HyperFuse: Fast Self-Supervised Node Embeddings for Attributed Hypergraphs

Megha P; Harshit Kumar; Srajan Agarwal; Anirban Banerjee; Olaf Wolkenhauer; Saptarshi Bej

cs.LGOct 2, 2026

HyperFuse: Fast Self-Supervised Node Embeddings for Attributed Hypergraphs

Authors: Megha P, Harshit Kumar, Srajan Agarwal, Anirban Banerjee, Olaf Wolkenhauer, Saptarshi Bej

Organizations: School of Data Science, Indian Institute of Science Education and Research Thiruvananthapuram, Thiruvananthapuram, 695551, Kerala, India. · Department of Mathematics and Statistics, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, West Bengal, India. · Institute of Computer Science, University of Rostock, Rostock, 18051, Germany. · Stellenbosch Institute for Advanced Study (STIAS), Stellenbosch, South Africa.

Abstract

Self-supervised hypergraph representation learning can produce informative node embeddings, but existing methods often require deep encoders trained for hundreds of epochs, making embedding generation costly even for hypergraphs with a few thousand nodes. This limits applications requiring embeddings for many or evolving hypergraphs. We present HyperFuse, a label-free pipeline for fast hypergraph representation learning. HyperFuse (i) computes structural node coordinates by maximizing a spectral relaxation of hypergraph modularity using Banerjee's hypergraph adjacency and a matrix-free operator with cost linear in node-hyperedge incidences; (ii) constructs multi-scale feature summaries and assigns bounded utility weights to hyperedges based on member stability under feature and membership masking; and (iii) trains a lightweight utility-weighted hypergraph encoder for 100 epochs using an invariance-decorrelation objective. We compare HyperFuse with TriCL, SE-HSSL, VilLain, and HypeBoy on nine public hypergraphs using six downstream classifiers and k-means clustering. On the eight datasets where all methods completed, HyperFuse required 8.7 s per dataset on average, achieving 13-179x geometric-mean speed-ups over the baselines. It achieved the highest average accuracy with five of six classifiers, while classification and clustering performance was not significantly different from TriCL and SE-HSSL. Compared with HypeBoy, HyperFuse was 13x faster and 2.1-4.1 percentage points more accurate across all classifiers. HyperFuse provides a practical approach for fast, repeated hypergraph embedding generation.

Figures & tables

Symbol	Meaning
$N$ , $M$ , $D$ , $d$	numbers of nodes, hyperedges, input features; embedding width
$d_{s}$ , $d_{f}$ , $d_{g}$	widths of the structural, feature and incidence summaries ( $d/4$ , $d/2$ , $d/4$ )
$\mathbf{H}$ , $\mathbf{D}_{v}$ , $\mathbf{D}_{e}$	incidence matrix, node-degree and hyperedge-size matrices
$\mathbf{A}$ , $\mathbf{k}$ , $\mathbf{B}$	Banerjee adjacency, strength vector, modularity matrix
$\mathbf{S}$ , $\mathbf{F}$ , $\mathbf{G}$	structural, feature and incidence summaries (Stages A, B)
$\mathbf{R}$ , $\mathcal{T}_{\mathbf{R}}$ , $\boldsymbol{\Phi}_{\ell}$	normalised incidence, lazy propagation, propagation at scale $\ell$

Table 1: Main notation

Panel of Figure 1 — Figure 1: Overview of HyperFuse. Stage A computes structural coordinates $\mathbf{S}$ by maximising a spectral relaxation of hypergraph modularity. Stage B computes feature summaries $\mathbf{F}$ and incidence summaries $\mathbf{G}$ , and hyperedge utility weights $\mathbf{u}$ derived from the stability of hyperedge members under feature and membership masking. Stage C trains a two-layer hypergraph encoder, whose hyperedge-to-node aggregation is weighted by $\mathbf{u}$ , on two corrupted views with an invariance-plus-decorrelation objective. No stage uses labels.

