Awesome TDL

A curated list of Topological Deep Learning (TDL) tools and resources.

1. Simplicial Neural Networks. Stefania Ebli, Michaël Defferrard, Gard Spreemann. NeurIPS 2020 Workshop TDA and Beyond. Paper, Code ,

2. Simplicial 2-Complex Convolutional Neural Nets. Eric Bunch, Qian You, Glenn Fung, Vikas Singh. NeurIPS 2020 Workshop TDA and Beyond. Paper, Code ,

3. Cell complex neural networks. Mustafa Hajij, Kyle Istvan, and Ghada Zamzmi. NeurIPS Workshop on Topological Data Analysis and Beyond, 2020. Paper,

4. Principled simplicial neural networks for trajectory prediction. Roddenberry, T. Mitchell, Nicholas Glaze, and Santiago Segarra. ICML 2021. Paper, Code

5. Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks. Cristian Bodnar, Fabrizio Frasca, Yu Guang Wang, Nina Otter, Guido Montúfar, Pietro Liò, Michael Bronstein. ICML 2021. Paper, Code

6. Weisfeiler and Lehman Go Cellular: CW Networks. Cristian Bodnar, Fabrizio Frasca, Nina Otter, Yu Guang Wang, Pietro Liò, Guido Montúfar, Michael Bronstein. NeurIPS 2021. Paper, Code

7. Simplicial Attention Neural Networks. Lorenzo Giusti, Claudio Battiloro, Paolo Di Lorenzo, Stefania Sardellitti, Sergio Barbarossa. arXiv 2022. Paper, Code

8. Simplicial Attention Networks. Christopher Wei Jin Goh, Cristian Bodnar, Pietro Liò. ICLR 2022 Workshop on Geometrical and Topological Representation Learning. Paper, Code

9. Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs. Cristian Bodnar, Francesco Di Giovanni, Benjamin Paul Chamberlain, Pietro Liò, Michael M. Bronstein. NeurIPS 2022. Paper, Code

10. Simplicial Convolutional Neural Networks. Maosheng Yang, Elvin Isufi, Geert Leus. ICASSP 2022. Paper, Code

11. Sheaf Neural Networks with Connection Laplacians. Federico Barbero, Cristian Bodnar, Haitz Sáez de Ocáriz Borde, Michael Bronstein, Petar Veličković, Pietro Liò. ICML 2022 Workshop on Topology, Algebra, and Geometry in Machine Learning. Paper

12. Sheaf Attention Networks. Federico Barbero, Cristian Bodnar, Haitz Sáez de Ocáriz Borde, Pietro Liò. NeurIPS 2022 NeurReps Workshop. Paper

13. Cell Attention Networks. Lorenzo Giusti, Claudio Battiloro, Lucia Testa, Paolo Di Lorenzo, Stefania Sardellitti, Sergio Barbarossa. IEEE IJCNN 2023. Paper, Code

14. Surfing on the Neural Sheaf. Julian Suk, Lorenzo Giusti, Tamir Hemo, Miguel Lopez, Konstantinos Barmpas, Cristian Bodnar. NeurIPS 2022 NeurReps Workshop. Paper

15. Architectures of Topological Deep Learning: A Survey on Topological Neural Networks. Mathilde Papillon, Sophia Sanborn, Mustafa Hajij, Nina Miolane. Paper

16. Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back. Claudio Battiloro, Zhiyang Wang, Hans Riess, Paolo Di Lorenzo, Alejandro Ribeiro. Paper, Code

17. Topological Graph Neural Networks. Max Horn, Edward De Brouwer, Michael Moor, Yves Moreau, Bastian Rieck, and Karsten Borgwardt. ICLR 2022. Paper, Code

18. Topological Autoencoders. Michael Moor, Max Horn, Bastian Rieck, and Karsten Borgwardt. ICML 2020. Paper, Code

19. E(n) Equivariant Message Passing Simplicial Networks. Floor Eijkelboom, Rob Hesselink, Erik Bekkers. ICML 2023. Paper

