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arxiv: 2605.10091 · v1 · submitted 2026-05-11 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

TopoU-Net: a U-Net architecture for topological domains

Gaurav Gaurav , Ibrahem ALJabea , Yaroslav Zakomornyy , Eric Frank , Mohamed Elhamdadi , Theodore Papamarkou , Mustafa Hajij
Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:49 UTC · model grok-4.3

classification 💻 cs.LG
keywords TopoU-Netcombinatorial complexesU-Net architecturetopological datanode classificationhypergraph learningincidence mapsencoder-decoder
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The pith

By treating ranks in combinatorial complexes as hierarchy levels, TopoU-Net provides a general U-Net template that works for graphs, hypergraphs, meshes, and images.

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

The paper establishes that the U-Net can be understood as a domain-independent hierarchical encoder-decoder principle rather than a grid-only design. It supplies the missing pieces—representation spaces at different ranks, incidence maps for moving information between ranks, and skip connections at matched ranks—by using combinatorial complexes whose cells and incidences already encode higher-order structure. The encoder lifts cochains upward along a chosen rank path, the decoder transports them downward, and the bottleneck support ratio shows when skips become structurally necessary. A sympathetic reader would care because many datasets contain groups, relations, and hyperedges that grids and standard graphs flatten, and this supplies one reusable template instead of inventing new pooling layers for each domain.

Core claim

The central claim is that combinatorial complexes supply cells at varying ranks, incidence relations for lifting and transport, and matched ranks for skips, so that a single rank-path U-Net architecture processes node, graph, hypergraph, mesh, and image data by selecting an input-to-bottleneck path rather than designing domain-specific scales; this yields the strongest mean accuracy among baselines on six of eight node-classification tasks and four of five hypergraph tasks, with largest gains on heterophilic graphs, and ablations confirm skips matter most under severe bottleneck compression.

What carries the argument

The rank path through the combinatorial complex together with incidence-based lifting maps in the encoder, transport maps in the decoder, and skip connections at equal ranks.

If this is right

  • Skip connections become structurally important precisely when the bottleneck support ratio is small relative to the input rank.
  • The architecture delivers the highest mean accuracy among evaluated baselines on six of eight node-classification datasets and four of five hypergraph datasets.
  • Selecting the rank path replaces the need to invent domain-specific pooling or unpooling operations.
  • The same encoder-decoder template applies directly to node classification, graph classification, hypergraph node classification, mesh classification, and image reconstruction.

Where Pith is reading between the lines

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

  • If rank paths could be selected or learned automatically, the method would need even less manual tuning for new datasets.
  • The lifting maps may help explain improved handling of heterophily by propagating information across dissimilar cells more effectively than standard convolutions.
  • The approach could be tested on dynamic topological data such as temporal hypergraphs or 3D point clouds with higher-order relations.
  • Connections to other higher-order models might arise by interpreting incidence lifts as specific forms of message aggregation.

Load-bearing premise

The chosen rank path and its incidence-based lifting and transport maps must preserve task-relevant information without substantial loss or the need for extensive domain-specific adjustments beyond path selection.

What would settle it

A concrete falsifier would be a higher-order dataset where the best rank-path choice still produces lower accuracy than a standard graph neural network baseline, or where ablating skip connections shows negligible performance change even when the bottleneck support ratio is very low.

Figures

Figures reproduced from arXiv: 2605.10091 by Eric Frank, Gaurav Gaurav, Ibrahem ALJabea, Mohamed Elhamdadi, Mustafa Hajij, Theodore Papamarkou, Yaroslav Zakomornyy.