Dataset	$N$	$M$	$\operatorname{nnz}(\mathbf{H})$	$\max_{j}\|e_{j}\|$	$n_{A}$	$D$	Classes	Feat.
20News	16,242	100	65,451	2,241	53,268,400	100	4	B
Citeseer	1,458	1,079	3,453	26	8,614	3,703	6	B
Cora-CA	2,388	1,072	4,585	43	29,884	1,433	7	B
Cora-CC	1,434	1,579	4,786	5	8,512	1,433	7	B
DBLP	41,302	22,363	99,561	202	865,262	1,425	6	B
ModelNet40	12,311	12,311	61,555	5	137,888	100	40	R

Table 2: Dataset statistics.

n_{A}

is the number of non-zeros that the Banerjee adjacency

\mathbf{A}

would have if materialised. Features: B, binary or categorical; S, sparse real-valued; R, dense real-valued. Zoo contains one single-node hyperedge, which HyperFuse discards

Figure 2: Embedding time per dataset (mean over three seeds, error bars show one standard deviation; logarithmic scale). Datasets are ordered by the embedding time of HyperFuse. Numbers above the bars give the speed-up of HyperFuse over the fastest baseline on that dataset. OOT: SE-HSSL did not complete on DBLP within 24 h

	HyperFuse	TriCL	SE-HSSL	VilLain	HypeBoy
Embedding time
Mean time (s) $\downarrow$	8.7	6242.8	2516.8	1693.0	1184.4
Geo.-mean time (s) $\downarrow$	6.4	912.3	611.5	1145.5	86.2
Total time (min) $\downarrow$	1.2	832.4	335.6	225.7	157.9
Speed-up (geo. mean)	–	143 $\times$	96 $\times$	179 $\times$	13 $\times$
Speed-up (range)	–	5.4–4520 $\times$	9.2–1720 $\times$	82–675 $\times$	1.7–461 $\times$

Table 3: Summary over the eight datasets on which all methods completed (DBLP is reported in Table 6 ). Embedding time is given first; NMI and ARI are obtained with

k

-means, and accuracy and macro-F1 are reported per downstream classifier in Table 4 . The total time is summed over the eight datasets; speed-ups are those of HyperFuse over each baseline. Best in bold, second best underlined. Average ranks are computed per dataset (1 = best); the last column gives the

p

-value of the Friedman test

	Accuracy						Macro-F1
Classifier	Raw	HF	TC	SH	VL	HB	Raw	HF	TC	SH	VL	HB
LogReg	70.63	80.37	80.08	79.18	64.69	77.88	63.29	73.19	74.08	73.03	58.59	71.41
MLP	64.46	78.61	79.49	79.22	61.57	74.54	57.40	70.47	73.06	72.52	55.47	66.39
HGNN	77.26	79.01	78.49	78.21	68.22	75.32	69.31	70.90	70.68	70.22	59.08	65.71
HNHN	73.45	78.85	78.59	78.31	70.97	75.91	65.70	71.12	70.61	70.60	61.99	67.92
UniGCNII	78.98	79.84	79.08	78.73	71.53	76.19	71.93	72.26	71.42	71.34	62.38	68.28

Table 4: Accuracy and macro-F1 (%) per downstream classifier, averaged over the eight common datasets and three seeds. Raw: the node features used in place of an embedding (reference; for the last four classifiers this is their standard semi-supervised use). LogReg and MLP ignore the hypergraph; the other four classifiers also use it. Best in bold, second best underlined, among the five embedding methods. HF: HyperFuse, TC: TriCL, SH: SE-HSSL, VL: VilLain, HB: HypeBoy

Figure 3: Embedding quality against geometric-mean embedding time over the eight common datasets. For accuracy and macro-F1, each marker is one downstream classifier (score averaged over the datasets), and the vertical line spans the six classifiers. HyperFuse attains quality comparable to TriCL and SE-HSSL at about two orders of magnitude lower embedding time, and higher quality than HypeBoy, the fastest baseline, at about one order of magnitude lower embedding time

Classifier	HF	TC	SH	VL	HB	$p$	HF	TC	SH	VL	HB	$p$
	Accuracy						Macro-F1
LogReg	1.75	2.00	3.12	4.75	3.38	$<$ 0.001	2.00	2.00	3.00	4.75	3.25	0.003
MLP	2.50	1.75	2.25	4.88	3.62	$<$ 0.001	2.88	1.75	2.00	4.88	3.50	$<$ 0.001
HGNN	2.25	1.62	2.12	4.75	4.25	$<$ 0.001	2.50	1.50	2.12	4.75	4.12	$<$ 0.001
HNHN	1.88	1.75	2.62	4.62	4.12	$<$ 0.001	2.25	1.88	2.25	4.62	4.00	$<$ 0.001
UniGCNII	1.50	1.88	2.62	4.75	4.25	$<$ 0.001	1.62	2.00	2.38	4.88	4.12	$<$ 0.001

