Pith. sign in

REVIEW 3 major objections 5 minor 48 references

Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learning

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper aims to establish that a hypergraph can be lifted, without loss of information, to a symmetric simplicial set whose degree-zero normalized sheaf Laplacian generalizes the graph one, enabling the first principled extension of…

desk verdict Has a real hole in its central graph-reduction proposition, but the lifting construction and HNSD recipe are worth engaging with. read the letter →

arxiv 2505.05702 v3 pith:FJQI4LP7 submitted 2025-05-09 cs.LG math.AT

Seongjin Choi , Gahee Kim , Yong-Geun Oh This is my paper · ORCID
classification cs.LGmath.AT
keywords cellularsheaftheoryLaplacianhypergraphneuralnetworkssymmetricsimplicialsetsdiffusionhigher-orderlearningnodeclassification
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's aim is to give hypergraphs a sheaf-theoretic Laplacian, which graphs have long had, by first resolving a structural obstacle: hypergraphs have no intrinsic adjacency between nodes or hyperedges. The proposed solution, symmetric simplicial lifting, records every hyperedge as all ordered tuples of its nodes while tagging each tuple with the hyperedge it came from, so the original hypergraph can be recovered from the lifted object. On this lifting the paper defines a degree-zero cellular sheaf Laplacian and proves that when the hypergraph is a graph the normalized operator reduces exactly to the classical normalized graph sheaf Laplacian. That reduction, plus the recovery property, is what licenses the paper's central architectural claim: Hypergraph Neural Sheaf Diffusion (HNSD) is a principled extension of neural sheaf diffusion to hypergraphs, and the paper reports competitive node-classification accuracy on five benchmark datasets.

What carries the argument

The central object is the symmetric simplicial lifting $\Delta(H)$ of a hypergraph: a symmetric simplicial set whose simplices are ordered tuples of vertices carrying the originating hyperedge as a label, glued only along nodes. Adjacency is defined canonically through facet maps, so two simplices are upper adjacent when they share a common cofacet and lower adjacent when they share a common facet, with signed incidences $(-1)^i$ governing diffusion. The load-bearing identity is Proposition 3: for a graph, the normalized degree-zero sheaf Laplacian built on $\Delta(G)$ equals the traditional normalized graph sheaf Laplacian, because each edge contributes two ordered cofacets $[v,w]_e$ and $[w,v]_e$ whose factor of $2$ cancels under normalization. This identity is what lets the paper call HNSD a principled hypergraph extension of neural sheaf diffusion rather than a merely analogous construction.

What would settle it

For one graph edge $e=\{v,w\}$, compute the degree-zero normalized Laplacian on $\Delta(G)$ under Definitions 4, 7 and 8 while including the degenerate cofacet $[v,v]_v$ (and $[w,w]_v$) in the diagonal and adjacency sums; if the diagonal gains extra identity terms, then $L^0_{\hat{\mathcal{F}}} = L_{\mathcal{F}}$ fails unless degenerate cofacets are explicitly excluded.

Watch

Extended reading notes

Core claim

The paper asserts that a hypergraph $H$ can be converted without loss of information into a symmetric simplicial set $\Delta(H)$ whose $n$-simplices are tagged ordered tuples $[v_0,\dots,v_n]_e$, with degenerate tuples shared across hyperedges only when they collapse to the same node. Maximal nondegenerate simplices reconstruct $H$ exactly (Proposition 1). When $H$ is a graph, any cellular sheaf $\mathcal{F}$ on the graph induces a sheaf $\hat{\mathcal{F}}$ on $\Delta(G)$ satisfying $L^0_{\hat{\mathcal{F}}} = L_{\mathcal{F}}$; the paper proves the normalized operators coincide because both the unnormalized Laplacian and the diagonal blocks acquire the same factor of $2$ from the two ordered $1$-simplices per edge (Proposition 3). The paper then instantiates degree-zero neural sheaf diffusion on $\Delta(H)$, with learnable restriction maps, and shows by experiments that the resulting HNSD model matches or exceeds existing hypergraph and sheaf-hypergraph baselines.

Load-bearing premise

The graph-reduction equality assumes that the only cofacets of a node contributing to the degree-zero Laplacian are the nondegenerate ordered 1-simplices of each incident edge, with degenerate self-simplices contributing nothing.

