为拓扑深度学习提供可视化诊断工具,看清数据升维后的结构是否合理。
Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning

- 通过哈斯图形式可视化升维后的邻域关系
- 多个结构指标与下游性能相关,可指导预处理设计
- 适合想理解拓扑升维效果的研究者和工程师
拓扑深度学习(TDL)方法将原始数据升维至单纯复形、细胞复形和超图等高阶离散域。实践中,升维步骤常被视为黑箱:研究者选择升维方式后仅调参模型,却难以判断生成的高阶连接是否对下游任务有意义。为此,我们提出名为TopoExplorer的可视化技术,利用拓扑数据的严格增强哈斯图形式进行探索性数据分析。首次实现对基于关联与邻接的邻居结构的直观可视化,并可读取描述其结构与特征景观的关键图指标。在多个数据集和升维方案上的大量实验表明,若干指标与下游模型性能相关,提示其可辅助指导TDL预处理设计。本视角将TDL流程从“升维-训练”重构为“升维-查看-设计-训练”,推动更系统、可解释且高效的模型开发。TopoExplorer已上线 https://topoexplorer.pagekite.me,源码见 github.com/geometric-intelligence/topoexplorer。
原文摘要 · Abstract (English)
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.
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