Table 5: Average ranks (1 = best) of the five methods over the eight common datasets for each downstream classifier, with the

p

-value of the Friedman test. Best (lowest) rank in bold. HF: HyperFuse, TC: TriCL, SH: SE-HSSL, VL: VilLain, HB: HypeBoy

		HyperFuse	TriCL	VilLain	HypeBoy
Time (s) $\downarrow$		110.4 $\pm$ 20.9	22322.3 $\pm$ 3053.9	12170.2 $\pm$ 193.0	5572.0 $\pm$ 99.7
Accuracy (%)	LogReg	89.39 $\pm$ 0.06	89.99 $\pm$ 0.12	75.08 $\pm$ 0.16	90.27 $\pm$ 0.02
	MLP	88.88 $\pm$ 0.15	91.10 $\pm$ 0.06	78.23 $\pm$ 0.65	89.57 $\pm$ 0.20
	HGNN	86.80 $\pm$ 0.16	90.50 $\pm$ 0.02	77.27 $\pm$ 0.12	88.78 $\pm$ 0.01
	HNHN	89.23 $\pm$ 0.18	91.22 $\pm$ 0.05	79.06 $\pm$ 0.16	89.61 $\pm$ 0.09
	UniGCNII	88.26 $\pm$ 0.09	91.02 $\pm$ 0.07	79.63 $\pm$ 0.08	89.34 $\pm$ 0.04

Table 6: Results on DBLP (mean

\pm

standard deviation over three seeds). SE-HSSL did not complete within 24 h on the NVIDIA T1000 (8 GB) GPU in any seed. Best in bold, second best underlined

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Stage	Setting	Value
A	structural width $d_{s}$	$d/4=32$
	step-size factor $c$ ; maximum iterations	$0.9$ ; $1{,}000$
	stopping rule	rel. change $<10^{-5}$ , checked every 5 iterations, patience 5, min. 20
B	feature and incidence widths $d_{f}$ , $d_{g}$	$64$ , $32$
	residualisation $\beta$ ; masking rate $\rho$	$0.5$ ; $0.10$
	laziness $\alpha$ ; hops $K$	$0.5$ ; $3$

Appendix

Table 7: Default configuration of HyperFuse, used unchanged on all datasets (

d=128

)

	TriCL		SE-HSSL
Dataset	Epochs	Width	Epochs	Width
20News	500	256	50	512
Citeseer	500	512	265	256
Cora-CA	800	512	160	512
Cora-CC	300	512	305	512
DBLP	500	256	60	512

Appendix

Table 8: Baseline settings taken from the official configurations: number of training epochs and embedding width per dataset. VilLain trains seven models (2–8 virtual labels), each for up to 5,000 epochs with early stopping; VilLain and HypeBoy output 128 dimensions on all datasets; HypeBoy uses its repository’s default configuration on all datasets

Dataset	HyperFuse	TriCL	SE-HSSL	VilLain	HypeBoy
20News	17.7 $\pm$ 2.9	10010.4 $\pm$ 14.4	2751.3 $\pm$ 0.3	2021.5 $\pm$ 4.1	8157.0 $\pm$ 1105.0
Citeseer	7.8 $\pm$ 1.8	253.3 $\pm$ 0.1	71.8 $\pm$ 0.2	634.8 $\pm$ 21.5	64.1 $\pm$ 2.7
Cora-CA	6.6 $\pm$ 0.2	1182.6 $\pm$ 30.6	1380.0 $\pm$ 1.2	624.5 $\pm$ 2.1	27.2 $\pm$ 0.4
Cora-CC	5.2 $\pm$ 0.1	205.3 $\pm$ 2.1	1114.5 $\pm$ 0.8	1228.9 $\pm$ 89.9	19.7 $\pm$ 1.4
DBLP	110.4 $\pm$ 20.9	22322.3 $\pm$ 3053.9	OOT	12170.2 $\pm$ 193.0	5572.0 $\pm$ 99.7
ModelNet40	17.2 $\pm$ 0.7	3872.1 $\pm$ 102.1	2107.1 $\pm$ 20.9	2975.7 $\pm$ 62.7	1120.7 $\pm$ 111.6

Appendix

Table 1: Embedding time (s) per dataset, and speed-up of HyperFuse over each baseline