Editorial extensions

If this is right

  • Because $\Delta(H)$ recovers $H$ exactly from maximal nondegenerate simplices, any hypergraph neural network built on the lifting can in principle be inverted back to the hypergraph, so no relational information is discarded by the construction.
  • Since the normalized degree-zero Laplacian on $\Delta(G)$ equals the classical normalized graph sheaf Laplacian, graph neural sheaf diffusion is recovered as the size-two hyperedge case, making HNSD a strict generalization rather than an unrelated operator.
  • The framework also defines degree-$k$ sheaf Laplacians on $\Delta(H)$, so hyperedge features can be diffused through cofacet adjacency, not only node features through edge adjacency.
  • HNSD's learnable restriction maps allow dissimilar nodes within a hyperedge to exchange features in a controlled way, which the paper argues is why it gains on heterophilic datasets such as Senate.
  • The construction removes the need for an arbitrary total ordering of vertices, resolving the orientation ambiguity that arises when hypergraphs are turned into simplicial complexes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the hyperedge tags in $\Delta(H)$ imply a context-aware family of diffusions: the same node pair can diffuse through different stalks when it appears in different hyperedges, a modeling choice the paper introduces but does not isolate in its ablations.
  • Degree-$k$ Laplacians on $\Delta(H)$ open a direct route to hyperedge-level tasks such as hyperedge classification or hypergraph link prediction without inventing a separate architecture.
  • Because recovery is exact, the lifting could serve as a canonical certified input representation for non-diffusive hypergraph networks as well, separating structure-preserving preprocessing from message-passing design.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper introduces symmetric simplicial lifting, a construction that turns a hypergraph H into a symmetric simplicial set Δ(H) by collecting all ordered tuples on each hyperedge fH(e) and gluing the diagonal degenerate tuples [v,...,v]_e across all hyperedges to a single simplex [v,...,v]_v for each node v. The authors argue that this construction avoids the two defects of the simplicial-complex filling: the provenance of each subrelation is preserved, and no total order on the vertex set is required for orientations. The paper proves (Proposition 1) that the original hypergraph can be recovered from Δ(H) up to isomorphism and claims (Proposition 3) that for a graph G the normalized degree-0 sheaf Laplacian on the lifting Δ(G) equals the traditional normalized graph sheaf Laplacian. On this basis it defines Hypergraph Neural Sheaf Diffusion (HNSD), a learned degree-0 sheaf diffusion model, and reports node-classification results on Cora, Citeseer, Cora-CA, DBLP-CA, and Senate, together with an ablation study and a comparison against established hypergraph GNN baselines.

Significance. If Proposition 3 were established, the contribution would be substantial: an order-independent, provenance-preserving combinatorial framework on which sheaf Laplacians of arbitrary degree can be defined uniformly, with an exact consistency check against the graph case. The structure-recovery property (Proposition 1) is demonstrated cleanly and is a genuine advantage over naive simplicial-complex filling. The empirical work is honest and reasonably complete: ten runs per configuration, grid-searched hyperparameters, ablations that isolate the roles of sheaf learning, diffusion, and left projection, and competitive accuracy on several datasets. The blocking issues are internal inconsistencies in the definition of the sheaf Laplacian and in the counting of cofacets used in the proof of the central reduction theorem; both are local and repairable in principle, but as the paper stands they invalidate the headline theoretical claim.

