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HyperFuse: Fast Self-Supervised Node Embeddings for Attributed Hypergraphs

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

arXiv:2610.03211v1cs.LG

TL;DR

Self-supervised hypergraph embeddings can be costly to generate, especially when many or evolving hypergraphs need repeated embeddings. HyperFuse combines matrix-free modularity, feature summaries, and short encoder training in a label-free pipeline. Across eight benchmark datasets, it was substantially faster than the baselines while matching the strongest methods' quality on the reported tests.

  • Problem

    Existing self-supervised hypergraph methods train neural encoders for hundreds to thousands of epochs, and repeated embeddings for collections or evolving hypergraphs make per-embedding time consequential.

    Source: §1 · p. 2

  • Method

    HyperFuse is a label-free three-stage pipeline whose inexpensive linear-algebraic stages provide structural and hyperedge-reliability information to a short self-supervised encoder.

    Source: §1 · p. 3, §4 · p. 5

  • Results

    On eight datasets, HyperFuse was 13× faster than HypeBoy on geometric mean, while classification and clustering scores were not significantly different from TriCL and SE-HSSL and exceeded HypeBoy's with every classifier.

    Source: §1 · p. 3, §7 · p. 20

  • Takeaways & Limitations

    At seconds per embedding, HyperFuse is suited to analyses requiring many embeddings, including patient-specific network collections, and is a natural starting point for evolving hypergraphs.

    Source: §8 · p. 21

    The study did not evaluate patient-specific network collections or evolving hypergraphs, and new snapshots are embedded from scratch rather than incrementally updated.

    Source: Towards evolving hypergraphs · p. 21

Abstract

from arXiv · show

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.

1 Introduction

HyperFuse targets the high cost of self-supervised hypergraph embeddings with a label-free pipeline that combines structural and feature information with short encoder training. On eight datasets, it was fastest on every dataset while retaining competitive downstream quality.

1 Introduction

  • Existing self-supervised methods can require hundreds to thousands of training epochs, with official configurations taking 4 seconds to 9.1 hours per hypergraph.On PubMed, TriCL took 9.1 hours, SE-HSSL 3.5 hours, and VilLain 1.4 hours; HypeBoy took 1.0 minute there but 2.3 hours on 20News.Source: §1 · p. 2
  • Embedding time matters especially when each network in a collection needs its own embedding or changing memberships and attributes require recomputing evolving-hypergraph snapshots.The paper gives patient-specific molecular networks as an example of collections.Source: §1 · p. 2
  • HyperFuse uses matrix-free modularity coordinates, corruption-consistent feature summaries with bounded hyperedge utilities, and a small encoder trained for 100 epochs.Its modularity operator uses Banerjee's hypergraph adjacency, and the encoder uses a correlation-based self-supervised objective.Source: §1 · p. 3
  • The benchmark evaluates four official-configuration baselines on nine public hypergraphs using six classifiers, two clustering scores, embedding time, and rank-based statistical tests.The four baselines are TriCL, SE-HSSL, VilLain, and HypeBoy.Source: §1 · p. 3
  • On eight datasets, HyperFuse was fastest on every dataset, had the highest average accuracy with five of six classifiers, and was not significantly different from TriCL and SE-HSSL in classification and clustering.Its classification and clustering scores were higher than HypeBoy's with every classifier.Source: §1 · p. 3

2 Related work

Related work spans hypergraph neural architectures, self-supervised learning methods, and efficient embedding approaches. HyperFuse draws on modularity and propagation ideas while replacing graph-based and label-aware components with a hypergraph-specific, label-free pipeline.

Hypergraph neural networks.

  • Hypergraph neural networks generalize graph convolution through node-to-hyperedge and hyperedge-to-node aggregation, with designs based on incidence operators, pairwise approximations, hyperedge neurons, transferred architectures, or multiset functions.Examples include HGNN (Feng et al. 2019), HyperGCN (Yadati et al. 2019), HNHN (Dong et al. 2020), UniGNN (Huang and Yang 2021), and AllSet (Chien et al. 2022); the paper uses these models as downstream classifiers.Source: Hypergraph neural networks · pp. 3–4

Self-supervised hypergraph learning.