20. CIN++: Enhancing Topological Message Passing. Lorenzo Giusti, Teodora Reu, Francesco Ceccarelli, Cristian Bodnar, Pietro Liò. Paper, Code

21. Simplicial Hopfield networks. Thomas F Burns, Tomoki Fukai. ICLR 2023. Paper, Code,

22. Topological Deep Learning: Graphs, Complexes, Sheaves. Cristian Bodnar. Thesis

23. Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes. Quang Truong and Peter Chin. AAAI 2024. Paper, Code

24. Generalized simplicial attention neural networks. Claudio Battiloro, Lucia Testa, Lorenzo Giusti, Stefania Sardellitti, Paolo Di Lorenzo, Sergio Barbarossa. Paper

25. TopoX: A Suite of Python Packages for Machine Learning on Topological Domains. Mustafa Hajij, Mathilde Papillon, Florian Frantzen et al. Paper, Code

26. Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactions. Lorenzo Giusti. Thesis

27. From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module. Claudio Battiloro, Indro Spinelli et al. Paper, Code, Blogpost

28. E(n) Equivariant Topological Neral Networks. Claudio Battiloro, Ege Karaismailoğlu, Mauricio Tec, George Dasoulas et al. Paper, Code, Blogpost

29. Signal Processing and Learning over Topological Spaces. Claudio Battiloro. Thesis

30. Gaussian Processes on Cellular Complexes. Mathieu Alain, So Takao, Brooks Paige, Marc Peter Deisenroth. ICML 2024. Paper

31. TopoTune: A Framework for Generalized Combinatorial Complex Neural Networks. Mathilde Papillon, Guillermo Bernárdez, Claudio Battiloro, and Nina Miolane. Paper, Code

32. Molecular topological deep learning for polymer property prediction. Cong Shen, Yipeng Zhang, Fei Han, Kelin Xia. Paper

33. Bayesian Sheaf Neural Networks. Patrick Gillespie, Vasileios Maroulas, Ioannis Schizas. Paper

34. Higher-Order Topological Directionality and Directed Simplicial Neural Networks. Manuel Lecha, Andrea Cavallo, Francesca Dominici, Elvin Isufi, Claudio Battiloro. Paper, Code

35. TopoBenchmarkX: A Framework for Benchmarking Topological Deep Learning. Lev Telyatnikov, Guillermo Bernardez, Marco Montagna, Pavlo Vasylenko, Ghada Zamzmi, Mustafa Hajij, Michael T Schaub, Nina Miolane, Simone Scardapane, Theodore Papamarkou. Paper, Code

36. Topological Network Traffic Compression. Guillermo Bernárdez, Lev Telyatnikov, Eduard Alarcón, Albert Cabellos-Aparicio, Pere Barlet-Ros, Pietro Liò. Proceedings of the 2nd on Graph Neural Networking Workshop 2023. Paper

37. Topological Deep Learning: Going Beyond Graph Data. Mustafa Hajij, Theodore Papamarkou, Ghada Zamzmi, Karthikeyan Natesan Ramamurthy, Tolga Birdal, Michael T. Schaub Book

38. HOG-Diff: Higher-Order Guided Diffusion for Graph Generation. Huang, Yiming, and Tolga Birdal. arXiv preprint arXiv:2502.04308 (2025). Paper, Code

39. Higher-Order Molecular Learning: The Cellular Transformer. Melih Barsbey, Rubén Ballester, Andac Demir, Carles Casacuberta, Pablo Hernández-García, David Pujol-Perich, Sarper Yurtseven, Sergio Escalera, Claudio Battiloro, Mustafa Hajij, Tolga Birdal (2025). Paper

40. Sheaf Hypergraph Networks. Iulia Duta, Giulia Cassarà, Fabrizio Silvestri, Pietro Liò. NeurIPS 2023. Paper, Code

41. Learning From Simplicial Data Based on Random Walks and 1D Convolutions (SCRaWl). Florian Frantzen, Harald Oberhauser, Michael T. Schaub. ICLR 2024. Paper, Code