major comments (3)
  1. [§V-B, Proposition 3, Eqs. (44)–(45)] In the proof of Proposition 3, the cofacets of [v]_v in Δ(G) are counted as exactly [v,w]_e and [w,v]_e for each incident edge e, but under Definition 8 the degenerate 1-simplex [v,v]_v is also in Δ(G)_1 (it is the common identification of all diagonal tuples (v,v)_e and (v,v)_v), and by Definition 4 one has d¹_0([v,v]_v) = d¹_1([v,v]_v) = [v]_v, so [v,v]_v is a cofacet of [v]_v. Definition 7's diagonal sum (21) and the Laplacian sum (20) contain no nondegeneracy restriction, and by (41)–(42) the induced sheaf bF assigns to this self-cofacet the stalk F(v) with the identity restriction map; hence [v,v]_v contributes an additional Id term to D⁰_bF and to L⁰_bF at every node. For a single-edge graph with identity restriction maps this gives D⁰_bF = 3Id rather than 2D_F = 2Id, so the equalities L⁰_bF = 2L_F and D⁰_bF = 2D_F in Eq. (44) are not justified and the normalization argument in Eq. (45) does not go through. Since the abstract, the introduction, and the conclusion all base the 'first principled extension' claim on this exact reduction, this is a load-bearing gap; it is repairable by explicitly restricting all cofacet sums to nondegenerate cofacets, but such a restriction is not stated and the proof must be redone under it.
  2. [§IV-C, Definition 7, Eq. (20); cf. Eq. (1) and Eq. (23)] There is an internal sign inconsistency between the definition of the Laplacian and its use in the graph-reduction claim. Using Definition 4.c, for τ = [v,w]_e we have [[v]_v : τ] = −1 and [[w]_w : τ] = +1, so the exponent (−1)^{[σ:τ]+[σ′:τ]} in Eq. (20) equals +1 for the cross term (σ=[v]_v, σ′=[w]_w); Eq. (20) therefore produces a positive off-diagonal block from upper adjacency, whereas the graph sheaf Laplacian in Eq. (1) and the worked computation in Example 4, Eq. (23), both have negative off-diagonal contributions. The proof of Proposition 3 asserts that Eq. (44) follows from 'Equations (1), (3), (21), and (39)', which requires one consistent sign convention; as written, L⁰_bF = 2L_F cannot hold even after the degenerate cofacets are excluded, because the two displays use opposite signs. The sign convention must be corrected in Eq. (20), or the definition of signed incidence must be aligned with Eq. (23), and the consequences for Eqs. (39), (44), and (45) must then be re-derived.
  3. [§V-B, Proposition 2, Eq. (39); §IV-C, Example 4, Eq. (23)] The omission of the degenerate self-cofacet also affects Proposition 2 and Example 4. The [v]_v-component of the degree-0 Laplacian in Eq. (39) is written as sums over [v,w]_e and [w,v]_e only, but the self-cofacet [v,v]_v contributes to the diagonal block and to the self-adjacency terms of (20); hence Eq. (39) does not follow from Definition 7 as stated. Similarly, in Example 4 the degenerate simplex (v,v)_V is a cofacet of (v)_V in ∆[V], so the computation in Eq. (23) is incomplete under the paper's own definitions. These are not merely cosmetic issues, because the proof of Proposition 3 explicitly invokes Eq. (39) as established input.
minor comments (5)
  1. [§III-B, Definition 2] The codomain of fH is printed as 2^{V(H)}\V(H); presumably the intended codomain is the set of nonempty subsets, 2^{V(H)}\{∅}, and the printed expression should be corrected.
  2. [§III-A, Eq. (1)] The summation notation 'Σ_{v,u∈e}' in Eq. (1) is ambiguous; the sum should be over edges e with v,u ∈ fG(e), with the quantification over e made explicit.
  3. [§V-B, last paragraph] The statement that 'Proposition 3 implies the normalized degree k sheaf Laplacian on ∆(G) is a generalization of the normalized sheaf Laplacian on G' overreaches, since Proposition 3 only concerns the degree-0 Laplacian; a separate argument is needed for k > 0.
  4. [§VI-B, Table III] The reported standard deviations on the Senate dataset are large (5.87 for HNSD, 10.29 for LEGCN), so the claimed 3.80% advantage over SheafHyperGNN should be interpreted cautiously; a significance test or per-seed reporting would strengthen the claim.
  5. [§VI-A, Table II] The table states that CE homophily is computed from clique expansion, but the cited homophily definition [43] is for ordinary graphs; a sentence explaining how the clique-expansion scores are computed would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Proposition 3's graph reduction is a derived consistency check, not a fitted or self-referential input.

full rationale

Proposition 3 is a theorem proved from the paper's own definitions: Definition 8 constructs the symmetric simplicial lifting, Definition 7 defines the degree-0 sheaf Laplacian and diagonal blocks, and Eqs. (41)-(42) define the induced sheaf bF on the graph lifting. The traditional graph sheaf Laplacian is not inserted as an assumption; it is computed from these definitions, so the equality in Eqs. (44)-(45) is a consistency check rather than a circular prediction. No parameter is fitted and then renamed as a prediction: the experimental section benchmarks a fixed architecture against external methods, which is not a fitting-as-prediction loop. The citation [37] is to prior work by one of the authors, but the present paper restates the construction of symmetric simplicial lifting and proves the needed properties, so the self-citation is background rather than load-bearing. The possible counting omission of the degenerate self-cofacet [v,v]_v in Proof 3 (around Eq. (44), under Definitions 4, 7, and 8) is a mathematical correctness concern, not a circularity: even if the equality L0_bF = L_F were not established by the proof as written, the claim would not be equivalent to its inputs by construction. Therefore no circular step is identified.

