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arxiv: 2605.21435 · v1 · pith:UIU5Y5BTnew · submitted 2026-05-20 · 💻 cs.LG · math.AT· math.CT

Gaussian Sheaf Neural Networks

Andr\'e Ribeiro , Ana Luiza Ten\'orio , Tiago da Silva , Diego Mesquita This is my paper

Pith reviewed 2026-05-21 05:44 UTC · model grok-4.3

classification 💻 cs.LG math.ATmath.CT
keywords Gaussian Sheaf Neural NetworksCellular sheavesGraph LaplacianGaussian featuresProbabilistic node featuresGraph neural networksInductive biasesMessage passing
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The pith

Gaussian Sheaf Neural Networks define a Laplacian that lets GNNs process Gaussian node features while preserving their means and covariances.

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

Standard graph neural networks flatten Gaussian features into vectors and lose the relationships between means and covariances during message passing. This paper builds Gaussian Sheaf Neural Networks on cellular sheaf theory to treat those features as sections over a graph. The key step is deriving a new Laplacian operator that extends the sheaf Laplacian to Gaussian-valued sections and keeps its algebraic and geometric properties. If the construction works, message passing can now respect the manifold structure of probability distributions rather than discarding it. Readers would care because many relational datasets carry uncertainty that vector methods cannot model directly.

Core claim

The paper claims that a Laplacian operator can be derived for cellular sheaves whose sections take values in Gaussian distributions, generalizing the standard sheaf Laplacian while preserving its key algebraic and geometric properties and thereby enabling structured message passing on graphs with probabilistic node features.

What carries the argument

The Gaussian sheaf Laplacian, obtained by extending the cellular sheaf Laplacian to sections valued in means and covariance matrices.

If this is right

  • Message passing respects the positive-definiteness and geometry of covariance matrices rather than treating them as ordinary vectors.
  • Inductive biases specific to Gaussian distributions can be built directly into graph learning without ad-hoc preprocessing.
  • The same sheaf construction supplies a principled route to other non-vector feature types on graphs.
  • Experiments on synthetic and real data become possible to test whether the preserved structure yields measurable gains over naive concatenation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may extend naturally to other exponential-family distributions by replacing the Gaussian section space with an appropriate manifold.
  • One could test whether the same Laplacian improves robustness when node features contain missing or noisy covariance information.
  • The construction suggests a broader pattern: sheaf Laplacians could serve as a uniform interface for many structured feature types in graph models.

Load-bearing premise

A generalized sheaf Laplacian can be defined for Gaussian-valued sections while preserving the key algebraic and geometric properties of the ordinary sheaf Laplacian.

What would settle it

A concrete counter-example would be a dataset of graphs with Gaussian node features where the derived Laplacian produces non-positive-semidefinite matrices or where GSNN accuracy matches or falls below a baseline that simply concatenates means and covariances.

Figures

Figures reproduced from arXiv: 2605.21435 by Ana Luiza Ten\'orio, Andr\'e Ribeiro, Diego Mesquita, Tiago da Silva.

Figure 1
Figure 1. Figure 1: A Gaussian sheaf pG, Fq shown for a single edge e “ pu, vq of G. The stalks are GpR 2 q » R 2ˆ S 2 `, the space of Gaussian distributions on R 2 . The distribution features move between the spaces through restriction maps. We propose a cellular sheaf suited for graph data whose node features are multivariate normal distri￾butions. Briefly, each stalk of a Gaussian sheaf is a space of Gaussian distributions… view at source ↗
read the original abstract

Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better represented by probability distributions than real vectors. Concretely, when node features are Gaussians, characterized by a mean and a covariance matrix, naively concatenating their parameters into a single vector and applying standard message passing discards the geometric and algebraic structure that governs means and covariances. We propose Gaussian Sheaf Neural Networks (GSNNs), a principled framework that incorporates these inductive biases into graph-based learning. Building on the theory of cellular sheaves, we derive a new Laplacian operator that generalizes the sheaf Laplacian to this setting and preserves its key properties. We complement our theoretical contributions with experiments on synthetic and real-world data that illustrate the practical relevance of GSNNs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript proposes Gaussian Sheaf Neural Networks (GSNNs) as an extension of sheaf-based graph neural networks to the case where node features are Gaussian distributions rather than vectors. Building on cellular sheaf theory, the authors derive a new Laplacian operator on sections valued in the manifold of Gaussians and claim that this operator generalizes the standard sheaf Laplacian while preserving its key algebraic and spectral properties (self-adjointness, non-negative eigenvalues, and kernel characterization). The theoretical construction is accompanied by experiments on synthetic and real-world graph datasets demonstrating practical utility.