42. Simplicial Representation Learning with Neural k-Forms. Kelly Maggs, Celia Hacker, Bastian Rieck. ICLR 2024. Paper, OpenReview, Code

43. Differentiable Euler Characteristic Transforms for Shape Classification (DECT). Ernst Röell, Bastian Rieck. ICLR 2024. Paper, Code

44. Topological Deep Learning with State-Space Models (Mamba Approach). Marco Montagna, Simone Scardapane, Lev Telyatnikov. arXiv 2024. Paper

45. Topological Blindspots: Understanding and Extending Topological Deep Learning. Yoav Gelberg, Yaniv Romano, Haggai Maron. ICLR 2025 (Oral). Paper, Code (SMCN)

46. Bundle Neural Networks for Message Diffusion on Graphs (BuNNs). Jacob Bamberger, Federico Barbero, Xiaowen Dong, Michael Bronstein. ICLR 2025. Paper, OpenReview, Code

47. Heterogeneous Sheaf Neural Networks. Oualid Zaghen, Azzedine El Moutaouakil, Jean-Guy Mailly, Sylvain Lamprier. arXiv 2024. Paper

48. Continuous Simplicial Neural Networks (COSIMO). Vasileios Margaris, Petar Kormushev. arXiv 2025. Paper

49. Quantum Simplicial Neural Networks. Simone Piperno, Claudio Battiloro, Andrea Ceschini, Francesca Dominici, Paolo Di Lorenzo, Massimo Panella. arXiv 2025. Paper

50. Fast and Simplex: 2-Simplicial Attention in Triton. Ari Koskela, Ufois Demangeat, Arthur Mensch. ICLR 2025 submission / arXiv 2024. Paper

51. Sheaf-based Positional Encodings for Graph Neural Networks. Yu He, Cristian Bodnar, Pietro Liò. NeurIPS 2024 Workshop (SGNR). Paper, OpenReview

52. A Sheaf Neural Framework for Influence Maximization. Adithya Hevapathige, Guni Sharon, Subbarao Kambhampati. AAAI 2025. Paper

53. Binarized Simplicial Convolutional Neural Networks. Yi Yan, Ercan E. Kuruoglu. arXiv 2024. Paper

54. MANTRA: The Manifold Triangulations Assemblage (Dataset/Benchmark for TDL). Rubén Ballester, Ernst Röell, Daniel Bin Schmid, Mathieu Alain, Sergio Escalera, Carles Casacuberta, Bastian Rieck. ICLR 2025 (Poster). Paper

55. Copresheaf Topological Neural Networks: A Generalized Framework for Learning on Sheaves. Mustafa Hajij, Mathilde Papillon, Florian Frantzen, et al. arXiv 2025. Paper

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Topological Signal Processing

1. Topological signal processing over simplicial complexes. Sergio Barbarossa, Stefania Sardellitti. IEEE Transactions on Signal Processing 2020. Paper
2. Signal processing on higher-order networks: Livin’ on the edge... and beyond. Michael T. Schaub, Yu Zhu, Jean-Baptiste Seby, T. Mitchell Roddenberry, Santiago Segarra. Signal Processing, 2021 - Elsevier Paper
3. Hodge Laplacians on Graphs. Lek-Heng Lim. Society for Industrial and Applied Mathematics 2020. Paper
4. Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian. Michael T. Schaub, Austin R. Benson, Paul Horn, Gabor Lippner, Ali Jadbabaie. SIAM 2020. Paper
5. What are higher-order networks? Christian Bick, Elizabeth Gross, Heather A. Harrington, Michael T. Schaub. arXiv 2021. Paper
6. Topological Signal Processing over Cell Complexes. Stefania Sardellitti, Sergio Barbarossa, Lucia Testa. arXiv 2021. Paper
7. Topological Signal Representation and Processing over Cell Complexes. Stefania Sardellitti, Sergio Barbarossa. arXiv 2022. Paper
8. Robust Signal Processing Over Simplicial Complexes. Stefania Sardellitti, Sergio Barbarossa. ICASSP 2022. Paper
9. The physics of higher-order interactions in complex systems. Battiston, Federico, Enrico Amico, Alain Barrat, Ginestra Bianconi, Guilherme Ferraz de Arruda, Benedetta Franceschiello, Iacopo Iacopini et al. Nature Physics Paper
10. Recovery of Signals on a Simplicial Complex from Subsampled Neighbourhood Aggregation. Siddartha Reddy; Sundeep Prabhakar Chepuri. IEEE Signal Processing Letters Paper

