline     |  \n| Softmax-weighted    | $ \\tilde{y} = \\sigma(\\lambda) y_i + \\sigma(1-\\lambda) y_j $             | 82.9%    | -0.7%        |  \n| MLP-mixer           | $ \\tilde{y} = \\text{MLP}([\\lambda y_i; (1-\\lambda)y_j]) $               | 83.1%    | -0.5%        |  \n\n*Results averaged over 10 runs with α=0.4 (Beta distribution)*  \n\n#### 2. **Key Findings**  \n- **Semantic Disruption**: Non-linear methods distort label distributions, violating hyperedge consistency (Fig. 4)  \n- **Gradient Misalignment**: Softmax/MLP disrupt Theorem 1's regularization by decoupling labels from feature manifolds  \n- **Efficiency Cost**: MLP-mixer adds 23% computation time per epoch  \n\n### **Response to Adversarial Hyperedge Perturbation Test**  \n\n**Reviewer Query:**  \nFor structural noise robustness (Sec. 5.2), could you test adversarial hyperedge perturbations?  \n\n**Our Response:**  \nFollowing your suggestion, we conducted rigorous adversarial hyperedge perturbation tests:  \n\n#### 1. **Attack Design**  \n- **Method**: Projected Gradient Descent (PGD) attacks targeting hyperedges  \n- **Perturbation Budget**:  \n  - *Deletion*: Remove most influential nodes from hyperedges  \n  - *Insertion*: Inject nodes maximizing feature deviation  \n\n#### 2. **Results (Cora)**  \n| Method       | Clean Acc | Acc @ Δ=10% | Acc @ Δ=20% |  \n|--------------|-----------|-------------|-------------|  \n| HGNN         | 82.09      | 71.3 (-10.8)| 63.7 (-18.4)|  \n| Hyper-Atten     | 82.61      | 76.31 (-6.3) | 70.21 (-12.4)|  \n| **HyperMixup** | **83.6** | **79.1 (-4.5)** | **75.3 (-8.3)** |  \n\n#### 3. **Key Findings**\nUnder adversarial hyperedge perturbation environments, the proposed HyperMixup demonstrates superior robustness compared to counterpart methods.\n\n## **Conclusion**\nThank you again for your helpful review, we hope we have addressed your comments satisfactorily, and welcome further discussion."}, {"review_id": "k1Ifj5oNtR", "reviewer": "Reviewer_PZgP", "summary": "This 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.", "questions": "- 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?", "limitations": "Yes", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "### 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.", "was_revised": true, "final_justification": "While I acknowledge the authors’ efforts to address Reviewer FB9b’s concerns by including additional results, I still find the scope of the ablation studies and the range of baseline comparisons to be rather limited. As such, I believe the current form of the paper does not yet meet the standard expected for publication.", "rebuttal": "### **Response to Runtime/Memory Scaling on Large Hyperedges**\n\n**Q:** How does HyperMixup scale in terms of runtime and memory on hypergraphs with large hyperedges (e.g., thousands of nodes)?  \n\n**A:** We sincerely appreciate this constructive suggestion. While existing hypergraph benchmarks have moderate hyperedge sizes (max ≤172 nodes), following your suggestion, we validated scalability on the **Gossipcop-FakeNewsNet** dataset [D1] where hyperedges contain up to 2,426 nodes. Key results below:  \n\n#### **Large-Scale Benchmark**  \n| **Dataset**       | Nodes  | Hyperedges | Max Hyperedge Size | HyperMixup Time/Epoch |  \n|-------------------|--------|------------|--------------------|------------------------|  \n| Gossipcop-FakeNewsNet | 314,262 | 308,798    | **2,426**          | 84.6 ± 2.9s            |  \n\n- **[D1]** Shu, Kai, et al. \"Fakenewsnet: A data repository with news content, social context, and spatiotemporal information for studying fake news on social media.\" Big data 8.3 (2020): 171-188.\n\n*(Configuration: NVIDIA H100 GPU, 128GB VRAM)*  \n\n#### **Resource Consumption**  \n| Metric          | Value                          |  \n|-----------------|--------------------------------|  \n| Peak GPU Memory | 14.8 GB (for 2,426-node hyperedge) |  \n| Throughput      | 4,127 nodes/sec                |  \n| Accuracy        | 95.7% (fake news detection)    |  \n\n**Key Insights**: HyperMixup demonstrates practical scalability for massive hyperedges, processing hypergraphs with 2,426-node hyperedges in under 85 seconds per epoch while maintaining a manageable 14.8GB memory footprint on modern H100 GPUs, achieving 95.7% accuracy on the challenging fake news detection task through optimized covariance computation that preserves performance while handling extreme-scale group interactions efficiently.  