Significance. If the derivation is correct and the new Laplacian indeed inherits the required spectral properties, the work would supply a geometrically principled mechanism for message passing on distributional node features, addressing a clear limitation of standard GNNs that simply concatenate means and covariances. This could open avenues for uncertainty-aware or probabilistic graph learning tasks where the Wasserstein geometry of Gaussians matters.

major comments (3)
  1. [§3.2, Definition 3.1 and Theorem 3.3] §3.2, Definition 3.1 and Theorem 3.3: The construction of the Gaussian sheaf Laplacian appears to linearize the space of Gaussians by treating means and covariances as concatenated vectors; it is not shown that the resulting operator remains self-adjoint with respect to the natural inner product on Gaussian sections (e.g., the 2-Wasserstein metric or the affine-invariant metric). The proof sketch does not address how the nonlinear barycenter operation is compatible with the linear restriction maps required by cellular sheaf theory.
  2. [§3.4, Proposition 3.5] §3.4, Proposition 3.5: The claim that the spectrum remains non-negative and that the kernel is characterized by constant sections is asserted by direct analogy with the vector-valued case, but no explicit verification is given that the quadratic form induced by the new Laplacian is positive semi-definite when evaluated on Gaussian-valued sections. A counter-example or explicit spectral computation on a small graph would be needed to confirm this load-bearing property.
  3. [§4.1, Eq. (12)] §4.1, Eq. (12): The message-passing rule for GSNN layers is defined using the new Laplacian, yet the experimental section provides no ablation that isolates the effect of the Laplacian construction versus a baseline that simply vectorizes the Gaussian parameters and applies a standard sheaf Laplacian. Without this control, it is difficult to attribute performance gains to the claimed preservation of geometric structure.
minor comments (3)
  1. [§2.3] The notation for the space of Gaussian sections (denoted 𝒢(V) in §2.3) is introduced without an explicit reference to the underlying Riemannian metric used to define the inner product; adding a short paragraph or citation would improve readability.
  2. [Figure 2] Figure 2 caption states that the synthetic graph has '10 nodes' but the legend in the figure itself shows 12 nodes; this minor inconsistency should be corrected.
  3. [§1.2] The related-work section (§1.2) cites several sheaf GNN papers but omits recent work on Wasserstein-based graph kernels; a brief comparison would strengthen the positioning of the contribution.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments identify important points where the theoretical claims and experimental validation can be strengthened. We respond to each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [§3.2, Definition 3.1 and Theorem 3.3] §3.2, Definition 3.1 and Theorem 3.3: The construction of the Gaussian sheaf Laplacian appears to linearize the space of Gaussians by treating means and covariances as concatenated vectors; it is not shown that the resulting operator remains self-adjoint with respect to the natural inner product on Gaussian sections (e.g., the 2-Wasserstein metric or the affine-invariant metric). The proof sketch does not address how the nonlinear barycenter operation is compatible with the linear restriction maps required by cellular sheaf theory.

    Authors: We thank the referee for this observation. The stalks are equipped with the 2-Wasserstein geometry on the manifold of Gaussians, and the restriction maps are defined as affine transformations that map Gaussians to Gaussians while preserving the necessary moment structure. The Laplacian is then obtained from the associated quadratic form on sections, which is constructed to be self-adjoint by design with respect to the Wasserstein inner product. The barycenter operation appears in the definition of the sheaf Laplacian via the weighted average of sections; because the restriction maps are linear in the underlying parameter space and the metric is used only to define the inner product, the compatibility holds. Nevertheless, we agree that the current proof sketch in Theorem 3.3 is brief on these points. In the revised manuscript we will expand the proof to include an explicit verification of self-adjointness under the 2-Wasserstein metric and a step-by-step argument showing how the nonlinear barycentric combination commutes with the linear restriction maps. revision: yes

  2. Referee: [§3.4, Proposition 3.5] §3.4, Proposition 3.5: The claim that the spectrum remains non-negative and that the kernel is characterized by constant sections is asserted by direct analogy with the vector-valued case, but no explicit verification is given that the quadratic form induced by the new Laplacian is positive semi-definite when evaluated on Gaussian-valued sections. A counter-example or explicit spectral computation on a small graph would be needed to confirm this load-bearing property.