Figure 1
Figure 1. Figure 1: A combinato￾rial complex with cells at ranks 0, 1, and 2. For an active rank r, a feature signal on the r-cells is represented as an r-cochain. We identify the corresponding cochain space with C r (X ; R dr ) := R nr×dr , where rows are indexed by cells in X r , and dr is the feature dimension at rank r. Thus H(r) ∈ C r (X ; R dr ) assigns one feature vector to each r-cell. 3.2 Incidence operators and rank… view at source ↗
Figure 2
Figure 2. Figure 2: Rank-induced hierarchy. Incidence maps transport features from lower to higher ranks in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Many modern datasets mix points, edges, regions, groups, objects, events, hyperedges, and relations. Yet neural architectures often force such data into grids, graphs, or sequences, obscuring higher-order structure and making encoder-decoder designs domain-specific. We view U-Net not as a grid-specific architecture, but as a hierarchical encoder-decoder principle: representation spaces, transport maps between levels, and skip connections between matched levels. Combinatorial complexes naturally supply these ingredients through cells, incidences, and ranks. We introduce TopoU-Net, a rank-path U-Net for topological domains. Given a path from an input rank to a bottleneck rank and back, the encoder lifts cochains upward along incidence maps, the decoder transports them downward, and skip connections merge features at matched ranks. Rank replaces spatial scale: choosing paths through nodes, edges, faces, hyperedges, or global cells becomes the central architectural decision. A key quantity is the bottleneck support ratio, the number of cells at the bottleneck relative to the number of cells at the input rank. This ratio is fixed by the complex and chosen path rather than by arbitrary pooling, and it clarifies when skip connections are optional, useful, or structurally important. Across node classification, graph classification, hypergraph node classification, mesh classification, and image reconstruction, TopoU-Net provides a reusable encoder-decoder template for higher-order structured data. Among the evaluated baselines, it achieves the strongest mean accuracy on six of eight node-classification datasets and four of five hypergraph datasets, with the largest gains on heterophilic graphs. Ablations show that removing skip connections is most damaging under severe bottleneck compression.

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

2 major / 3 minor

Summary. The manuscript introduces TopoU-Net, a U-Net-style encoder-decoder architecture adapted to combinatorial complexes for higher-order topological data. Ranks replace spatial scales: a chosen path through cells determines the hierarchy, with the encoder lifting cochains upward via incidence maps, the decoder transporting them downward, and skip connections merging features at matched ranks. The bottleneck support ratio is fixed by the complex and path rather than learned pooling. Empirical evaluation across node classification (graphs and hypergraphs), graph classification, mesh classification, and image reconstruction shows competitive or superior mean accuracies, with largest gains on heterophilic node-classification datasets and ablations indicating skip connections are most critical under severe compression.

Significance. If the performance claims hold under rigorous verification, the work offers a reusable, domain-agnostic template for hierarchical processing of mixed-rank structured data, reducing the need for bespoke encoder-decoder designs per modality. The combinatorial-complex foundation and fixed bottleneck ratio provide a principled alternative to ad-hoc pooling, with potential impact on topological deep learning.

major comments (2)
  1. [Method] Method section on incidence-based lifting and transport: the central claim that these maps preserve task-relevant heterophilic signals (needed to attribute largest gains on heterophilic graphs to the U-Net template rather than path selection) lacks any derivation, bound, or analysis showing that cochain transport does not average or project away distinguishing features, as occurs in standard graph convolutions.
  2. [Experiments] Experiments, node-classification results: while strongest mean accuracy is reported on six of eight datasets and largest gains on heterophilic graphs, the absence of reported statistical significance tests, variance across runs, or ablation isolating incidence lifting from path choice leaves the attribution of gains load-bearing for the reusable-template claim unverifiable from the presented evidence.
minor comments (3)
  1. [Method] The definition and computation of the bottleneck support ratio should be given an explicit equation or pseudocode in the method section for reproducibility.
  2. [Figure 1] Figure captions for the architecture diagram should explicitly label the rank path, incidence maps, and skip-connection merges to match the textual description.
  3. [Related Work] The related-work section would benefit from explicit comparison to prior topological neural networks that also use incidence or cochain structures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below, providing clarifications and indicating the revisions we will make to the next version of the paper.

read point-by-point responses

  1. Referee: [Method] Method section on incidence-based lifting and transport: the central claim that these maps preserve task-relevant heterophilic signals (needed to attribute largest gains on heterophilic graphs to the U-Net template rather than path selection) lacks any derivation, bound, or analysis showing that cochain transport does not average or project away distinguishing features, as occurs in standard graph convolutions.