  • Self-supervised hypergraph methods span augmented-view contrast, sampling-free correlation objectives, structure-only virtual labels, and generative hyperedge filling.The closest approaches are TriCL (Lee and Shin 2023), SE-HSSL (Li et al. 2024), VilLain (Lee et al. 2024), and HypeBoy (Kim et al. 2024a); HyperGCL was excluded because official runs across datasets and seeds already required about 111 GPU-hours.Source: Self-supervised hypergraph learning · p. 4

Efficient embeddings and modularity.

  • FUSE (Chakraborty et al. 2026) combines relaxed graph modularity with label-aware terms, whereas HyperFuse uses exact modularity, Banerjee's hypergraph adjacency, no labels, and added feature and self-supervised stages.The paper also adopts multi-hop averaging from SGC (Wu et al. 2019) and SSGC (Zhu and Koniusz 2021).Source: Efficient embeddings and modularity · p. 4

3 Problem setting and notation

This section specifies an attributed hypergraph through its nodes, hyperedges, features, and incidence structure, then frames the task as quickly producing label-free embeddings for downstream use.

3 Problem setting and notation

  • The notation distinguishes italic scalars, bold lowercase vectors, bold uppercase matrices, and calligraphic sets.It also defines row notation, identity and all-ones symbols, Frobenius norm, column-wise concatenation, and the orthonormal factor of a thin QR decomposition.Source: §3 · p. 4
  • The incidence matrix H records node–hyperedge membership, and nnz(H) counts the incidences.The setup discards hyperedges with fewer than two members.Source: §3 · p. 5
  • The task is to compute a label-free embedding matrix that is useful for downstream node classification and clustering, and to do so quickly.The attributed hypergraph includes node features and a node set connected by hyperedges.Source: §3 · p. 5

4 HyperFuse

This section presents HyperFuse, a label-free pipeline combining structural coordinates, multi-scale feature summaries, hyperedge utility weights, and a lightweight encoder, and describes its computational scaling in contrast with all-node contrastive training.

4 HyperFuse

  • HyperFuse computes structural coordinates in Stage A, feature and incidence summaries plus hyperedge utilities in Stage B, and trains a utility-weighted encoder in Stage C.No stage uses labels; Stage C is the only stage using a neural network trained by gradient descent.Source: §4 · p. 5, Figure 1 · p. 6

4.1 Stage A: modularity on Banerjee’s hypergraph adjacency

  • Stage A maximizes a spectral relaxation of modularity using node strengths equal to incident-hyperedge counts and computes matrix products directly from the sparse incidence matrix.This avoids materializing the adjacency or modularity matrix; the product costs O((nnz(H) + N)ds). Projected ascent converges geometrically under the stated assumptions, while Zoo has a non-unique leading 32-dimensional eigenspace.Source: §4.1 · pp. 6, 7, 9

Feature summary F.

  • Feature summaries compare three propagation scales across feature-masked and structure-masked views, while the incidence summary uses leading left singular vectors of the normalized incidence matrix.The feature summary is a truncated SVD of scale representations weighted by node-level agreement between views; propagation includes a multi-hop average.Source: Propagation · pp. 9–10, Corruptions · p. 10, Feature summary F · p. 10

Hyperedge utility u.

  • HyperFuse assigns hyperedge utilities from member stability under feature and membership corruptions, comparing each hyperedge with size-matched random groups and clipping weights to [0.65, 1.35].A ridge regression predicts stability targets from 13 hyperedge descriptors; the resulting weights have mean one and retain every hyperedge.Source: Hyperedge utility u · p. 11

Aggregation.

  • The encoder aggregates node representations to hyperedges by retained-member means and back to nodes by utility-weighted means, then applies a two-layer hypergraph encoder with propagation.Nodes without retained incidences receive zero aggregates; the encoder uses raw features alongside the Stage-B summaries.Source: Figure 1 · p. 6, Aggregation · p. 12, Encoder · p. 12

Objective.

  • Stage C trains on two independently corrupted views with an invariance-plus-decorrelation objective, then evaluates the encoder on the uncorrupted hypergraph to produce normalized embeddings.The objective uses a fixed 100-epoch budget and requires no negative pairs, projection heads, or target networks.Source: Objective · pp. 12–13, Output · p. 13

Relation to SE-HSSL.