Assumptions & free parameters 2 free parameters · 2 assumptions · 0 invented entities

The theoretical part has no fitted constants, but the construction and the graph-reduction claim rely on the domain assumption that simplicial-set adjacency is the correct model. The model itself has grid-searched hyperparameters and trained MLP weights. The unresolved counting of degenerate cofacets in Propositions 2 and 3 is the main gap: the ledger shows that no independent evidence fixes the Laplacian convention.

free parameters (2)
  • Grid-searched hyperparameters (learning rate, weight decay, dropout, hidden dimension) = Per dataset, e.g. Cora: lr=0.001, wd=1e-5, dim=128, dropout=0.5
    Selected by validation accuracy over 10 splits; they directly affect the reported HNSD numbers in Table III.
  • Learned sheaf restriction maps and MLP weights = Trained end-to-end
    Sheaf maps F([v]_v < [v,w]_e) are MLP outputs learned from node features; no closed-form constraint ties them to a fixed sheaf.
assumptions (2)
  • domain assumption The degree-k sheaf Laplacian of Definition 7 is the correct diffusion operator for learning on simplicial sets.
    The HNSD layer follows this definition with no alternative basis for why this operator should be used.
  • domain assumption The symmetric simplicial lifting Δ(H) of Definition 8 defines the right notion of adjacency and preserves all information needed for hypergraph learning.
    Motivated in Section V-A but not derived from first principles; Proposition 1 shows recoverability but not that this adjacency is optimal or unique for learning.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learning." pith.science (2026). https://pith.science/paper/FJQI4LP7

@misc{pith2026250505702,
  author       = {Pith},
  title        = {Pith review of: Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FJQI4LP7}},
  note         = {Machine review of arXiv:2505.05702}
}
read the original abstract

The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets derived directly from hypergraphs, called symmetric simplicial lifting, which encode all possible oriented subrelations within each hyperedge as ordered tuples. This construction canonically defines adjacency via facet maps while inherently preserving hyperedge provenance. We establish that the normalized degree zero sheaf Laplacian on our symmetric simplicial lifting reduces exactly to the traditional graph normalized sheaf Laplacian when restricted to graphs, validating its mathematical consistency with prior graph-based sheaf theory. Furthermore, the induced structure preserves all structural information from the original hypergraph, ensuring that every multi-way relational detail is faithfully retained. Leveraging this framework, we introduce Hypergraph Neural Sheaf Diffusion (HNSD), the first principled extension of neural sheaf diffusion to hypergraphs. HNSD operates via normalized degree zero sheaf Laplacian over symmetric simplicial lifting, resolving orientation ambiguity and adjacency sparsity inherent to hypergraph learning. Experimental evaluations demonstrate HNSDs competitive performance across established benchmarks.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 31 canonical work pages

  1. [37]

    Cellular sheaf Laplacians on the set of simplices of symmetric simplicial set induced by hypergraph

    S. Choi and J. Park, “Cellular sheaf laplacians on the set of simplices of symmetric simplicial set induced by hypergraph,” arXiv preprint arXiv:2411.08458, 2024

    work page Pith review arXiv 2024

  2. [1]

    Hypergraph theory,

    A. Bretto, “Hypergraph theory,” An introduction. Mathematical Engi- neering. Cham: Springer , vol. 1, pp. 209–216, 2013

    work page 2013

  3. [2]

    3-d object retrieval and recognition with hypergraph analysis,

    Y . Gao, M. Wang, D. Tao, R. Ji, and Q. Dai, “3-d object retrieval and recognition with hypergraph analysis,” IEEE transactions on image processing, vol. 21, no. 9, pp. 4290–4303, 2012. 14 (a) Cora - Raw. (b) Cora - HyperGCN. (c) Cora - HNSD. (d) Citeseer - Raw. (e) Citeseer - HyperGCN. (f) Citeseer - HNSD. (g) Cora-CA - Raw. (h) Cora-CA - HyperGCN. (i) C...