    Authors: We agree that an explicit analysis of signal preservation would strengthen the attribution of gains to the overall architecture. In the revised manuscript we will add a dedicated paragraph in the Method section deriving the action of the incidence-based lifting and transport maps. These maps are realized by the (un-normalized) incidence matrices of the combinatorial complex; they transfer cochain values exactly along incidences between distinct ranks and perform no intra-rank averaging or normalization of the kind present in standard graph convolutions. Consequently, heterophilic distinctions encoded at the input rank are not smoothed during upward or downward transport. We will also show that, in the absence of bottleneck compression, the round-trip composition of lift and transport recovers the original cochain, and we will discuss how skip connections mitigate information loss under compression. A general theoretical bound that holds for arbitrary heterophily measures would require additional distributional assumptions and lies outside the scope of the present work; the empirical results and ablations remain the primary support for the practical utility of the template. revision: yes

  2. Referee: [Experiments] Experiments, node-classification results: while strongest mean accuracy is reported on six of eight datasets and largest gains on heterophilic graphs, the absence of reported statistical significance tests, variance across runs, or ablation isolating incidence lifting from path choice leaves the attribution of gains load-bearing for the reusable-template claim unverifiable from the presented evidence.

    Authors: We acknowledge that the current experimental reporting is insufficient to fully substantiate the attribution of gains. In the revised version we will augment all node-classification tables with standard deviations computed over ten independent runs using different random seeds. We will also add paired t-test p-values comparing TopoU-Net against the strongest baseline on each dataset. In addition, we will include a new ablation that fixes the rank path and replaces the incidence-based lifting/transport with learned linear projections of matching dimensions; the performance difference between the two variants will help isolate the contribution of the incidence maps from the choice of path. These additions will make the experimental support for the reusable-template claim verifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain.

full rationale

The paper defines TopoU-Net constructively by adapting the U-Net encoder-decoder template to combinatorial complexes: encoder lifts cochains along incidence maps, decoder transports downward, and skip connections merge at matched ranks, with rank replacing spatial scale and bottleneck support ratio fixed by the input complex and chosen path. This is a first-principles architectural definition, not a derivation that reduces to fitted parameters or self-referential equations by construction. All performance claims (strongest mean accuracy on six of eight node-classification datasets, etc.) are empirical results from experiments rather than predictions derived from the model equations themselves. No load-bearing self-citation chains or ansatzes are invoked to justify the central template; the architecture and evaluations are self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard definitions and properties of combinatorial complexes and incidence maps from topological data analysis; no new free parameters are fitted and no new entities are postulated.

axioms (1)
  • domain assumption Combinatorial complexes supply cells, incidence relations, and ranks that can serve as representation spaces and transport maps for hierarchical encoder-decoder networks.
    Invoked when the paper reframes U-Net as a general principle and substitutes combinatorial complexes for grids.

pith-pipeline@v0.9.0 · 5629 in / 1373 out tokens · 55540 ms · 2026-05-12T03:49:13.956879+00:00 · methodology

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Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages · 4 internal anchors

  1. [1]

    MixHop: Higher-order graph convolutional architectures via sparsified neighborhood mixing

    Sami Abu-El-Haija, Bryan Perozzi, Amol Kapoor, Nazanin Alipourfard, Kristina Lerman, Hrayr Harutyunyan, Greg Ver Steeg, and Aram Galstyan. MixHop: Higher-order graph convolutional architectures via sparsified neighborhood mixing. InProceedings of the 36th International Conference on Machine Learning, volume 97 ofProceedings of Machine Learning Research, p...

    work page 2019

  2. [2]

    HyperSAGE: Gen- eralizing inductive representation learning on hypergraphs

    Devanshu Arya, Deepak K. Gupta, Stevan Rudinac, and Marcel Worring. Hypersage: Gener- alizing inductive representation learning on hypergraphs.arXiv preprint arXiv:2010.04558, 2020

    work page arXiv 2010

  3. [3]

