Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning

Mathilde Papillon, Guillermo Bernardez, Álvaro Ballón Barreiro, Marco Montagna, Rémi Devaux, Antoine JARDIN, Nina Miolane
Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), PMLR 334(2):298-315, 2026.

Abstract

Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs. In practice, this lifting step is often treated as a black box: practitioners select a lifting and then tune architectures, with limited visibility into whether the induced higher-order connectivity is meaningful for the downstream task. To address this missing diagnostic layer, we propose a visualization technique called TopoExplorer that leverages the strictly augmented Hasse graph form of topological datasets for exploratory data analysis. For the first time, practitioners can easily visualize the incidence- and adjacency-based neighborhoods that define the lifted dataset, as well as read off key graph metrics that describe its structural and feature landscape. Via an extensive set of experiments across many datasets and liftings, we show that several of these metrics correlate with downstream model performance, suggesting they can help inform TDL preprocessing design. Our perspective reframes the TDL workflow from *lift-train* to *lift-look-design-train*, enabling more principled, interpretable, and efficient model development. TopoExplorer is hosted at topoexplorer.pagekite.me, and its source code is available at github.com/geometric-intelligence/topoexplorer.

Cite this Paper

BibTeX
@InProceedings{pmlr-v334-papillon26a, title = {Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning}, author = {Papillon, Mathilde and Bernardez, Guillermo and Barreiro, {\'{A}}lvaro Ball{\'{o}}n and Montagna, Marco and Devaux, R{\'{e}}mi and JARDIN, Antoine and Miolane, Nina}, booktitle = {Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026)}, pages = {298--315}, year = {2026}, editor = {Berman, Eddie and Bernárdez, 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/papillon26a/papillon26a.pdf}, url = {https://proceedings.mlr.press/v334/papillon26a.html}, abstract = {Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs. In practice, this lifting step is often treated as a black box: practitioners select a lifting and then tune architectures, with limited visibility into whether the induced higher-order connectivity is meaningful for the downstream task. To address this missing diagnostic layer, we propose a visualization technique called TopoExplorer that leverages the strictly augmented Hasse graph form of topological datasets for exploratory data analysis. For the first time, practitioners can easily visualize the incidence- and adjacency-based neighborhoods that define the lifted dataset, as well as read off key graph metrics that describe its structural and feature landscape. Via an extensive set of experiments across many datasets and liftings, we show that several of these metrics correlate with downstream model performance, suggesting they can help inform TDL preprocessing design. Our perspective reframes the TDL workflow from *lift-train* to *lift-look-design-train*, enabling more principled, interpretable, and efficient model development. TopoExplorer is hosted at topoexplorer.pagekite.me, and its source code is available at github.com/geometric-intelligence/topoexplorer.} }
Endnote
%0 Conference Paper %T Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning %A Mathilde Papillon %A Guillermo Bernardez %A Álvaro Ballón Barreiro %A Marco Montagna %A Rémi Devaux %A Antoine JARDIN %A Nina Miolane %B Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026) %C Proceedings of Machine Learning Research %D 2026 %E Eddie Berman %E Guillermo Bernárdez %E Samantha Chen %E Alex Cloninger %E Timothy Doster %E Tegan Emerson %E J. Elisenda Grigsby %E Henry Kvinge %E Hannah Lawrence %E Tim Marrinan %E Audun Myers %E Mathilde Papillon %E Behrooz Tahmasebi %E Lev Telyatnikov %E Robin Walters %E Melanie Weber %E YuQing Xie %E Eric Yeats %F pmlr-v334-papillon26a %I PMLR %P 298--315 %U https://proceedings.mlr.press/v334/papillon26a.html %V 334 %N 2 %X Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs. In practice, this lifting step is often treated as a black box: practitioners select a lifting and then tune architectures, with limited visibility into whether the induced higher-order connectivity is meaningful for the downstream task. To address this missing diagnostic layer, we propose a visualization technique called TopoExplorer that leverages the strictly augmented Hasse graph form of topological datasets for exploratory data analysis. For the first time, practitioners can easily visualize the incidence- and adjacency-based neighborhoods that define the lifted dataset, as well as read off key graph metrics that describe its structural and feature landscape. Via an extensive set of experiments across many datasets and liftings, we show that several of these metrics correlate with downstream model performance, suggesting they can help inform TDL preprocessing design. Our perspective reframes the TDL workflow from *lift-train* to *lift-look-design-train*, enabling more principled, interpretable, and efficient model development. TopoExplorer is hosted at topoexplorer.pagekite.me, and its source code is available at github.com/geometric-intelligence/topoexplorer.
APA
Papillon, M., Bernardez, G., Barreiro, Á.B., Montagna, M., Devaux, R., JARDIN, A. & Miolane, N.. (2026). Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning. Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), in Proceedings of Machine Learning Research 334(2):298-315 Available from https://proceedings.mlr.press/v334/papillon26a.html.

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