    work page 2012

  4. [3]

    Learning multi-granular hypergraphs for video-based person re-identification,

    Y . Yan, J. Qin, J. Chen, L. Liu, F. Zhu, Y . Tai, and L. Shao, “Learning multi-granular hypergraphs for video-based person re-identification,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2020, pp. 2899–2908

    work page 2020

  5. [4]

    Multitask hypergraph convolutional networks: A heterogeneous traffic prediction framework,

    J. Wang, Y . Zhang, L. Wang, Y . Hu, X. Piao, and B. Yin, “Multitask hypergraph convolutional networks: A heterogeneous traffic prediction framework,” IEEE Transactions on Intelligent Transportation Systems , vol. 23, no. 10, pp. 18 557–18 567, 2022

    work page 2022

  6. [5]

    Hypergraph neural net- works,

    Y . Feng, H. You, Z. Zhang, R. Ji, and Y . Gao, “Hypergraph neural net- works,” in Proceedings of the AAAI conference on artificial intelligence , vol. 33, no. 01, 2019, pp. 3558–3565

    2019

  7. [6]

    Hypergraph learning: Methods and practices,

    Y . Gao, Z. Zhang, H. Lin, X. Zhao, S. Du, and C. Zou, “Hypergraph learning: Methods and practices,” IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 44, no. 5, pp. 2548–2566, 2020

    work page 2020

  8. [7]

    Hypergraph collaborative network on vertices and hyperedges,

    H. Wu, Y . Yan, and M. K.-P. Ng, “Hypergraph collaborative network on vertices and hyperedges,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 3, pp. 3245–3258, 2022

    work page 2022

Show all 48 references
  1. [8]

    Semi-supervised classification with graph convolutional networks,

    T. N. Kipf and M. Welling, “Semi-supervised classification with graph convolutional networks,” in International Conference on Learning Rep- resentations, 2017

    2017

  2. [9]

    Convolutional neural networks on graphs with fast localized spectral filtering,

    M. Defferrard, X. Bresson, and P. Vandergheynst, “Convolutional neural networks on graphs with fast localized spectral filtering,” Advances in neural information processing systems , vol. 29, 2016

    2016

  3. [10]

    Graph learning: A survey,

    F. Xia, K. Sun, S. Yu, A. Aziz, L. Wan, S. Pan, and H. Liu, “Graph learning: A survey,” IEEE Transactions on Artificial Intelligence, vol. 2, no. 2, pp. 109–127, 2021

    2021

  4. [11]

    Deep learning on graphs: A survey,

    Z. Zhang, P. Cui, and W. Zhu, “Deep learning on graphs: A survey,” IEEE Transactions on Knowledge and Data Engineering , vol. 34, no. 1, pp. 249–270, 2020

    2020

  5. [12]

    A comprehensive survey on graph neural networks,

    Z. Wu, S. Pan, F. Chen, G. Long, C. Zhang, and P. S. Yu, “A comprehensive survey on graph neural networks,” IEEE transactions on neural networks and learning systems , vol. 32, no. 1, pp. 4–24, 2020

    2020

  6. [13]

    Explainability in graph neural networks: A taxonomic survey,

    H. Yuan, H. Yu, S. Gui, and S. Ji, “Explainability in graph neural networks: A taxonomic survey,” IEEE transactions on pattern analysis and machine intelligence , vol. 45, no. 5, pp. 5782–5799, 2022

    2022

  7. [14]

    J. M. Curry, Sheaves, cosheaves and applications . University of Pennsylvania, 2014

    2014

  8. [15]

    Toward a spectral theory of cellular sheaves,

    J. Hansen and R. Ghrist, “Toward a spectral theory of cellular sheaves,” Journal of Applied and Computational Topology, vol. 3, no. 4, pp. 315– 358, 2019

    2019

  9. [16]

    Laplacians of cellular sheaves: Theory and applications,

    J. Hansen, “Laplacians of cellular sheaves: Theory and applications,” Ph.D. dissertation, University of Pennsylvania, 2020

    2020

  10. [17]

    Neural sheaf diffusion: A topological perspective on heterophily and oversmoothing in gnns,

