AutoHGNN: Robust and Efficient Neural Architecture Search for Hypergraph Neural Networks

Sirui Li; Pietro Liò b; Xinsheng Li; Baisong Liu; Chengbin Peng

cs.LGSep 27, 2026

AutoHGNN: Robust and Efficient Neural Architecture Search for Hypergraph Neural Networks

Authors: Sirui Li, Pietro Liò b, Xinsheng Li, Baisong Liu, Chengbin Peng

Organizations: Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo, 315211, Zhejiang, China · Department of Computer Science and Technology, University of Cambridge, Cambridge, CB2 1TN, Cambridgeshire, United Kingdom

Abstract

Hypergraph neural networks have achieved significant success in recent years. However, manual architecture crafting is labor-intensive and often fails to capture complex, higher-order relations, making the automation of hypergraph neural network structure design crucial. To improve the automation and adaptability of hypergraph learning, this paper proposes AutoHGNN, a neural architecture search framework tailored for hypergraph neural networks. First, we introduce a Hyper-Interaction Module (HIM) into the search space to address the mismatch between conventional graph neural network designs and hypergraph data. Second, we propose Hypergraph Stable Topological Distance (HyperSTD) as a structural selection criterion to identify architectures that best preserve the intrinsic structural affinities of the original hypergraph during differentiable search. Extensive experiments on various benchmark datasets demonstrate that AutoHGNN consistently outperforms manually designed and automatically searched baselines in classification accuracy and time efficiency, proving that the discovered architectures are significantly more effective.

Figures & tables

Method	Type	Message Passing	Complexity
HGNN [ 10 ]	Spectral	Laplacian	$\mathcal{O}(n^{2})$
HyperGCN [ 45 ]	Spectral	Graph conversion	$\mathcal{O}(m\cdot d)$
HNHN [ 7 ]	Spectral	Hyperedge neurons	$\mathcal{O}(n\cdot d)$
HyperSAGE [ 1 ]	Spatial	Two-stage aggregation	$\mathcal{O}(\text{sampling})$
HGNN+ [ 14 ]	Spatial	Aggregation + update	$\mathcal{O}(nd+md)$
UniG-Encoder [ 49 ]	Spatial	Projection-encoding-decoding	$\mathcal{O}(nd)$

Table 1: Comparison of representative hypergraph neural network methodologies.

Figure 1: The overview of AutoHGNN. Green, orange and blue denote vertex-to-hyperedge aggregation, hyperedge-to-vertex aggregation and post-processing operations respectively. Varying depth of same color indicates different members of the same operation type that share the same weight

\omega

. (a) The HGNN search space whose details are in Fig. 2 . (b) The search module with a weight-sharing supernet constructed from search space, a differentiable sampler and a supernet training modules. (c) Hypergraph neural architecture selection. In stage 1, promising candidates are selected from the j-th round of sampling and gradually merged into promising candidates set, so that the final architectures can be selected from them in stage 2.

Figure 2: Definition of search space in AutoHGNN. Each network layer consists of (a) a Hyper-Interaction Module layer with a vertex-to-hyperedge aggregator and a hyperedge-to-vertex aggregator and (b) a post-processing layer. All layers’ outputs are fused by the (c) feature aggregation operator

\mathcal{F}

to get final output

Z

for downstream tasks.

X_{v}^{(l)}

means vertex features of the

l

-th layer.

$Agg_{e}$	$X_{e}^{(l)}$
sum	$H^{T}X_{v}^{(l-1)}$
mean	$D_{e}^{-1}H^{T}X_{v}^{(l-1)}$
softmax-sum	$softmax(H^{T})X_{v}^{(l-1)}$
softmax-mean	$D_{e}^{-1}softmax(H^{T})X_{v}^{(l-1)}$

Table 2: vertex-to-hyperedge aggregation operations

$Agg_{v}$	$\tilde{X}_{v}^{(l)}$
sum	$HX_{e}^{(l)}$
mean	$D_{v}^{-1}HX_{e}^{(l)}$
softmax-sum	$softmax(H)X_{e}^{(l)}$
softmax-mean	$D_{v}^{-1}softmax(H)X_{e}^{(l)}$

Table 3: hyperedge-to-vertex aggregation operations

Name	$Z$
sum	$\sum_{l=1}^{L-1}X_{v}^{(l)}$
mean	$\frac{1}{L-1}\sum_{l=1}^{L-1}X_{v}^{(l)}$
max	$max\{X_{v}^{(1)},X_{v}^{(2)},...,X_{v}^{(L-1)}\}$
concat	$X_{v}^{(1)}\|\|X_{v}^{(2)}\|\|...\|\|X_{v}^{(L-1)}$
None	$X_{v}^{(L-1)}$