Dataset	HyperFuse	TriCL	SE-HSSL	VilLain	HypeBoy
20News	43.59 $\pm$ 0.70	31.36 $\pm$ 3.68	38.17 $\pm$ 0.22	38.91 $\pm$ 0.12	31.61 $\pm$ 1.48
Citeseer	42.19 $\pm$ 1.16	44.12 $\pm$ 0.23	42.80 $\pm$ 2.27	24.93 $\pm$ 0.31	39.01 $\pm$ 0.51
Cora-CA	49.04 $\pm$ 3.02	50.03 $\pm$ 1.28	46.53 $\pm$ 0.67	9.43 $\pm$ 0.87	44.76 $\pm$ 0.80
Cora-CC	55.68 $\pm$ 0.66	55.20 $\pm$ 0.87	54.35 $\pm$ 1.66	36.56 $\pm$ 1.55	42.68 $\pm$ 0.47
DBLP	55.21 $\pm$ 0.89	62.33 $\pm$ 1.45	OOT	37.99 $\pm$ 0.50	59.42 $\pm$ 1.33
ModelNet40	93.75 $\pm$ 0.27	95.54 $\pm$ 0.15	95.51 $\pm$ 0.27	75.23 $\pm$ 0.28	79.32 $\pm$ 0.17

Appendix

Table 2: NMI (%) per dataset (

k

-means)

Dataset	HyperFuse	TriCL	SE-HSSL	VilLain	HypeBoy
20News	47.42 $\pm$ 1.45	20.43 $\pm$ 5.46	39.98 $\pm$ 0.52	38.86 $\pm$ 0.12	15.98 $\pm$ 2.18
Citeseer	41.66 $\pm$ 0.64	45.02 $\pm$ 0.31	42.02 $\pm$ 1.74	17.78 $\pm$ 0.70	38.63 $\pm$ 1.51
Cora-CA	44.30 $\pm$ 5.56	45.96 $\pm$ 3.13	38.52 $\pm$ 3.29	2.29 $\pm$ 0.76	37.15 $\pm$ 2.63
Cora-CC	50.05 $\pm$ 0.67	49.04 $\pm$ 0.12	45.55 $\pm$ 3.60	23.99 $\pm$ 2.26	27.75 $\pm$ 1.86
DBLP	42.52 $\pm$ 1.52	48.88 $\pm$ 2.33	OOT	30.14 $\pm$ 0.70	49.34 $\pm$ 1.23
ModelNet40	87.10 $\pm$ 0.78	94.33 $\pm$ 0.86	94.52 $\pm$ 0.77	55.61 $\pm$ 0.65	56.59 $\pm$ 0.79

Appendix

Table 3: ARI (%) per dataset (

k

-means)

Figure 1: Per-dataset NMI and ARI (

k

-means; mean over three seeds, error bars show one standard deviation). Avg. (8): mean over the eight datasets other than DBLP

Dataset	Classifier	Raw	HyperFuse	TriCL	SE-HSSL	VilLain	HypeBoy
20News	LogReg	78.65 $\pm$ 0.00	79.71 $\pm$ 0.17	77.22 $\pm$ 0.04	76.31 $\pm$ 0.27	79.20 $\pm$ 0.07	79.84 $\pm$ 0.09
	MLP	79.10 $\pm$ 0.18	79.48 $\pm$ 0.25	79.55 $\pm$ 0.20	78.76 $\pm$ 0.12	78.38 $\pm$ 0.33	79.80 $\pm$ 0.02
	HGNN	80.00 $\pm$ 0.08	79.12 $\pm$ 0.05	79.83 $\pm$ 0.11	79.62 $\pm$ 0.13	74.82 $\pm$ 0.09	77.76 $\pm$ 0.37
	HNHN	79.60 $\pm$ 0.05	79.78 $\pm$ 0.17	80.07 $\pm$ 0.06	79.65 $\pm$ 0.08	79.33 $\pm$ 0.28	79.74 $\pm$ 0.34
	UniGCNII	80.10 $\pm$ 0.08	79.73 $\pm$ 0.05	80.19 $\pm$ 0.07	79.84 $\pm$ 0.06	78.14 $\pm$ 0.08	78.64 $\pm$ 0.18
	AllSetTr.	79.62 $\pm$ 0.21	79.94 $\pm$ 0.20	80.31 $\pm$ 0.15	79.81 $\pm$ 0.36	80.23 $\pm$ 0.08	80.05 $\pm$ 0.18