  • Unlike SE-HSSL, HyperFuse uses a single node-level objective, no hyperedge- or membership-level terms, utility-weighted aggregation, and precomputed structural and spectral inputs.Its training budget is fixed at 100 epochs.Source: Relation to SE-HSSL · p. 13

4.4 Computational cost

  • Stage A runs for at most 1,000 iterations and Stage C for 100 epochs; the stated cost analysis also accounts for Stage B’s propagation, truncated SVDs, and hyperedge descriptors.Stage A’s iteration cost is based on the sparse-incidence product and QR factorization; Stage B stores dense N × D and N × 3D arrays.Source: §4.4 · p. 13
  • For fixed widths, HyperFuse’s stages scale linearly in nH and nX except dense feature operations and small-graph dense SVD; it uses LOBPCG otherwise.When min(N, M) ≤ 3,000, dense SVD of R costs O(NM min(N, M)) time and O(NM) memory.Source: §4.4 · pp. 13–14
  • Official TriCL configurations without negative subsampling require O(N^2d) operations and O(N^2) memory per epoch to compare every node with all others.Source: §4.4 · p. 14

5 Experimental setup

The experiments benchmark HyperFuse and four self-supervised hypergraph embedding methods across nine public datasets, using classification, clustering, runtime, and statistical comparisons to assess their performance.

5.1 Datasets

  • The nine datasets span 101–41,302 nodes, hyperedges of up to 2,241 nodes, varied feature types, and 3–67 classes.Nodes belonging to no hyperedge were removed from the preprocessed datasets.Source: §5.1 · p. 14

5.2 Baselines

  • Four public-code baselines were run with their authors’ released configurations, including VilLain’s virtual-label models and HypeBoy’s 128-dimensional embeddings.The baselines were TriCL, SE-HSSL, VilLain, and HypeBoy; VilLain used 100 propagation steps at inference.Source: §5.2 · pp. 14–15

5.3 HyperFuse configuration

  • HyperFuse used one default configuration with d = 128 and no per-dataset hyperparameters; feature dropout was set by feature type.The dropout rate was 0.3 for sparse or discrete features and 0 for dense real-valued descriptors.Source: §5.3 · p. 15

5.4 Evaluation protocol

  • Each dataset, method, and seed produced one embedding for evaluation.The benchmark used three seeds, {0, 1, 2}.Source: §5.4 · p. 15

Classification.

  • Six downstream classifiers were evaluated on 10%/10%/80% train/validation/test splits, with test accuracy and macro-F1 averaged over three fixed splits.LogReg and MLP ignore the hypergraph; the other four classifiers also use it.Source: Classification · p. 15

Clustering.

  • K-means used k equal to the number of classes, and clustering was measured by mean ARI and NMI.The evaluation used 10 initialisations and five k-means seeds.Source: Clustering · p. 15

Runtime.

  • Embedding time included each method’s internal preprocessing but excluded dataset loading and downstream evaluation.Methods ran on the same workstation with an NVIDIA T1000 GPU; HyperFuse’s Stages A and B ran on the CPU.Source: Runtime · pp. 15–16

Aggregation and statistics.

  • Results were averaged over three seeds; averages and paired tests used the eight datasets where all methods completed, with DBLP reported separately.The authors report uncorrected p-values and note that tests across eight datasets have limited power to detect small differences.Source: Aggregation and statistics · p. 16

6 Results

On the common datasets, HyperFuse was substantially faster while matching the classification and clustering quality of TriCL and SE-HSSL; DBLP results were reported separately because SE-HSSL did not complete there.

6.1 Embedding time

  • 143×, 96×, 179×, and 13× were HyperFuse’s geometric-mean speed-ups over TriCL, SE-HSSL, VilLain, and HypeBoy, respectively.HyperFuse was fastest on all nine datasets; its mean time was 8.7 s on the eight common datasets.Source: §6.1 · p. 16, Figure 2 · p. 17

6.2 Embedding quality

  • 60.22% NMI and 55.76% ARI were HyperFuse’s clustering scores, but no method dominated across datasets.HyperFuse led on both measures on 20News, Cora-CC, and NTU2012, while TriCL led on most other datasets.Source: §6.2 · p. 18

Statistical comparison.