Table 4: Feature aggregation strategies

Dataset Name	Nodes	Edges/Hyperedges	Feature dims	Classes
Pubmed	18,333	81,894	6,805	15
Computers	13,381	245,778	767	10
Physics	34,493	247,962	8,415	5
Cora_CA	2,708	1,072	1,433	7
DBLP	41,302	22,363	1,425	6

Table 5: Details of datasets

Method	Pubmed		Computers		Physics
	Acc(%)	STPE(s)	Acc(%)	STPE(s)	Acc(%)	STPE(s)
GAT	78.85 $\pm$ 0.55	-	75.89 $\pm$ 0.66	-	92.19 $\pm$ 0.66	-
GraphSAGE	80.90 $\pm$ 0.19	-	78.34 $\pm$ 0.48	-	92.90 $\pm$ 0.56	-
SGC	78.86 $\pm$ 0.27	-	81.87 $\pm$ 0.56	-	94.49 $\pm$ 0.22	-
GraphConv	75.88 $\pm$ 0.23	-	76.03 $\pm$ 0.30	-	89.04 $\pm$ 1.55	-
GATv2	79.82 $\pm$ 0.41	-	76.19 $\pm$ 0.26	-	93.00 $\pm$ 0.70	-

Table 6: Result on graph datasets. Bold and underlined texts indicate best and second-best models respectively. STPE indicates Search Time Per Epoch for NAS methods.

Method	Cora_CA		DBLP
	Mean (%)	Std (%)	Mean (%)	Std (%)
GAT	66.95	1.00	83.06	0.48
GraphSAGE	72.38	0.95	84.69	0.09
SGC	66.56	0.47	83.05	0.32
GraphConv	70.71	0.40	83.17	0.37
GATv2	67.01	0.77	83.68	0.70

Table 7: Result on hypergraph datasets. Bold and underlined texts indicate best and second-best models respectively.

Panel of Figure 3 — Figure 3: Hyperparameter sensitivity analysis of AutoHGNN Hyperparameter sensitivity analysis of AutoHGNN on (a) search epochs, (b) network depth, (c) temperature, and (d) training sample size. The X axis is the parameter value and Y axis is the average accuracy of 10 experiments on best architecture found by AutoHGNN.

Variant	Pubmed	Computers	Physics	Cora_CA	DBLP
AutoHGNN(mean+mean)	81.95 $\pm$ 0.12	84.92 $\pm$ 0.09	93.82 $\pm$ 0.08	67.26 $\pm$ 0.21	77.02 $\pm$ 0.11
AutoHGNN(w/o fusion)	79.98 $\pm$ 0.65	84.39 $\pm$ 0.37	93.97 $\pm$ 0.16	66.18 $\pm$ 0.12	86.47 $\pm$ 0.20
AutoHGNN(w/o HyperSTD)	82.01 $\pm$ 0.11	85.10 $\pm$ 0.09	94.85 $\pm$ 0.03	72.65 $\pm$ 0.44	88.09 $\pm$ 0.09
AutoHGNN	83.17 $\pm$ 0.23	87.02 $\pm$ 0.17	95.53 $\pm$ 0.04	73.76 $\pm$ 0.41	88.91 $\pm$ 0.07

Table 8: Ablation study results. Bold texts indicate the best model.

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Anchor-guided Hypergraph Condensation with Dual-level Discrimination

Fan Li, Xiaoyang Wang, Chen Chen, Wenjie Zhang

School of Computer Science and Engineering, University of New South Wales, Sydney, Australia · School of Artificial Intelligence, Shenzhen University, Shenzhen, China.

Hypergraphs Graph Neural Networks

Open paper AskPDF arXiv

The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet informative synthetic ones, beyond graph condensation (GC) methods limited to pairwise relations. However, existing HGC methods rely on decoupled training architectures, where structure generators are pre-trained on the original hypergraph but not jointly optimized with condensed features during refinement, resulting in misaligned structures that degrade downstream utility. Moreover, trajectory-based optimization incurs substantial computational overhead in refinement, limiting condensation efficiency. To tackle these issues, we propose \textbf{A}nchor-guided \textbf{H}yper\textbf{G}raph \textbf{C}ondensation with \textbf{D}ual-level \textbf{D}iscrimination (\textbf{AHGCDD}), which consists of three key components: (1) a node initialization module based on Heat Kernel PageRank (HKPR) to encode structural knowledge into feature semantics; (2) an anchor-guided hyperedge synthesis strategy for joint optimization of condensed features and structure; (3) a theoretically grounded dual-level discrimination objective for utility-preserving condensation without redundant HNN training. Extensive experiments demonstrate the superior effectiveness and efficiency of AHGCDD.

Abstract

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