    Topological signal processing over simplicial complexes.IEEE Transactions on Signal Processing, 68:2992–3007, 2020

    Sergio Barbarossa and Stefania Sardellitti. Topological signal processing over simplicial complexes.IEEE Transactions on Signal Processing, 68:2992–3007, 2020

    work page 2020

  4. [4]

    Generalized simplicial attention neural networks.arXiv preprint arXiv:2309.02138, 2023

    Claudio Battiloro, Lucia Testa, Lorenzo Giusti, Stefania Sardellitti, Paolo Di Lorenzo, and Sergio Barbarossa. Generalized simplicial attention neural networks.arXiv preprint arXiv:2309.02138, 2023

    work page arXiv 2023

  5. [5]

    Spectral clustering with graph neural networks for graph pooling

    Filippo Maria Bianchi, Daniele Grattarola, and Cesare Alippi. Spectral clustering with graph neural networks for graph pooling. InProceedings of the 37th International Conference on Machine Learning, volume 119 ofProceedings of Machine Learning Research, pages 874–883, 2020

    work page 2020

  6. [6]

    Bronstein

    Cristian Bodnar, Francesco Di Giovanni, Benjamin Paul Chamberlain, Pietro Liò, and Michael M. Bronstein. Neural sheaf diffusion: A topological perspective on heterophily and oversmoothing in GNNs. InAdvances in Neural Information Processing Systems, volume 35, pages 18527–18541, 2022

    work page 2022

  7. [7]

    Towards sparse hierarchical graph classifiers

    C˘at˘alina Cangea, Petar Veliˇckovi´c, Nikola Jovanovi´c, Thomas Kipf, and Pietro Liò. Towards sparse hierarchical graph classifiers. InNeurIPS Workshop on Relational Representation Learning, 2018. arXiv:1811.01287

    work page arXiv 2018

  8. [8]

    Pooling strategies for simplicial convolutional networks

    Domenico Mattia Cinque, Claudio Battiloro, and Paolo Di Lorenzo. Pooling strategies for simplicial convolutional networks. InIEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1–5, 2023

    work page 2023

  9. [9]

    Hnhn: Hypergraph networks with hyperedge neurons

    Yihe Dong, Will Sawin, and Yoshua Bengio. Hnhn: Hypergraph networks with hyperedge neurons. InICML 2020 Workshop on Graph Representation Learning and Beyond (GRL+), 2020

    work page 2020

  10. [10]

    Mark Everingham, Luc Van Gool, Christopher K. I. Williams, John Winn, and Andrew Zis- serman. The pascal visual object classes (voc) challenge.International Journal of Computer Vision, 88(2):303–338, 2010

    work page 2010

  11. [11]

    Hypergraph neural networks

    Yifan Feng, Haoxuan You, Zizhao Zhang, Rongrong Ji, and Yue Gao. Hypergraph neural networks. InProceedings of the AAAI Conference on Artificial Intelligence, volume 33, pages 3558–3565, 2019

    work page 2019

  12. [12]

    Graph U-Nets

    Hongyang Gao and Shuiwang Ji. Graph U-Nets. InProceedings of the 36th International Conference on Machine Learning, volume 97 ofProceedings of Machine Learning Research, pages 2083–2092, 2019

    work page 2083

  13. [13]

    Hgnn+: General hypergraph neural networks

    Yue Gao, Yifan Feng, Shuyi Ji, and Rongrong Ji. Hgnn+: General hypergraph neural networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(3):3181–3199, 2023

    work page 2023

  14. [14]

    Simplicial attention neural networks.arXiv preprint arXiv:2203.07485, 2022

    Lorenzo Giusti, Claudio Battiloro, Paolo Di Lorenzo, Stefania Sardellitti, and Sergio Barbarossa. Simplicial attention neural networks.arXiv preprint arXiv:2203.07485, 2022

    work page arXiv 2022

  15. [15]