Appendix

Table 1: Accuracy (%) per dataset and classifier (part 1)

Dataset	Classifier	Raw	HyperFuse	TriCL	SE-HSSL	VilLain	HypeBoy
ModelNet40	LogReg	95.63 $\pm$ 0.00	97.18 $\pm$ 0.03	96.96 $\pm$ 0.08	96.95 $\pm$ 0.05	86.54 $\pm$ 0.10	93.75 $\pm$ 0.06
	MLP	94.53 $\pm$ 0.13	96.02 $\pm$ 0.23	96.79 $\pm$ 0.19	96.83 $\pm$ 0.22	85.97 $\pm$ 0.49	91.83 $\pm$ 0.43
	HGNN	94.06 $\pm$ 0.02	93.61 $\pm$ 0.10	92.56 $\pm$ 0.06	92.46 $\pm$ 0.06	87.04 $\pm$ 0.16	88.93 $\pm$ 0.10
	HNHN	96.18 $\pm$ 0.20	96.73 $\pm$ 0.16	94.99 $\pm$ 0.17	94.63 $\pm$ 0.31	86.71 $\pm$ 0.06	90.90 $\pm$ 0.15
	UniGCNII	96.59 $\pm$ 0.01	95.80 $\pm$ 0.05	93.76 $\pm$ 0.09	93.71 $\pm$ 0.06	87.00 $\pm$ 0.03	90.00 $\pm$ 0.17
	AllSetTr.	97.04 $\pm$ 0.18	97.15 $\pm$ 0.07	95.55 $\pm$ 0.13	95.51 $\pm$ 0.11	87.05 $\pm$ 0.02	92.69 $\pm$ 0.31

Appendix

Table 2: Accuracy (%) per dataset and classifier (part 2)

Dataset	Classifier	Raw	HyperFuse	TriCL	SE-HSSL	VilLain	HypeBoy
20News	LogReg	76.25 $\pm$ 0.00	77.37 $\pm$ 0.22	74.84 $\pm$ 0.07	74.03 $\pm$ 0.29	76.52 $\pm$ 0.05	77.40 $\pm$ 0.06
	MLP	76.57 $\pm$ 0.13	76.85 $\pm$ 0.48	76.91 $\pm$ 0.25	76.36 $\pm$ 0.17	75.73 $\pm$ 0.50	77.23 $\pm$ 0.05
	HGNN	77.28 $\pm$ 0.14	75.98 $\pm$ 0.12	76.81 $\pm$ 0.23	76.67 $\pm$ 0.17	67.39 $\pm$ 0.29	73.61 $\pm$ 0.83
	HNHN	77.18 $\pm$ 0.05	77.26 $\pm$ 0.21	77.47 $\pm$ 0.14	77.19 $\pm$ 0.12	76.39 $\pm$ 0.37	76.96 $\pm$ 0.48
	UniGCNII	77.67 $\pm$ 0.03	76.96 $\pm$ 0.03	77.53 $\pm$ 0.04	77.32 $\pm$ 0.24	74.11 $\pm$ 0.13	75.28 $\pm$ 0.26
	AllSetTr.	77.24 $\pm$ 0.39	77.44 $\pm$ 0.24	78.01 $\pm$ 0.24	77.46 $\pm$ 0.37	77.70 $\pm$ 0.14	77.47 $\pm$ 0.15

Appendix

Table 3: Macro-F1 (%) per dataset and classifier (part 1)

Dataset	Classifier	Raw	HyperFuse	TriCL	SE-HSSL	VilLain	HypeBoy
ModelNet40	LogReg	94.19 $\pm$ 0.00	96.00 $\pm$ 0.07	95.97 $\pm$ 0.10	95.96 $\pm$ 0.03	83.27 $\pm$ 0.12	91.58 $\pm$ 0.07
	MLP	91.78 $\pm$ 0.22	93.21 $\pm$ 0.46	95.53 $\pm$ 0.37	95.51 $\pm$ 0.60	81.60 $\pm$ 0.80	87.62 $\pm$ 1.35
	HGNN	91.88 $\pm$ 0.09	91.19 $\pm$ 0.15	89.86 $\pm$ 0.18	89.59 $\pm$ 0.25	82.90 $\pm$ 0.36	82.18 $\pm$ 0.15
	HNHN	94.45 $\pm$ 0.34	95.10 $\pm$ 0.23	92.92 $\pm$ 0.29	92.55 $\pm$ 0.48	82.37 $\pm$ 0.21	86.93 $\pm$ 0.38
	UniGCNII	95.31 $\pm$ 0.04	94.21 $\pm$ 0.02	91.63 $\pm$ 0.07	91.60 $\pm$ 0.05	82.89 $\pm$ 0.17	85.30 $\pm$ 0.32
	AllSetTr.	95.79 $\pm$ 0.25	95.85 $\pm$ 0.13	93.94 $\pm$ 0.27	93.91 $\pm$ 0.21	82.95 $\pm$ 0.18	90.04 $\pm$ 0.46