    C. Bodnar, F. Di Giovanni, B. Chamberlain, P. Lio, and M. Bronstein, “Neural sheaf diffusion: A topological perspective on heterophily and oversmoothing in gnns,” Advances in Neural Information Processing Systems, vol. 35, pp. 18 527–18 541, 2022

    2022

  11. [18]

    Sheaf neural networks with connection lapla- cians,

    F. Barbero, C. Bodnar, H. S. de Oc ´ariz Borde, M. Bronstein, P. Veliˇckovi´c, and P. Li`o, “Sheaf neural networks with connection lapla- cians,” in Topological, Algebraic and Geometric Learning Workshops

  12. [19]

    The simpliciality of higher-order networks,

    N. W. Landry, J.-G. Young, and N. Eikmeier, “The simpliciality of higher-order networks,” EPJ data science , vol. 13, no. 1, p. 17, 2024

    2024

  13. [20]

    Simplicial convolutional neural networks,

    M. Yang, E. Isufi, and G. Leus, “Simplicial convolutional neural networks,” in ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) . IEEE, 2022, pp. 8847–8851

    2022

  14. [21]

    Persistent sheaf laplacians,

    X. Wei and G.-W. Wei, “Persistent sheaf laplacians,” Foundations of Data Science, vol. 7, no. 2, pp. 446–463, 2025

    2025

  15. [22]

    Persistent sheaf cohomology,

    F. Russold, “Persistent sheaf cohomology,” arXiv preprint arXiv:2204.13446, 2022

    2022 arXiv

  16. [23]

    Weisfeiler and lehman go topological: Message passing simplicial networks,

    C. Bodnar, F. Frasca, Y . Wang, N. Otter, G. F. Montufar, P. Lio, and M. Bronstein, “Weisfeiler and lehman go topological: Message passing simplicial networks,” in International conference on machine learning . PMLR, 2021, pp. 1026–1037

    2021

  17. [24]

    Beyond homophily in graph neural networks: Current limitations and effective designs,

    J. Zhu, Y . Yan, L. Zhao, M. Heimann, L. Akoglu, and D. Koutra, “Beyond homophily in graph neural networks: Current limitations and effective designs,” Advances in neural information processing systems , vol. 33, pp. 7793–7804, 2020

    2020

  18. [25]

    Revisiting graph neural networks: All we have is low-pass filters,

    H. Nt and T. Maehara, “Revisiting graph neural networks: All we have is low-pass filters,” arXiv preprint arXiv:1905.09550 , 2019

    1905 arXiv

  19. [26]

    Graph neural networks exponentially lose expressive power for node classification,

    K. Oono and T. Suzuki, “Graph neural networks exponentially lose expressive power for node classification,” in International Conference on Learning Representations , 2020

    2020

  20. [27]

    Sheaf neural networks,

    J. Hansen and T. Gebhart, “Sheaf neural networks,” In NeurIPS 2020 Workshop on Topological Data Analysis and Beyond , 2020

    2020

  21. [28]

    Hypergcn: A new method for training graph convolutional networks on hypergraphs,

    N. Yadati, M. Nimishakavi, P. Yadav, V . Nitin, A. Louis, and P. Talukdar, “Hypergcn: A new method for training graph convolutional networks on hypergraphs,” Advances in neural information processing systems , vol. 32, 2019

    2019

  22. [29]

    Hnhn: Hypergraph networks with hyperedge neurons,

    Y . Dong, W. Sawin, and Y . Bengio, “Hnhn: Hypergraph networks with hyperedge neurons,” arXiv preprint arXiv:2006.12278 , 2020

    2006 arXiv

  23. [30]

    Hypergraph convolution and hyper- graph attention,

    S. Bai, F. Zhang, and P. H. Torr, “Hypergraph convolution and hyper- graph attention,” Pattern Recognition, vol. 110, p. 107637, 2021

    2021

  24. [31]

    Learnable hyper- graph laplacian for hypergraph learning,

    J. Zhang, Y . Chen, X. Xiao, R. Lu, and S.-T. Xia, “Learnable hyper- graph laplacian for hypergraph learning,” in ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2022, pp. 4503–4507

    2022

  25. [32]

    Hgnn+: General hypergraph neural networks,

    Y . Gao, Y . Feng, S. Ji, and R. Ji, “Hgnn+: General hypergraph neural networks,” IEEE Transactions on Pattern Analysis and Machine Intelli- gence, vol. 45, no. 3, pp. 3181–3199, 2022