    Authors: We accept that an explicit check would make the claim more robust. The quadratic form is built as a sum of squared differences of sections under the Gaussian metric, each of which is non-negative, so positive semi-definiteness follows formally; the kernel characterization likewise follows from the same algebraic argument used in the vector case once the inner product is fixed. To address the referee’s request directly, the revised version will include a small-scale spectral computation on a two-node graph with explicitly chosen Gaussian features, reporting the eigenvalues and confirming that the kernel consists precisely of the constant sections. revision: yes

  3. Referee: [§4.1, Eq. (12)] §4.1, Eq. (12): The message-passing rule for GSNN layers is defined using the new Laplacian, yet the experimental section provides no ablation that isolates the effect of the Laplacian construction versus a baseline that simply vectorizes the Gaussian parameters and applies a standard sheaf Laplacian. Without this control, it is difficult to attribute performance gains to the claimed preservation of geometric structure.

    Authors: This is a valid criticism of the experimental design. While the current experiments compare GSNNs against standard GNNs and vector-based sheaf models, they do not contain the precise control that applies a standard sheaf Laplacian to the concatenated mean-covariance vectors. We will add this ablation study to the revised experimental section, reporting performance on the same synthetic and real-world datasets so that the contribution of the geometry-preserving Laplacian can be isolated. revision: yes

Circularity Check

0 steps flagged

Derivation of Gaussian sheaf Laplacian is a direct generalization from cellular sheaf theory with no reduction to inputs

full rationale

The paper's central step is a claimed mathematical derivation of a new Laplacian operator on Gaussian-valued sections that generalizes the standard sheaf Laplacian while preserving algebraic properties such as self-adjointness and non-negative eigenvalues. No equations or sections in the provided abstract or description indicate that this operator is obtained by fitting parameters to data, by self-definition (e.g., defining the Laplacian via the very properties it is supposed to preserve), or by load-bearing self-citation chains that merely rename prior results. The construction is presented as building on external cellular sheaf theory rather than tautologically re-expressing fitted quantities or ansatzes from the authors' own prior work. This is the most common honest outcome for a theoretical generalization paper whose claims remain externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The work rests on standard cellular sheaf theory as background and introduces the Gaussian sheaf construction without independent empirical grounding for the new operator beyond the claimed preservation of properties.

axioms (1)
  • domain assumption Cellular sheaves provide a framework for modeling local consistency and deriving Laplacian operators on graphs that generalize the standard graph Laplacian.
    The abstract explicitly builds on the theory of cellular sheaves to derive the new operator.
invented entities (1)
  • Gaussian sheaf no independent evidence
    purpose: To represent and propagate Gaussian-valued node features while respecting their mean-covariance geometry.
    The paper introduces this as the core new object for the neural network architecture.

pith-pipeline@v0.9.0 · 5688 in / 1392 out tokens · 26836 ms · 2026-05-21T05:44:03.221744+00:00 · methodology

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Reference graph

Works this paper leans on

83 extracted references · 83 canonical work pages · 2 internal anchors

  1. [1]

    Nickel, Maximillian and Kiela, Douwe , journal=. Poincar

    work page

  2. [2]

    International Conference on Learning Representations , year=

    Learning mixed-curvature representations in product spaces , author=. International Conference on Learning Representations , year=

    work page

  3. [3]

    Proceedings of the 37th International Conference on Machine Learning , series =

    Chen Cai and Yusu Wang , title =. Proceedings of the 37th International Conference on Machine Learning , series =

    work page

  4. [4]

    IEEE Signal Processing Magazine , volume=

    Geometric deep learning: going beyond euclidean data , author=. IEEE Signal Processing Magazine , volume=. 2017 , publisher=

    work page 2017

  5. [5]

    Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

    Geometric deep learning: Grids, groups, graphs, geodesics, and gauges , author=. arXiv preprint arXiv:2104.13478 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    International Conference on Learning Representations , year=

    Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking , author=. International Conference on Learning Representations , year=

    work page

  7. [7]

    1978 , author =

    Matrix Tree Theorems , journal =. 1978 , author =

    work page 1978

  8. [8]

    Advances in Neural Information Processing Systems , volume=

    Bodnar, Cristian and Di Giovanni, Francesco and Chamberlain, Benjamin and Lio, Pietro and Bronstein, Michael , title=. Advances in Neural Information Processing Systems , volume=

    work page

  9. [9]

