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

2026-08-15

AI Summary

This study addresses the lack of interpretability in data augmentation and the ad hoc design of higher-order connectivity in Topological Deep Learning (TDL) by proposing TopoExplorer, a novel visualization tool. Leveraging augmented Hasse diagrams to construct diagnostic layers, this method reveals quantitative correlations between topological structural metrics and model performance, thereby restructuring the development workflow into an "augment-observe-design-train" closed loop. Experimental results demonstrate significant correlations between key graph metrics and model efficacy, effectively informing preprocessing decisions. By bridging the gap in visual diagnostics for topological data augmentation, this work establishes a more principled, interpretable, and efficient TDL development paradigm. The tool has been released as open-source software to facilitate further research.

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

Problem

• Topological Deep Learning
• Lifting Step
• Black Box
• Diagnostics
• Higher-order Connectivity

Innovation

• Topological Deep Learning
• TopoExplorer
• Hasse Graph
• Visual Diagnostics
• Data Lifting