    Cell attention networks

    Lorenzo Giusti, Claudio Battiloro, Lucia Testa, Paolo Di Lorenzo, Stefania Sardellitti, and Sergio Barbarossa. Cell attention networks. InInternational Joint Conference on Neural Networks (IJCNN), pages 1–8, 2023. 10

    work page 2023

  16. [16]

    Cell complex neural networks

    Mustafa Hajij, Kyle Istvan, and Ghada Zamzmi. Cell complex neural networks. InNeurIPS Workshop on Topological Data Analysis and Beyond, 2020. arXiv:2010.00743 [cs.LG]

    work page arXiv 2020

  17. [17]

    Samaga, Simone Scardapane, Michael T

    Mustafa Hajij, Mathilde Papillon, Florian Frantzen, Jens Agerberg, Ibrahem AlJabea, Ruben Ballester, Claudio Battiloro, Guillermo Bernárdez, Tolga Birdal, Aiden Brent, Peter Chin, Sergio Escalera, Simone Fiorellino, Odin Hoff Gardaa, Gurusankar Gopalakrishnan, Devendra Govil, Josef Hoppe, Maneel Reddy Karri, Jude Khouja, Manuel Lecha, Neal Livesay, Jan Me...

    work page arXiv 2024

  18. [18]

    High skip networks: A higher order generalization of skip connections

    Mustafa Hajij, Karthikeyan Natesan Ramamurthy, Aldo Guzmán-Sáenz, and Ghada Zamzmi. High skip networks: A higher order generalization of skip connections. InICLR 2022 Workshop on Geometrical and Topological Representation Learning, 2022

    work page 2022

  19. [19]

    Topological deep learning: Going beyond graph data

    Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou, Nina Miolane, Aldo Guzmán-Sáenz, Karthikeyan Natesan Ramamurthy, Tolga Birdal, Tamal K. Dey, Soham Mukherjee, Shreyas N. Samaga, Neal Livesay, Robin Walters, Paul Rosen, and Michael T. Schaub. Topological deep learning: Going beyond graph data.arXiv preprint arXiv:2206.00606, 2023

    work page arXiv 2023

  20. [20]

    Hamilton, Rex Ying, and Jure Leskovec

    William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large graphs. InAdvances in Neural Information Processing Systems, volume 30, pages 1024–1034, 2017

    work page 2017

  21. [21]

    Unet 3+: A full-scale connected unet for medical image segmentation

    Huimin Huang, Lanfen Lin, Ruofeng Tong, Hongjie Hu, Qiaowei Zhang, Yutaro Iwamoto, Xianhua Han, Yen-Wei Chen, and Jian Wu. Unet 3+: A full-scale connected unet for medical image segmentation. InIEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1055–1059, 2020

    work page 2020

  22. [22]

    Semi-Supervised Classification with Graph Convolutional Networks

    Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolu- tional networks. InInternational Conference on Learning Representations (ICLR), 2017. arXiv:1609.02907

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  23. [23]

    Hodge laplacians on graphs.SIAM Review, 62(3):685–715, 2020

    Lek-Heng Lim. Hodge laplacians on graphs.SIAM Review, 62(3):685–715, 2020

    work page 2020

  24. [24]

    Attention U-Net: Learning Where to Look for the Pancreas

    Ozan Oktay, Jo Schlemper, Loic Le Folgoc, Matthew Lee, Mattias Heinrich, Kazunari Misawa, Kensaku Mori, Steven McDonagh, Nils Y . Hammerla, Bernhard Kainz, Ben Glocker, and Daniel Rueckert. Attention u-net: Learning where to look for the pancreas. InMedical Imaging with Deep Learning (MIDL), 2018. arXiv:1804.03999

    work page internal anchor Pith review arXiv 2018

  25. [25]

    Parkhi, Andrea Vedaldi, Andrew Zisserman, and C

    Omkar M. Parkhi, Andrea Vedaldi, Andrew Zisserman, and C. V . Jawahar. Cats and dogs. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3498–3505, 2012

    work page 2012

  26. [26]

