杯积与帽积拓扑神经网络
Cup and Cap Topological Neural Network
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中文总结 AI 辅助
针对现有拓扑深度学习每层仅能跨越一个维度处理特征的限制，本文提出杯积与帽积拓扑神经网络（CCNN），利用多体相互作用学习节点变量，在TopoBench数据集上验证了其竞争力。
中文摘要 AI 辅助
拓扑深度学习（TDL）旨在学习与高维单纯形相关的特征，不仅包括节点，还包括边、三角形等。然而，大多数TDL方法基于边界算子和霍奇拉普拉斯算子，存在每层特征和信号无法跨越超过一个维度进行提升或降低的限制。为克服此限制，本文提出采用杯积与帽积。具体而言，我们构建了杯积与帽积拓扑神经网络（CCNN），这是一种拓扑深度学习架构，旨在通过考虑数据中存在的多体相互作用（如三角形）来学习基于节点的变量（或0-上链）。我们通过在TopoBench数据集上评估CCNN的性能来验证其有效性，结果显示其相对于其他单纯复形神经网络具有竞争力。
英文摘要
Topological Deep Learning (TDL) is designed to learn features associated with higher-dimensional simplices including not only nodes but also edges, triangles and so on. However, most TDL approaches, being based on boundary operators and Hodge Laplacians, have the limitation that features and signals cannot be lifted or lowered across more than one dimension per layer. To overcome this limitation, in this work, we propose the adoption of the cup and cap products. Specifically, we formulate the Cup and Cap Topological Neural Network (CCNN), a topological deep learning architecture designed to learn node-based variables (or 0-cochains) by taking into account their many-body interactions (e.g. triangles) present in the data. We validate CCNN by assessing its performance on the TopoBench datasets, revealing its competitiveness with respect to other simplicial complex neural networks.
发表机构
- Queen Mary University of London（伦敦大学玛丽女王学院）
- University of Cambridge（剑桥大学）
- Sapienza University of Rome（罗马第一大学）
- Freie Universität Berlin（柏林自由大学）
机构由 AI 辅助整理，请以论文原文为准。
