Publications 2026
Topological Deep Learning Challenge 2026: Bridging the Gap
Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science (TAG-DS 2026, PMLR) Track 1 Winner
The 2026 TDL Challenge set GNNs and TNNs side by side in TopoBench on GraphUniverse graphs; our DSNN implementation took first place in Track 1.
Abstract
This paper describes the 2026 edition of the Topological Deep Learning Challenge: Bridging the Gap, hosted at the second Topology, Algebra, and Geometry in Data Science (TAG-DS) Conference. Where previous editions grew the modelling and data ecosystem of Topological Deep Learning (TDL), this edition set out to place Graph Neural Networks (GNNs) and Topological Neural Networks (TNNs) side by side under a single evaluation pipeline. Participants implemented recent state-of-the-art architectures in TopoBench, with Track 1 covering GNNs and Track 2 covering TNNs. They evaluated these implementations on shared synthetic benchmarks generated with GraphUniverse, which independently controls homophily, average degree and degree-distribution heaviness. The challenge yielded 68 qualifying submissions from 34 teams, spanning the graph, simplicial, cellular, hypergraph and combinatorial domains. For the first time, submissions were also tracked on a public leaderboard, which we summarize and analyze here. Our analysis finds that the differences between the submitted tracks are strongly task-dependent: the mean accuracy gap is modest on community detection, while on triangle counting the Track 1 mean error is 1.85 times the Track 2 mean. Several structurally informed GNNs also outperform the Track 2 mean on triangle counting.
Cite
@inproceedings{pmlr-v334-bernardez26a,
title = {Topological Deep Learning Challenge 2026: Bridging the Gap},
author = {Bern{\'a}rdez, Guillermo and Telyatnikov, Lev and Papillon, Mathilde and Montagna, Marco and Cornelis, Louisa and Van Langendonck, Louis and Purificato, Antonio and Neri, Bruno and Leko, David and Genovese, Donatella and Grassucci, Eleonora and Van Looy, Jan-Willem and Mathe, Johan and Testa, Lucia and Beni{\'c}, Luka and Weber, Melanie and Zaghen, Olga and Vasylenko, Pavlo and Theiler, Raffael and Mahan, Scott and Khanal, Gaurav and S{\'a}nchez, Valentina and Loi, Dario and Onorato, Gabriele and Devadiga, Prasanna and Paik, Taejin and Velasco Sotomayor, Anier and M{\"u}ller, Jonas and Gupta, Aarav and Patel, Riyan and Mboya, Grold Otieno and Devadiga, Pushparaj and Gohain, Adam and Filipiak, Dominik and Banf, Michael and Mohammadian, Alireza and Akbari, Amirreza and Chaviano D{\'i}az, Gabriel and Ch{\'a}vez Mesa, Marcos and Grover, Ankit and Bourgerie, R{\'e}mi and Comparini, Alessio and Kumar, Ankit and Yusuf, Mohammad and Kaushal, Devesh and Orsi, Francesco and Mostofi, Ghazal and Lettl, Kolya and Khattami, Salwa and Franco, Gabriel and Falkouskaya, Yelizaveta and Franco, Jorge Luiz and Singla, Kajal and Espinosa I{\~n}iguez, Fernando David and Patil, Raj and Dolores-Cuenca, Eric and Petti, Luigi and Xu, Chenguang and Blando, Stefano and Zeh, Christine and Bastian, Lennart and Zheng, Kaden and Tiwari, Vihan and Athreya, Sud and Kajita, Hisataka and Micheron, Hugo and Devaux, R{\'e}mi and Jardin, Antoine and Emerson, Tegan and Fink, Olga and Miolane, Nina},
booktitle = {Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science (TAG-DS 2026)},
pages = {4--29},
year = {2026},
editor = {Berman, Eddie and Bern{\'a}rdez, Guillermo and Chen, Samantha and Cloninger, Alex and Doster, Timothy and Emerson, Tegan and Grigsby, J. Elisenda and Kvinge, Henry and Lawrence, Hannah and Marrinan, Tim and Myers, Audun and Papillon, Mathilde and Tahmasebi, Behrooz and Telyatnikov, Lev and Walters, Robin and Weber, Melanie and Xie, YuQing and Yeats, Eric},
volume = {334},
number = {2},
series = {Proceedings of Machine Learning Research},
month = {18--20 Aug},
publisher = {PMLR},
pdf = {https://raw.githubusercontent.com/mlresearch/v334/main/assets/bernardez26a/bernardez26a.pdf},
url = {https://proceedings.mlr.press/v334/bernardez26a.html}
}