  • On the benchmarks, HyperFuse matched TriCL and SE-HSSL in classification and clustering quality and exceeded HypeBoy and VilLain, but evidence did not support greater accuracy than TriCL or SE-HSSL.Only one of 24 classification comparisons with TriCL and SE-HSSL was significant; none of the clustering comparisons with them was significant.Source: Table 3 · p. 17, Statistical comparison · p. 19

6.3 Results on DBLP

  • On DBLP, HyperFuse took 110.4 s; its accuracy was within 3.7 points of the most accurate method across downstream classifiers.SE-HSSL did not complete within 24 hours; HyperFuse was 202× faster than TriCL, 110× faster than VilLain, and 50× faster than HypeBoy.Source: §6.3 · p. 19

7 Discussion and limitations

On the eight benchmark hypergraphs where all methods completed, HyperFuse matched TriCL and SE-HSSL statistically on classification and clustering while running much faster, and outperformed HypeBoy. The discussion identifies potential uses and design considerations for evolving hypergraphs, alongside evaluation, runtime, memory, and statistical-power limitations.

7 Discussion and limitations

  • 13× faster on geometric mean than HypeBoy, HyperFuse’s embeddings performed better than HypeBoy’s, while classification and clustering scores did not differ significantly from TriCL and SE-HSSL.The comparison covers the eight datasets on which all methods completed; HyperFuse was also described as two orders of magnitude faster than TriCL and SE-HSSL.Source: §7 · pp. 19–20
  • Stages A and B scale with incidences rather than node pairs, and Stage C costs O(Nd^2) per epoch rather than O(N^2d).HyperFuse trained Stage C for 100 epochs and used one configuration across datasets, unlike TriCL and SE-HSSL, which used author-provided per-dataset configurations.Source: §7 · p. 20
  • About 12 min for 100 PubMed-sized hypergraphs with HyperFuse versus about 38 days with TriCL, under an illustrative assumption that runtimes add and all collection members resemble PubMed.The estimate ignores parallelism and is arithmetic based on measured PubMed times, not a measurement of a collection.Source: §7 · p. 20

Towards evolving hypergraphs.

  • For evolving hypergraphs, Stage A could start from the previous snapshot’s structural subspace and Stage C weights could be carried over and fine-tuned.The authors had not evaluated HyperFuse on evolving hypergraphs; successive spectral summaries may need adaptation, and rotational invariance requires aligning embeddings across snapshots.Source: Towards evolving hypergraphs · pp. 20–21
  • The evaluation did not cover patient-specific collections or evolving hypergraphs, inductive settings, or hyperedge prediction; most results used informative node features.On citation hypergraphs, structural stages did not help when features were weak, apart from the artificial feature degradation experiment.Source: Towards evolving hypergraphs · p. 21
  • Runtime comparisons used one workstation, with HyperFuse’s Stages A and B on CPU and other training on GPU; absolute times may differ on other hardware.Baselines used their official epoch budgets and widths, which differed from HyperFuse’s 128 dimensions; SE-HSSL’s DBLP timeout applies to the tested hardware.Source: Towards evolving hypergraphs · p. 21
  • Stage B’s dense feature arrays scale in memory with node count times feature dimension, a concern for very high-dimensional features but not these benchmarks.The arrays have dimensions N × D and N × 3D.Source: Towards evolving hypergraphs · p. 21
  • Eight datasets, three seeds, and three of TriCL’s 20 splits provided limited power to detect differences; no detected difference does not establish equivalence.Source: Towards evolving hypergraphs · p. 21

8 Conclusion

HyperFuse combines matrix-free modularity maximisation, corruption-consistent feature summaries with bounded hyperedge utility weights, and short correlation-based training. On eight benchmark hypergraphs it was substantially faster than four self-supervised baselines, with classification and clustering quality not significantly different from two strong baselines and higher than HypeBoy’s; evaluating collections and evolving hypergraphs remains a next step.

8 Conclusion

  • HyperFuse combines matrix-free modularity maximisation on Banerjee’s hypergraph adjacency, corruption-consistent feature summaries with bounded hyperedge utility weights, and short correlation-based training.Source: §8 · p. 21
  • 13–179× faster on geometric mean than four self-supervised baselines on eight benchmark hypergraphs, with classification and clustering quality not significantly different from TriCL and SE-HSSL and higher than HypeBoy’s.Source: §8 · p. 21
  • Seconds-per-embedding makes HyperFuse suited to analyses requiring many embeddings, such as patient-specific network collections, and a natural starting point for evolving hypergraphs.The authors identify evaluation in those settings as the next step.Source: §8 · p. 21

Declarations

The declarations report funding, competing interests, data availability, and code availability. Appendices A and B describe the configurations and the dataset-wise timing, clustering, and classifier results.

