用热核构建高效拓扑表示，提升分子性质预测精度
Heat Kernel Goes Topological
- 基于组合复形上的拉普拉斯算子，快速计算节点热核描述符
- 在分子数据集上计算效率显著优于现有拓扑方法，准确率媲美顶尖模型
- 适合需要高表达力与可扩展性的分子分类与属性预测任务
拓扑神经网络作为图神经网络的有力继承者，通常依赖高阶消息传递，导致计算开销大。本文提出一种新型拓扑框架，在组合复形（CCs）上引入拉普拉斯算子，实现热核的高效计算，作为节点描述符。该方法捕捉多尺度信息，生成置换等变表示，可轻松融入现代Transformer架构。理论上，该方法具有最大表达能力，能区分任意非同构的组合复形。实验表明，其计算效率显著优于现有拓扑方法；在标准分子数据集上表现媲美最先进描述符，且在复杂拓扑结构区分和拓扑基准测试中展现出更强能力，避免了盲点问题。本工作通过提供高表达性且可扩展的拓扑表示，推动了拓扑深度学习的发展，为分子分类与性质预测开辟新路径。
原文摘要 · Abstract (English)
Topological neural networks have emerged as powerful successors of graph neural networks. However, they typically involve higher-order message passing, which incurs significant computational expense. We circumvent this issue with a novel topological framework that introduces a Laplacian operator on combinatorial complexes (CCs), enabling efficient computation of heat kernels that serve as node descriptors. Our approach captures multiscale information and enables permutation-equivariant representations, allowing easy integration into modern transformer-based architectures. Theoretically, the proposed method is maximally expressive because it can distinguish arbitrary non-isomorphic CCs. Empirically, it significantly outperforms existing topological methods in terms of computational efficiency. Besides demonstrating competitive performance with the state-of-the-art descriptors on standard molecular datasets, it exhibits superior capability in distinguishing complex topological structures and avoiding blind spots on topological benchmarks. Overall, this work advances topological deep learning by providing expressive yet scalable representations, thereby opening up exciting avenues for molecular classification and property prediction tasks.
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