Appendix

Table 4: Macro-F1 (%) per dataset and classifier (part 2)

Variant	Raw features $\hat{\mathbf{X}}$	Feature summary $\mathbf{F}$	Incidence summary $\mathbf{G}$
HyperFuse	✓	✓	✓
No side input	✓	–	–
Side F	✓	✓	–
Side G	✓	–	✓
Side only	–	✓	✓

Appendix

Table 1: Encoder inputs of the ablation variants. Stages A and B and the hyperedge weights are used in all variants

Dataset	HyperFuse	No side input	Side F	Side G	Side only
20News	79.71 $\pm$ 0.17	79.45 $\pm$ 0.01	79.50 $\pm$ 0.05	79.59 $\pm$ 0.07	79.09 $\pm$ 0.13
Citeseer	70.23 $\pm$ 0.55	70.74 $\pm$ 0.41	70.42 $\pm$ 0.60	68.25 $\pm$ 0.19	64.16 $\pm$ 0.19
Cora-CA	81.11 $\pm$ 0.41	81.07 $\pm$ 0.38	80.91 $\pm$ 0.39	79.65 $\pm$ 0.13	73.72 $\pm$ 0.70
Cora-CC	80.18 $\pm$ 0.36	80.14 $\pm$ 0.43	80.81 $\pm$ 0.28	80.09 $\pm$ 0.65	72.02 $\pm$ 1.11
ModelNet40	97.18 $\pm$ 0.03	96.83 $\pm$ 0.13	97.08 $\pm$ 0.08	96.97 $\pm$ 0.10	97.08 $\pm$ 0.02
NTU2012	74.91 $\pm$ 0.36	74.41 $\pm$ 0.14	74.37 $\pm$ 0.45	74.15 $\pm$ 0.17	73.67 $\pm$ 0.19

Appendix

Table 2: Ablation of the side input

[\mathbf{F}\mid\mathbf{G}]

: accuracy (%) with logistic regression. HyperFuse: full model (main results); No side input: raw features only; Side F / Side G: raw features and one block; Side only:

[\mathbf{F}\mid\mathbf{G}]

only. Mean

\pm

standard deviation over three seeds. Best in bold. Average: over the eight datasets other than DBLP

Dataset	HyperFuse	No side input	Side F	Side G	Side only
20News	77.37 $\pm$ 0.22	77.02 $\pm$ 0.06	77.06 $\pm$ 0.04	77.20 $\pm$ 0.04	76.74 $\pm$ 0.13
Citeseer	64.57 $\pm$ 0.50	65.23 $\pm$ 0.26	64.65 $\pm$ 0.97	62.34 $\pm$ 0.20	58.37 $\pm$ 0.18
Cora-CA	79.47 $\pm$ 0.64	79.36 $\pm$ 0.51	79.11 $\pm$ 0.37	77.80 $\pm$ 0.09	71.64 $\pm$ 0.74
Cora-CC	78.35 $\pm$ 0.54	78.10 $\pm$ 0.73	78.85 $\pm$ 0.40	77.90 $\pm$ 0.86	69.47 $\pm$ 1.05
ModelNet40	96.00 $\pm$ 0.07	95.62 $\pm$ 0.18	95.93 $\pm$ 0.06	95.77 $\pm$ 0.12	96.18 $\pm$ 0.08
NTU2012	62.21 $\pm$ 0.44	62.17 $\pm$ 0.35	61.96 $\pm$ 0.64	61.39 $\pm$ 0.22	61.28 $\pm$ 0.12

Appendix

Table 3: Ablation of the side input

[\mathbf{F}\mid\mathbf{G}]