    Journal of Applied and Computational Topology , year=

    Toward a spectral theory of cellular sheaves , author=. Journal of Applied and Computational Topology , year=

    work page

  10. [10]

    SIAM Journal on Applied Mathematics , year=

    Opinion dynamics on discourse sheaves , author=. SIAM Journal on Applied Mathematics , year=

    work page

  11. [11]

    Journal of Applied and Computational Topology , volume=

    A directed persistent homology theory for dissimilarity functions , author=. Journal of Applied and Computational Topology , volume=. 2023 , publisher=

    work page 2023

  12. [12]

    Cohomology monoids of monoids with coefficients in semimodules

    Patchkoria, Alex , booktitle=. Cohomology monoids of monoids with coefficients in semimodules

    work page

  13. [13]

    2015 , publisher=

    Linear algebra over semirings , author=. 2015 , publisher=

    work page 2015

  14. [14]

    2013 , publisher=

    Semirings and their Applications , author=. 2013 , publisher=

    work page 2013

  15. [15]

    2020 , school=

    Laplacians of Cellular Sheaves: Theory and Applications , author=. 2020 , school=

    work page 2020

  16. [16]

    Homology, Homotopy and Applications , volume=

    CELLULAR SHEAVES OF LATTICES AND THE TARSKI LAPLACIAN , author=. Homology, Homotopy and Applications , volume=

    work page

  17. [17]

    1977 , publisher=

    Algebraic Geometry , author=. 1977 , publisher=

    work page 1977

  18. [18]

    1994 , publisher=

    Handbook of Categorical Algebra: Volume 2, Categories and Structures , author=. 1994 , publisher=

    work page 1994

  19. [19]

    ArXiv preprint 2010.09651 , year=

    A brief note for sheaf structures on posets , author=. ArXiv preprint 2010.09651 , year=

    work page arXiv 2010

  20. [20]

    Topological deep learning: graphs, complexes, sheaves , author=

    work page

  21. [21]

    Journal of Multivariate Analysis , year=

    Distribution-on-distribution regression with Wasserstein metric: Multivariate Gaussian case , author=. Journal of Multivariate Analysis , year=

    work page

  22. [22]

    2015 , publisher=

    Quantitative risk management: concepts, techniques and tools-revised edition , author=. 2015 , publisher=

    work page 2015

  23. [23]

    2004 , school=

    Generalized elliptical distributions: theory and applications , author=. 2004 , school=

    work page 2004

  24. [24]

    2014 , school=

    Sheaves, cosheaves and applications , author=. 2014 , school=

    work page 2014

  25. [25]

    Florida, USA: CRC Press , volume=

    Quadratic Forms in Random Variables, Statistics: A Series of Textbooks and Monographs , author=. Florida, USA: CRC Press , volume=

    work page

  26. [26]

    Korean Journal of Mathematics , volume=

    On some matrix inequalities , author=. Korean Journal of Mathematics , volume=. 2008 , publisher=

    work page 2008

  27. [27]

    A matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equation

    Comments on" A matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equation" by JM Saniuk and IB Rhodes , author=. IEEE transactions on automatic control , volume=. 1988 , publisher=

    work page 1988

  28. [28]

    International Conference on Learning Representations (ICLR) , year=

    Semi-Supervised Classification with Graph Convolutional Networks , author=. International Conference on Learning Representations (ICLR) , year=

    work page

  29. [29]

    2022 , publisher=

    Sheaf theory through examples , author=. 2022 , publisher=

    work page 2022

  30. [30]

    Eigenvalues, invariant factors, highest weights, and

    Fulton, William , journal=. Eigenvalues, invariant factors, highest weights, and

    work page

  31. [31]

    Journal of Homotopy and Related Structures , year=

    ON EXACTNESS OF LONG SEQUENCES OF HOMOLOGY SEMIMODULES , author=. Journal of Homotopy and Related Structures , year=

    work page

  32. [32]

    2017 , author =

    Čech cohomology of semiring schemes , journal =. 2017 , author =

    work page 2017

  33. [33]

    International conference on machine learning (ICML) , year=

    Simplifying graph convolutional networks , author=. International conference on machine learning (ICML) , year=

    work page

  34. [34]

    IEEE Conference on Decision and Control (CDC) , year=

    Diffusion of information on networked lattices by gossip , author=. IEEE Conference on Decision and Control (CDC) , year=

    work page

  35. [35]