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Algebraic Topology

1. Computational and applied topology, tutorial. Paweł Dłotko. 2018. Paper
2. Algebraic topology. Allen Hatcher. Cambridge Univ. Press. 2000. Book
3. Cell Complexes through Time. Reinhard Klette. Vision Geometry. 2000. Paper
4. Computational Topology for Data Analysis. Tamal Krishna Dey. Cambridge University Press 2022. Book
5. Topological Methods in Machine Learning: A Tutorial for Practitioners. Baris Coskunuzer, Cüneyt Gürcan Akçora. 2024. Paper

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Differential Geometry

1. Introduction to Differential Geometry. Joel W. Robbin, Dietmar A. Salamon. Book
2. Differential Geometry and Stochastic Dynamics with Deep Learning Numerics Line Kühnel, Alexis Arnaudon, and Stefan Sommer. arXiv 2017. Paper
3. Differential Geometry meets Deep Learning (DiffGeo4DL) Joey Bose · Emile Mathieu · Charline Le Lan · Ines Chami · Frederic Sala · Christopher De Sa · Maximilian Nickel · Christopher Ré · Will Hamilton. NeurIPS 2020 Workshop. Link
4. Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges. Michael M. Bronstein, Joan Bruna, Taco Cohen, Petar Veličković. 2021. Book
5. Mathematical Foundations of Geometric Deep Learning. Haitz Sáez de Ocáriz Borde, Michael Bronstein. 2025. Paper

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Discrete Calculus

1. Discrete Exterior Calculus. Anil N. Hirani. Caltech Library 2003. PhD Thesis

2. Discrete Calculus: Applied Analysis on Graphs for Computational Science. Leo J. Grady, Jonathan R. Polimeni. Springer 2010 . Book

3. Discrete Differential Forms for Computational Modeling. Mathieu Desbrun, Eva Kanso & Yiying Tong. SIGGRAPH 2006. Paper

4. Exterior Calculus in Graphics. Stephanie Wang, Mohammad Sina Nabizadeh, and Albert Chern. Course notes for a SIGGRAPH 2023 course Notes

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Courses

1. Computational Algebraic Topology. Vidit Nanda. Website, Notes, Lectures

2. Discrete Differential Geometry. Keenan Crane. Website, Notes, Lectures

3. Shape Analysis. Justin Solomon. Website, Lectures

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Blog

1. Learning on Topological Spaces: A new computational fabric for Graph Neural Networks. Michael Bronstein, Cristian Bodnar and Fabrizio Frasca. URL

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Libraries

1. GUDHI: Geometry Understanding in Higher Dimensions. Website, Code, Tutorial
2. PyDEC: Software and Algorithms for Discretization of Exterior Calculus. Nathan Bell, Anil N. Hirani. 2011. Paper, Code
3. TopoX: A Suite of Python Packages for Machine Learning on Topological Domains. 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 Meißner, Soham Mukherjee, Alexander Nikitin, Theodore Papamarkou, Jaro Prílepok, Karthikeyan Natesan Ramamurthy, Paul Rosen, Aldo Guzmán-Sáenz, Alessandro Salatiello, Shreyas N. Samaga, Simone Scardapane, Michael T. Schaub, Luca Scofano, Indro Spinelli, Lev Telyatnikov, Quang Truong, Robin Walters, Maosheng Yang, Olga Zaghen, Ghada Zamzmi, Ali Zia, Nina Miolane. Paper Code