先看再提升：拓扑深度学习的视觉与定量诊断

中文摘要 AI 辅助

拓扑深度学习（TDL）方法依赖于将原始数据提升到高阶离散域，如单纯复形、胞腔复形和超图。在实践中，这一提升步骤常被视为黑箱：从业者选择一种提升方式后调整架构，却难以知晓所诱导的高阶连通性对下游任务是否有意义。为解决这一缺失的诊断层，我们提出一种名为TopoExplorer的可视化技术，它利用拓扑数据集的严格增强哈塞图形式进行探索性数据分析。从业者首次可轻松可视化定义提升后数据集的基于关联和邻接的邻域，还可读取描述其结构与特征态势的关键图指标。通过在多个数据集和提升方式上开展的大量实验，我们表明其中部分指标与下游模型性能相关，这意味着它们可辅助TDL的预处理设计。我们的视角将TDL工作流从“提升-训练”重构为“提升-查看-设计-训练”，使模型开发更具原则性、可解释性和高效性。TopoExplorer托管于此https URL，其源代码可在此http URL获取。

英文摘要

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.

发表机构

• University of California Santa Barbara（加州大学圣巴巴拉分校）
• Sapienza Universitá di Roma（罗马大学）
• Arlequin AI

机构由 AI 辅助整理，请以论文原文为准。