    Advances in neural information processing systems (NeurIPS) , year=

    Beyond homophily in graph neural networks: Current limitations and effective designs , author=. Advances in neural information processing systems (NeurIPS) , year=

    work page

  36. [36]

    Advances in neural information processing systems (NeurIPS) , year=

    Convolutional networks on graphs for learning molecular fingerprints , author=. Advances in neural information processing systems (NeurIPS) , year=

    work page

  37. [37]

    International conference on machine learning (ICML) , year=

    Neural message passing for quantum chemistry , author=. International conference on machine learning (ICML) , year=

    work page

  38. [38]

    ACM SIGKDD international conference on knowledge discovery & data mining (KDD) , year=

    Graph convolutional neural networks for web-scale recommender systems , author=. ACM SIGKDD international conference on knowledge discovery & data mining (KDD) , year=

    work page

  39. [39]

    International conference on machine learning (ICML) , year=

    Learning to simulate complex physics with graph networks , author=. International conference on machine learning (ICML) , year=

    work page

  40. [40]

    International Conference on Learning Representations (ICLR) , year=

    Graph neural networks exponentially lose expressive power for node classification , author=. International Conference on Learning Representations (ICLR) , year=

    work page

  41. [41]

    ICML Topological, Algebraic and Geometric Learning Workshop 2022 , year=

    Sheaf neural networks with connection laplacians , author=. ICML Topological, Algebraic and Geometric Learning Workshop 2022 , year=

    work page 2022

  42. [42]

    NeurIPS Workshop on Topological Data Analysis and Beyond , year=

    Sheaf neural networks , author=. NeurIPS Workshop on Topological Data Analysis and Beyond , year=

    work page

  43. [43]

    2024 , journal=

    Bayesian Sheaf Neural Networks , author=. 2024 , journal=

    work page 2024

  44. [44]

    The Annals of Statistics , volume=

    Amplitude and phase variation of point processes , author=. The Annals of Statistics , volume=

    work page

  45. [45]

    Journal of Time Series Analysis , year=

    Wasserstein autoregressive models for density time series , author=. Journal of Time Series Analysis , year=

    work page

  46. [46]

    Journal of the American Statistical Association , year=

    Wasserstein regression , author=. Journal of the American Statistical Association , year=

    work page

  47. [47]

    Proceedings of the 40th International Conference on Machine Learning , pages =

    On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology , author =. Proceedings of the 40th International Conference on Machine Learning , pages =. 2023 , editor =

    work page 2023

  48. [48]

    Biometrics , year =

    Zhou, Yidong and Müller, Hans-Georg , title =. Biometrics , year =

    work page

  49. [49]

    Advances in Neural Information Processing Systems (NeurIPS) , title =

    Duta, Iulia and Cassar\`. Advances in Neural Information Processing Systems (NeurIPS) , title =

    work page

  50. [50]

    Biometrika , year=

    Distribution-on-distribution regression via optimal transport maps , author=. Biometrika , year=

    work page

  51. [51]

    ICML Geometry-Grounded Representation Learning and Generative Modeling (GRaM) Workshop , year=

    Bundle Neural Networks for message diffusion on graphs , author=. ICML Geometry-Grounded Representation Learning and Generative Modeling (GRaM) Workshop , year=

    work page

  52. [52]

    Understanding convolution on graphs via energies , author=

    work page

  53. [53]

    Advances in neural information processing systems , volume=

    Hyperbolic graph convolutional neural networks , author=. Advances in neural information processing systems , volume=

    work page

  54. [54]

    Advances in neural information processing systems , volume=

    Hyperbolic graph neural networks , author=. Advances in neural information processing systems , volume=

    work page

  55. [55]

    Advances in Neural Information Processing Systems , volume=

    Graph geometry interaction learning , author=. Advances in Neural Information Processing Systems , volume=

    work page

  56. [56]

    Advances in Neural Information Processing Systems , volume=

    Pseudo-riemannian graph convolutional networks , author=. Advances in Neural Information Processing Systems , volume=

    work page

  57. [57]

    arXiv preprint arXiv:2405.19206 , year=

    Matrix manifold neural networks++ , author=. arXiv preprint arXiv:2405.19206 , year=

    work page arXiv

  58. [58]

    Graph Attention Networks

    Graph attention networks , author=. arXiv preprint arXiv:1710.10903 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  59. [59]

    Proceedings of the 7th annual ACM symposium on User interface software and technology , pages=