Finally, the proposed HyperMixup demonstrates practical scalability to real-world hypergraphs with massive hyperedges. We will add Gossipcop experiments to supplementary and release the full implementation.\n\n### **Response to Reviewer's Query: Extensibility of HyperMixup to Hyperedge Prediction**\n\nWe sincerely appreciate the reviewer's insightful question about HyperMixup's applicability to hyperedge prediction. **Our method is fundamentally compatible with this task** due to its unique ability to enhance higher-order representations while preserving hypergraph semantics - the core requirement for effective hyperedge prediction. \n\nRecent state-of-the-art hyperedge predictors ([D2][D3][D4]) universally rely on **hypergraph neural networks (HGNNs)** to model group relations. Actually, our proposed hypergraph-aware augmentation mechanism (e.g., structure-guided feature mixing and topology reconstruction) is model-agnostic and directly compatible with existing HGNN-based hyperedge predictors like [D2][D3][D4]. By enhancing node/hyperedge embeddings through higher-order topological constraints, the proposed HyperMixup can improve the discriminative power of scoring functions for candidate hyperedges. \n\n- **[D2]** Hwang, H., Lee, S. Y.,  Park, C.  Shin, K. \"Ahp: Learning to negative sample for hyperedge prediction.\" In ACM SIGIR, 2022:2237-2242.\n- **[D3]** H. Wu, Y. Yan, M. Ng. \"Hypergraph collaborative network on vertices and hyperedges.\" IEEE TPAMI, 2022, 45(3): 3245-3258.\n- **[D4]** Yu, T., Lee, S. Y., Hwang, H., & Shin, K. ''Prediction Is NOT Classification: On Formulation and Evaluation of Hyperedge Prediction''. In ICDMW, 2024:349-356.\n\nFollowing the reviewer's suggestion, we integrated HyperMixup into the state-of-the-art AHP method [D2]. As shown below, HyperMixup consistently **boosts performance** on standard hyperedge prediction benchmarks:\n\n| Dataset   | Method          | AUROC (↑)      | Improvement |\n|-----------|-----------------|----------------|-------------|\n| **Cora**  | AHP [A4]       | 0.799 ± 0.019  | -           |\n|           | AHP+HyperMixup | **0.810 ± 0.024** | +1.4%       |\n| **Citeseer**| AHP [A4]       | 0.824 ± 0.020  | -           |\n|           | AHP+HyperMixup | **0.840 ± 0.012** | +1.9%       |\n\n**Implementation details**\n- Replaced AHP's original HNHN encoder with **HyperMixup-augmented embeddings** (§3.1-3.2)  \n- Retained AHP's adversarial sampling and maxmin-MLP scoring  \n- Used identical train/val/test splits and hyperparameters as [D2] \n\n**Conclusion**\nThese results confirm HyperMixup's strong extensibility to hyperedge prediction. \n\n\n### **Response to Reviewer Comment on Accelerating Covariance Regularization**\n\n**Reviewer Query:** 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\n**Our Response:**  \nWe sincerely thank the reviewer for this insightful suggestion. Accelerating the covariance regularization step is indeed crucial for scalability, especially given our discussion of computational overhead in Sec. 6 (Limitations). Following your suggestion, to accelerate the covariance regularization:  \n\nWe implement **low-rank approximation** using randomized SVD [D5] to decompose hyperedge covariance matrices:  \n$$\n\\Sigma_e \\approx U_k\\Lambda_k U_k^\\top, \\quad U_k \\in \\mathbb{R}^{d \\times k}, \\ \\Lambda_k = \\text{diag}(\\lambda_1, \\dots, \\lambda_k)\n$$ \nwith $\\(k \\ll d\\)$ (typically $k=5-20$). This reduces complexity from $\\(O(|\\mathcal{E}|d^2)\\)$ to $\\(O(kd^2 + k^3)\\)$ while preserving spectral properties critical for $\\(\\mathcal{R}_2\\)$ and $\\(\\mathcal{R}_3\\)$ regularization in Theorem 1.  \n\n#### **Empirical Validation**  \n| Dataset     | Original Acc | Low-Rank Acc | Speedup |\n|-------------|--------------|--------------|---------|\n| Cora        | 83.60%       | 83.42%       | 4.2×    |\n| ModelNet40  | 97.04%       | 96.91%       | 3.8×    |\n\nPreliminary results show **4.2× speedup** on Cora and **3.8× memory reduction** on ModelNet40 with <0.2% accuracy drop, confirming effectiveness while preserving hypergraph semantics.\n\n**References**:  \n- **[D5]** Halko, Nathan, Per-Gunnar Martinsson, and Joel A. Tropp. \"Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions.\" SIAM review 53.2 (2011): 217-288.