: macro-F1 (%) with logistic regression. HyperFuse: full model (main results); No side input: raw features only; Side F / Side G: raw features and one block; Side only:

[\mathbf{F}\mid\mathbf{G}]

only. Mean

\pm

standard deviation over three seeds. Best in bold. Average: over the eight datasets other than DBLP

Dataset	Model	100%	50%	20%	5%	Noise	Noise ∗
20News	HyperFuse	79.71 $\pm$ 0.17	77.46 $\pm$ 0.66	77.82 $\pm$ 0.33	78.39 $\pm$ 0.01	29.57 $\pm$ 0.84	75.35 $\pm$ 0.78
20News	Encoder	79.49 $\pm$ 0.16	77.56 $\pm$ 0.21	78.02 $\pm$ 0.29	78.12 $\pm$ 0.37	28.20 $\pm$ 0.47	43.73 $\pm$ 0.77
Citeseer	HyperFuse	70.23 $\pm$ 0.55	67.00 $\pm$ 2.03	59.40 $\pm$ 1.61	42.14 $\pm$ 2.62	18.95 $\pm$ 0.63	23.41 $\pm$ 0.53
Citeseer	Encoder	70.75 $\pm$ 0.53	66.76 $\pm$ 1.69	60.85 $\pm$ 0.94	47.68 $\pm$ 1.48	19.45 $\pm$ 0.73	24.13 $\pm$ 1.08
Cora-CA	HyperFuse	81.11 $\pm$ 0.41	73.44 $\pm$ 3.58	61.39 $\pm$ 3.83	43.22 $\pm$ 0.99	17.96 $\pm$ 0.55	23.55 $\pm$ 0.96
Cora-CA	Encoder	81.23 $\pm$ 0.47	74.26 $\pm$ 2.78	64.14 $\pm$ 2.70	46.03 $\pm$ 1.87	18.60 $\pm$ 0.42	21.78 $\pm$ 0.28

Appendix

Table 1: Accuracy (%) of logistic regression with degraded node features. Columns: fraction of feature columns kept, or Gaussian noise features (Noise: automatic feature dropout,

p_{f}=0

; Noise ∗ :

p_{f}=0.3

). Encoder: the Stage-C encoder alone, without Stages A and B. Mean

\pm

standard deviation over three seeds. Better of the two models in bold

Dataset	Model	100%	50%	20%	5%	Noise	Noise ∗
20News	HyperFuse	77.37 $\pm$ 0.22	74.92 $\pm$ 0.54	75.13 $\pm$ 0.36	75.79 $\pm$ 0.16	26.30 $\pm$ 0.92	72.16 $\pm$ 0.92
20News	Encoder	77.06 $\pm$ 0.16	74.99 $\pm$ 0.15	75.28 $\pm$ 0.27	75.23 $\pm$ 0.39	24.85 $\pm$ 0.45	39.29 $\pm$ 1.31
Citeseer	HyperFuse	64.57 $\pm$ 0.50	61.75 $\pm$ 2.54	54.28 $\pm$ 1.90	37.49 $\pm$ 2.95	17.26 $\pm$ 0.79	21.44 $\pm$ 0.51
Citeseer	Encoder	65.31 $\pm$ 0.24	61.64 $\pm$ 1.59	55.59 $\pm$ 0.91	42.22 $\pm$ 1.20	17.46 $\pm$ 0.61	21.84 $\pm$ 0.88
Cora-CA	HyperFuse	79.47 $\pm$ 0.64	71.10 $\pm$ 3.93	58.81 $\pm$ 2.41	38.22 $\pm$ 0.72	14.62 $\pm$ 0.71	19.32 $\pm$ 0.92
Cora-CA	Encoder	79.58 $\pm$ 0.67	72.28 $\pm$ 2.86	61.60 $\pm$ 1.64	41.07 $\pm$ 3.17	15.21 $\pm$ 0.55	17.62 $\pm$ 0.24

Appendix

Table 2: Macro-F1 (%) of logistic regression with degraded node features. Columns: fraction of feature columns kept, or Gaussian noise features (Noise: automatic feature dropout,

p_{f}=0

; Noise ∗ :

p_{f}=0.3

). Encoder: the Stage-C encoder alone, without Stages A and B. Mean

\pm

standard deviation over three seeds. Better of the two models in bold

Hypergraph Learning

Hypergraph learning models relationships among groups of entities to capture interactions that pairwise graphs cannot represent.