    Mitchell Roddenberry and Santiago Segarra

    T. Mitchell Roddenberry and Santiago Segarra. Hodgenet: Graph neural networks for edge data. InAsilomar Conference on Signals, Systems, and Computers, pages 220–224, 2019

    work page 2019

  27. [27]

    U-net: Convolutional networks for biomedical image segmentation

    Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. InMedical Image Computing and Computer-Assisted Interven- tion (MICCAI), volume 9351 ofLecture Notes in Computer Science, pages 234–241. Springer, 2015

    work page 2015

  28. [28]

    Schaub, Yu Zhu, Jean-Baptiste Seby, T

    Michael T. Schaub, Yu Zhu, Jean-Baptiste Seby, T. Mitchell Roddenberry, and Santiago Segarra. Signal processing on higher-order networks: Livin’ on the edge... and beyond.Signal Processing, 187:108149, 2021

    work page 2021

  29. [29]

    Graph Attention Networks

    Petar Veliˇckovi´c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph attention networks. InInternational Conference on Learning Representations (ICLR), 2018. arXiv:1710.10903. 11

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  30. [30]

    3d shapenets: A deep representation for volumetric shapes

    Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguang Zhang, Xiaoou Tang, and Jianxiong Xiao. 3d shapenets: A deep representation for volumetric shapes. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1912–1920, 2015

    work page 1912

  31. [31]

    How Powerful are Graph Neural Networks?

    Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? InInternational Conference on Learning Representations (ICLR), 2019. arXiv:1810.00826

    work page internal anchor Pith review arXiv 2019

  32. [32]

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

    Naganand Yadati, Madhav Nimishakavi, Prateek Yadav, Vihari Nitin, Anand Louis, and Partha Talukdar. Hypergcn: A new method for training graph convolutional networks on hypergraphs. In Hanna Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d’Alché Buc, Emily Fox, and Roman Garnett, editors,Advances in Neural Information Processing Systems, volume 32, ...

    work page 2019

  33. [33]

    Hamilton, and Jure Leskovec

    Rex Ying, Jiaxuan You, Christopher Morris, Xiang Ren, William L. Hamilton, and Jure Leskovec. Hierarchical graph representation learning with differentiable pooling. InAdvances in Neural Information Processing Systems, volume 31, pages 4800–4810, 2018

    work page 2018

  34. [34]

    Road extraction by deep residual u-net

    Zhengxin Zhang, Qingjie Liu, and Yunhong Wang. Road extraction by deep residual u-net. IEEE Geoscience and Remote Sensing Letters, 15(5):749–753, 2018

    work page 2018

  35. [35]

    Unet++: A nested u-net architecture for medical image segmentation

    Zongwei Zhou, Md Mahfuzur Rahman Siddiquee, Nima Tajbakhsh, and Jianming Liang. Unet++: A nested u-net architecture for medical image segmentation. InDeep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, volume 11045 ofLecture Notes in Computer Science, pages 3–11. Springer, 2018

    work page 2018

  36. [36]

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

    Jiong Zhu, Yujun Yan, Lingxiao Zhao, Mark Heimann, Leman Akoglu, and Danai Koutra. Beyond homophily in graph neural networks: Current limitations and effective designs. In Advances in Neural Information Processing Systems, volume 33, pages 7790–7801, 2020

    work page 2020

  37. [37]

    Topological deep learning: A review of an emerging paradigm.Artificial Intelligence Review, 57(4):77, 2024

    Ali Zia, Abdelwahed Khamis, James Nichols, Usman Bashir Tayab, Zeeshan Hayder, Vivien Rolland, Eric Stone, and Lars Petersson. Topological deep learning: A review of an emerging paradigm.Artificial Intelligence Review, 57(4):77, 2024. A Proofs and additional theoretical elaborations A.1 Additional rank-transport parameterizations This appendix lists sever...

    work page 2024