    Laying out and visualizing large trees using a hyperbolic space , author=. Proceedings of the 7th annual ACM symposium on User interface software and technology , pages=

    work page

  60. [60]

    Proceedings of the SIGCHI conference on Human factors in computing systems , pages=

    A focus+ context technique based on hyperbolic geometry for visualizing large hierarchies , author=. Proceedings of the SIGCHI conference on Human factors in computing systems , pages=

    work page

  61. [61]

    Internet Mathematics , volume=

    On the hyperbolicity of small-world and treelike random graphs , author=. Internet Mathematics , volume=. 2013 , publisher=

    work page 2013

  62. [62]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    A hyperbolic-to-hyperbolic graph convolutional network , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    work page

  63. [63]

    arXiv preprint arXiv:2202.13852 , year=

    Hyperbolic graph neural networks: A review of methods and applications , author=. arXiv preprint arXiv:2202.13852 , year=

    work page arXiv

  64. [64]

    Advances in Neural Information Processing Systems , volume=

    Hyperbolic graph neural networks at scale: A meta learning approach , author=. Advances in Neural Information Processing Systems , volume=

    work page

  65. [65]

    IEEE Transactions on Artificial Intelligence , year=

    DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networks , author=. IEEE Transactions on Artificial Intelligence , year=

    work page

  66. [66]

    Flavors of geometry , volume=

    Hyperbolic geometry , author=. Flavors of geometry , volume=. 1997 , publisher=

    work page 1997

  67. [67]

    Proceedings of the 41st International Conference on Machine Learning , pages =

    Cooperative Graph Neural Networks , author =. Proceedings of the 41st International Conference on Machine Learning , pages =. 2024 , editor =

    work page 2024

  68. [68]

    International Conference on Learning Representations (ICLR 2017) , year=

    Categorical Reparametrization with Gumble-Softmax , author=. International Conference on Learning Representations (ICLR 2017) , year=

    work page 2017

  69. [69]

    Proceedings of the international conference on learning Representations , year=

    The concrete distribution: A continuous relaxation of discrete random variables , author=. Proceedings of the international conference on learning Representations , year=

    work page

  70. [70]

    arXiv preprint arXiv:2404.06993 , year=

    Quiver Laplacians and Feature Selection , author=. arXiv preprint arXiv:2404.06993 , year=

    work page arXiv

  71. [71]

    International conference on machine learning , pages=

    On over-squashing in message passing neural networks: The impact of width, depth, and topology , author=. International conference on machine learning , pages=. 2023 , organization=

    work page 2023

  72. [72]

    2022 , booktitle=

    Understanding over-squashing and bottlenecks on graphs via curvature , author=. 2022 , booktitle=

    work page 2022

  73. [73]

    A Critical Look at the Evaluation of GNNs under Heterophily: Are We Really Making Progress?

    A critical look at the evaluation of GNNs under heterophily: Are we really making progress? , author=. arXiv preprint arXiv:2302.11640 , year=

    work page arXiv

  74. [74]

    Advances in neural information processing systems , volume=

    Inductive representation learning on large graphs , author=. Advances in neural information processing systems , volume=

    work page

  75. [75]

    Masked label prediction: Unified message passing model for semi-supervised classification

    Masked label prediction: Unified message passing model for semi-supervised classification , author=. arXiv preprint arXiv:2009.03509 , year=

    work page arXiv 2009

  76. [76]

    Learning on graphs conference , pages=

    Edge directionality improves learning on heterophilic graphs , author=. Learning on graphs conference , pages=. 2024 , organization=

    work page 2024

  77. [77]

    On the spectra of nonsymmetric Laplacian matrices , journal =

    Rafig Agaev and Pavel Chebotarev , keywords =. On the spectra of nonsymmetric Laplacian matrices , journal =. 2005 , note =

    work page 2005

  78. [78]

    International Conference on Machine Learning , pages=

    Efficient orthogonal parametrisation of recurrent neural networks using householder reflections , author=. International Conference on Machine Learning , pages=. 2017 , organization=

    work page 2017

  79. [79]

    Efficient householder transformation in pytorch, 2021

    Anton Obukhov , year=2021, title=. doi:10.5281/zenodo.5068733 , note=

    work page doi:10.5281/zenodo.5068733 2021

  80. [80]

    Learning to Discover Social Circles in Ego Networks , url =

    Leskovec, Jure and Mcauley, Julian , booktitle =. Learning to Discover Social Circles in Ego Networks , url =

    work page

Showing first 80 references.