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Mar 10, 2026

From Representation to Clusters: A Contrastive Learning Approach for Attributed Hypergraph Clustering

Contrastive learning has demonstrated strong performance in attributed hypergraph clustering. Typically, existing methods based on contrastive learning first learn node embeddings and then apply clustering algorithms, such as k-means, to these embeddings to obtain the clustering results.However, these methods lack direct clustering supervision, risking the inclusion of clustering-irrelevant information in the learned graph.To this end, we propose a Contrastive learning approach for Attributed Hypergraph Clustering (CAHC), an end-to-end method that simultaneously learns node embeddings and obtains clustering results. CAHC consists of two main steps: representation learning and cluster assignment learning. The former employs a novel contrastive learning approach that incorporates both node-level and hyperedge-level objectives to generate node embeddings.The latter joint embedding and clustering optimization to refine these embeddings by clustering-oriented guidance and obtains clustering results simultaneously.Extensive experimental results demonstrate that CAHC outperforms baselines on eight datasets.

Li Ni, Shuaikang Zeng, Lin Mu +1

School of Computer Science and Technology, Anhui University, Hefei, China · School of Computer Science and Technology, Southwest University, Chongqing, China

Hypergraph Learning Deep Clustering Contrastive Learning

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Feb 16, 2026

BHyGNN+: Unsupervised Representation Learning for Heterophilic Hypergraphs

Hypergraph Neural Networks (HyGNNs) have demonstrated remarkable success in modeling higher-order relationships among entities. However, their performance often degrades on heterophilic hypergraphs, where nodes connected by the same hyperedge tend to have dissimilar semantic representations or belong to different classes. While several HyGNNs, including our prior work BHyGNN, have been proposed to address heterophily, their reliance on labeled data significantly limits their applicability in real-world scenarios where annotations are scarce or costly. To overcome this limitation, we introduce BHyGNN+, a self-supervised learning framework that extends BHyGNN for representation learning on heterophilic hypergraphs without requiring ground-truth labels. The core idea of BHyGNN+ is hypergraph duality, a structural transformation where the roles of nodes and hyperedges are interchanged. By contrasting augmented views of a hypergraph against its dual using cosine similarity, our framework captures essential structural patterns in a fully unsupervised manner. Notably, this duality-based formulation eliminates the need for negative samples, a common requirement in existing hypergraph contrastive learning methods that is often difficult to satisfy in practice. Extensive experiments on eleven benchmark datasets demonstrate that BHyGNN+ consistently outperforms state-of-the-art supervised and self-supervised baselines on both heterophilic and homophilic hypergraphs. Our results validate the effectiveness of leveraging hypergraph duality for self-supervised learning and establish a new paradigm for representation learning on challenging, unlabeled hypergraphs.

Tianyi Ma, Yiyue Qian, Zehong Wang +3

♠University of Notre Dame · ♣Amazon GenAI · ♦University of Connecticut

Hypergraph Learning Hypergraph Neural Networks Unsupervised Representation Learning Contrastive Learning

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Apr 30, 2026

A Unified Framework of Hyperbolic Graph Representation Learning Methods

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result, numerous hyperbolic graph representation learning methods have been proposed in recent years. However, their practical adoption and systematic comparison remain challenging, as implementations are fragmented and shared tools for reproducible and fair evaluation are lacking. In this work, we introduce a unified open-source framework for hyperbolic graph representation learning that integrates several widely used embedding methods under a common optimization interface. The novel framework enables consistent training, visualization, and evaluation of hyperbolic embeddings, and interfaces seamlessly with standard network analysis tools. Leveraging this unified setup, we conduct an experimental study of hyperbolic embedding methods on real-world networks, focusing on two canonical downstream tasks: link prediction and node classification. Beyond predictive accuracy, the study offers practical insights into the strengths and limitations of existing approaches, thereby facilitating informed method selection and fostering reproducible research in hyperbolic graph representation learning.

Sofía Pérez Casulo, Marcelo Fiori, Bernardo Marenco +1

Facultad de Ingenier´ıa, Universidad de la Rep´ublica, Uruguay · Centro Interdisciplinario en Ciencia de Datos y Aprendizaje Autom´atico (CICADA), Universidad de la Rep´ublica, Uruguay

Graph Representation Learning Graph Embedding Hyperbolic Representation Learning

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Abstract

Hypergraph Learning

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