Declarations

  • The work reports funding for Anirban Banerjee, no competing interests, publicly available preprocessed datasets, and code availability.Ethics approval and consent to participate, and consent for publication, are listed as not applicable.Source: Declarations · p. 22

Appendix A Configurations

  • HyperFuse’s default configuration uses d = 128 unchanged across datasets, while the baseline settings follow official configurations and include dataset-specific epoch counts and embedding widths.VilLain trains seven models with 2–8 virtual labels, each for up to 5,000 epochs with early stopping; VilLain and HypeBoy output 128 dimensions on all datasets.Source: Table A1 · p. 26, Table A2 · p. 27

Appendix B Dataset-wise results

  • Appendix B’s table values are means and standard deviations over three seeds, with accuracy and macro-F1 by downstream classifier reported in Appendix C.Source: Appendix B · p. 27
  • Appendix B reports embedding time and speed-up per dataset, plus per-dataset k-means NMI and ARI; its average covers eight datasets other than DBLP.The NMI and ARI figure reports means over three seeds with one-standard-deviation error bars.Source: Table B1 · p. 27, Table B2 · p. 28, Table B3 · p. 28

Appendix C Results per downstream classifier

Appendix C reports per-dataset accuracy and macro-F1 across downstream classifiers. Its results are presented in four tables, divided into parts 1 and 2 for each metric.

Appendix C Results per downstream classifier

  • Scores are means and standard deviations over three seeds, with each test score averaged over three splits; raw node features are included as a reference, not among the five embedding methods ranked best or second-best.For the four hypergraph-aware classifiers, raw features are evaluated in their standard semi-supervised use.Source: Appendix C · p. 29
  • Accuracy (%) per dataset and classifier is reported in Tables C1 and C2, divided into parts 1 and 2.Source: Table C1 · p. 29, Table C2 · p. 30
  • Macro-F1 (%) per dataset and classifier is reported in Tables C3 and C4, divided into parts 1 and 2.Source: Table C3 · p. 31, Table C4 · p. 32

Appendix D Ablation of the side input

The Appendix D ablation compares encoder side-input variants using logistic regression on frozen embeddings. The full side input gives the highest average accuracy, though its margin over the other variants is small.

Appendix D Ablation of the side input

  • Logistic regression on frozen embeddings evaluates how linearly separable the classes are in each variant’s embedding.Stages A and B and hyperedge weights remain unchanged across variants.Source: Appendix D · p. 33, Table D1 · p. 33
  • The variants compare raw features alone, raw features plus one or both side-input blocks, and the side input alone.Table D1 lists the encoder inputs for each variant.Source: Table D1 · p. 33, Appendix D · p. 33
  • 80.37% average accuracy with the full side input, versus 80.24% without it, 80.14% with F only, and 79.75% with G only.The average excludes DBLP; results are means over three seeds.Source: Appendix D · p. 33, Table D2 · p. 33

Appendix E Robustness to weak node features

The appendix tests whether HyperFuse’s structural stages help when node features are degraded. The full model and encoder alone perform alike with full features, while their accuracy gap grows as features are removed.

Appendix E Robustness to weak node features

  • 19.37 points separated HyperFuse and the encoder alone with Noise* features, and 5.23 points with 5% of feature columns.The difference was concentrated on ModelNet40, NTU2012, PubMed, Zoo, and, for noise features, 20News; on citation hypergraphs, the encoder alone was up to 5.5 points more accurate with 20% or 5% of columns.Source: Appendix E · p. 35, Table E1 · p. 35
  • With full features, HyperFuse and the Stage-C encoder alone achieved 80.37% and 80.23% average accuracy, respectively.The encoder-alone condition uses raw features only and uniform hyperedge weights; both models receive the same degraded features in the tests.Source: Appendix E · p. 35, Table E1 · p. 35
  • The evaluation varies the fraction of feature columns retained and includes Gaussian noise features with automatic dropout or dropout set to 0.3.Macro-F1 follows the same pattern as accuracy.Source: Table E1 · p. 35, Appendix E · p. 35, Table E2 · p. 36
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