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

arXiv: https://arxiv.org/abs/2608.15388 · HTML: https://mlsanity.com/paper/2608.15388/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 15 Aug 2026.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [GraphWorld: Fake Graphs Bring Real Insights for GNNs](https://mlsanity.com/paper/2203.00112/) (2022)
- [Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature](https://mlsanity.com/paper/2309.09384/) (2023)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows](https://mlsanity.com/paper/1607.08654/) (2016)
- [TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks](https://mlsanity.com/paper/2410.06530/) (2024)
- [Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design](https://mlsanity.com/paper/2310.07684/) (2023)
- [Effective Structural Encodings via Local Curvature Profiles](https://mlsanity.com/paper/2311.14864/) (2023)
- [MANTRA: The Manifold Triangulations Assemblage](https://mlsanity.com/paper/2410.02392/) (2024)
- [HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations](https://mlsanity.com/paper/2505.15405/) (2025)
- [ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain](https://mlsanity.com/paper/2409.05211/) (2024)
- [Have Graph -- Will Lift? The Case for Higher-Order Benchmarks](https://mlsanity.com/paper/2605.07397/) (2026)

## Abstract (arXiv)

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 https://topoexplorer.pagekite.me, and its source code is available at github.com/geometric-intelligence/topoexplorer.