    2022

  26. [33]

    Hypergraph convolution on nodes-hyperedges network for semi-supervised node classification,

    H. Wu and M. K. Ng, “Hypergraph convolution on nodes-hyperedges network for semi-supervised node classification,” ACM Transactions on Knowledge Discovery from Data (TKDD), vol. 16, no. 4, pp. 1–19, 2022

    2022

  27. [34]

    Collabo- rative contrastive learning for hypergraph node classification,

    H. Wu, N. Li, J. Zhang, S. Chen, M. K. Ng, and J. Long, “Collabo- rative contrastive learning for hypergraph node classification,” Pattern Recognition, vol. 146, p. 109995, 2024

    2024

  28. [35]

    Sheaf hypergraph net- works,

    I. Duta, G. Cassar `a, F. Silvestri, and P. Li `o, “Sheaf hypergraph net- works,” Advances in Neural Information Processing Systems , vol. 36, pp. 12 087–12 099, 2023

    2023

  29. [36]

    Higher-dimensional models of networks,

    D. I. Spivak, “Higher-dimensional models of networks,” arXiv preprint arXiv:0909.4314, 2009

    2009 arXiv

  30. [38]

    Simplicial complex neural networks,

    H. Wu, A. Yip, J. Long, J. Zhang, and M. K. Ng, “Simplicial complex neural networks,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 46, no. 1, pp. 561–575, 2023

    2023

  31. [39]

    Finite sets and symmetric simplicial sets

    M. Grandis, “Finite sets and symmetric simplicial sets.” Theory and Applications of Categories [electronic only] , vol. 8, pp. 244–252, 2001

    2001

  32. [40]

    Weisfeiler and lehman go cellular: Cw networks,

    C. Bodnar, F. Frasca, N. Otter, Y . Wang, P. Lio, G. F. Montufar, and M. Bronstein, “Weisfeiler and lehman go cellular: Cw networks,” Advances in neural information processing systems , vol. 34, pp. 2625– 2640, 2021

    2021

  33. [41]

    High-order pooling for graph neural networks with tensor decomposition,

    C. Hua, G. Rabusseau, and J. Tang, “High-order pooling for graph neural networks with tensor decomposition,” Advances in Neural Information Processing Systems, vol. 35, pp. 6021–6033, 2022

    2022

  34. [42]

    Legislative cosponsorship networks in the us house and senate,

    J. H. Fowler, “Legislative cosponsorship networks in the us house and senate,” Social networks, vol. 28, no. 4, pp. 454–465, 2006

    2006

  35. [43]

    Geom- gcn: Geometric graph convolutional networks,

    H. Pei, B. Wei, K. C. C. Chang, Y . Lei, and B. Yang, “Geom- gcn: Geometric graph convolutional networks,” in 8th International Conference on Learning Representations, ICLR , 2020

    2020

  36. [44]

    Beyond pairwise clustering,

    S. Agarwal, J. Lim, L. Zelnik-Manor, P. Perona, D. Kriegman, and S. Be- longie, “Beyond pairwise clustering,” in 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05) , vol. 2. IEEE, 2005, pp. 838–845

    2005

  37. [45]

    Learning with hypergraphs: Clus- tering, classification, and embedding,

    D. Zhou, J. Huang, and B. Sch ¨olkopf, “Learning with hypergraphs: Clus- tering, classification, and embedding,” Advances in neural information processing systems, vol. 19, 2006

    2006

  38. [46]

    Semi-supervised hyper- graph node classification on hypergraph line expansion,

    C. Yang, R. Wang, S. Yao, and T. Abdelzaher, “Semi-supervised hyper- graph node classification on hypergraph line expansion,” in Proceedings of the 31st ACM International Conference on Information & Knowledge Management, 2022, pp. 2352–2361

    2022

  39. [47]

    You are allset: A multiset learning framework for hypergraph neural networks,

    E. Chien, C. Pan, J. Peng, and O. Milenkovic, “You are allset: A multiset learning framework for hypergraph neural networks,” in 10th International Conference on Learning Representations, ICLR 2022 , 2022

    2022

  40. [2022]

    PMLR, 2022, pp. 28–36

    2022

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.