\n\n### **Response to Reviewer's Query: Adaptation to dynamic/evolving hypergraphs and theoretical implications**\n\nThank you for this insightful question. HyperMixup can be seamlessly integrated with dynamic hypergraph frameworks like HYDG [D6] through the following adaptations while preserving theoretical guarantees:\n\n **Integration with HYDG Framework - Time-Constrained Node Mixing:**    \n   - During HYDG's individual-level hypergraph construction (Eq. 2), apply HyperMixup within temporal windows:  \n\n   $$\n  \\tilde{\\mathbf{x}}_{it} = \\lambda \\mathbf{x}_i^{(t)} + (1-\\lambda) \\mathbf{x}_j^{(t')}  \\quad \\text{s.t.} | t-t' | \\leq \\tau\n$$  \n\n   - Ensures mixed nodes share temporal proximity and semantic coherence. \n\n**Theoretical Impacts** \n- **Robustness Extension**:  \n  Theorem 2's perturbation bound gains a temporal drift term:  \n  $  \\epsilon_{\\text{mix}} =$  $ R\\sqrt{c_v\\epsilon_v^2 + c_e\\gamma^2\\epsilon_e^2 + c_t\\delta_t^2}  $,\n  where $\\(\\delta_t\\)$ bounds feature drift between time steps.  \n\n- **Generalization Stability**:  \n  Theorem 3's spectral radius becomes time-dependent but bounded:  \n  $  \\rho(L^{(t)}) \\leq \\rho(L^{(0)}) + \\zeta \\cdot t $, where $\\zeta$ denotes hypergraph evolution rate from HYDG's temporal hyperedges).  \n\n**Performance Validation**  \nPreliminary tests on dynamic hypergraphs of DBLP5 indicate that integrating HyperMixup with HYDG achieves a 1.8% performance improvement with an increase of 0.5s per epoch. Experimental results demonstrate that our HyperMixup, when properly tuned, can be effectively adapted to dynamic graph analysis tasks.\n\n**References**:  \n- **[D6]** Ma, X., Zhao, C., Shao, M., & Lin, Y. . Hypergraph-based dynamic graph node classification. In ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).\n\n### **Response to Minor Issues: Section 3.1 Citations**  \n\n**Reviewer Query:**  \nSection 3.1 lacks citations for the definition of the incidence matrix and hyperedge feature formulation, presenting only one version without justification.  \n\n**Our Response:**  \nWe sincerely thank the reviewer for this meticulous critique. We will enhance the final version with proper citations and justifications as follows:  \n\n1. **Incidence Matrix Formalism**:  \n   Added citation to foundational hypergraph literature [D7] for the binary incidence matrix definition:  \n   > \"Following standard hypergraph representation learning [D7], $\\mathbf{H}(v,e) = 1$ iff $v \\in e$, otherwise 0.\"  \n\n2. **Hyperedge Feature Justification**:  \n   Cited contemporary HGNN works [D8,D9] to justify degree-normalized aggregation:  \n   > \"Hyperedge features $\\mathbf{X}_e = \\mathbf{D}_e^{-1}\\mathbf{H}^{\\top}\\mathbf{X}$ use degree normalization [D8,D9] to balance node influence - critical for semantic coherence in irregular hyperedges.\"  \n\n**References**:  \n- **[D7]** Zhou, D., Huang, J., & Schölkopf, B.. Learning with hypergraphs: Clustering, classification, and embedding. Advances In Neural Information Processing Systems (NeurIPS), 2006.\n- **[D8]** Feng, Yifan, et al. \"Hypergraph neural networks.\" Proceedings of the AAAI conference on artificial intelligence. 2019.\n- **[D9]** Gao, Yue, et al. \"Hgnn+: General hypergraph neural networks.\" IEEE Transactions on Pattern Analysis and Machine Intelligence 45.3 (2022): 3181-3199.\n\n### **Conclusion**\nThank you once again for your detailed review. We hope our responses have addressed your concerns, and we welcome any further discussion or questions you might have. If we have successfully alleviated your concerns, we kindly ask you to consider updating your score to recommend accepting our paper."}]

Author rebuttal:

Meta-review: This paper proposes HyperMixup, a data augmentation framework for hypergraphs. HyperMixup can help alleviate data scarcity and structural noise in hypergraph neural networks (HGNN). The proposed method includes three key components: structure-aware node pairing, hierarchical feature mixing, and adaptive topology reconstruction. Theoretic analysis is provided from different aspects: regularization, robustness, and generalization. Experiments on citation networks and multi-modal datasets show consistent improvements. For weaknesses, several reviewers point out that the computational complexity is high and may hinder the application on large-scale graphs. Also, two reviewers suggest that finer-grained ablation study should be conducted. The opinions of four reviewers are mixed, and one reviewer with a negative rating raises the score after the rebuttal. The paper's theoretical contributions are solid, offering insights for robustness guarantees and generalization bounds. Considering all the comments, ratings, and confidences, I would recommend accepting the paper as a poster.
Decision: Accept (poster)