发表机构
University of Georgia; University of San Francisco; Cambridge University（佐治亚大学; 旧金山大学; 剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出数学不变量启发的拓扑神经网络（MITNN），通过多视角数学不变量与拓扑架构结合，提升分子和材料性质预测性能，并在多个任务中优于现有方法。
AI 中文摘要
现有的分子和材料学习方法通常依赖于有限的结构表示集，这可能仅捕捉复杂三维结构的选定方面。在此，我们引入数学不变量启用的拓扑神经网络（MITNNs），这是一个通过多种互补的数学视角表示复杂结构并将其与拓扑神经架构集成的框架。MITNNs结合了来自拓扑学、谱理论、交换代数、微分几何和离散曲率的多尺度不变量，从同一系统中捕捉互补的结构信息。系统性的不变量子集、架构子集和集成分析表明，预测性能取决于数学表示与神经架构的配对方式，选定的组合优于单个模型以及所有可用组件的聚合。在蛋白质-配体结合、金属有机框架性质、突变诱导的蛋白质溶解性和分子毒性预测中，MITNN持续优于现有方法。这些结果确立了MITNN作为科学机器学习的一个数学多模态框架。
英文摘要
Existing molecular and materials learning approaches often rely on a limited set of structural representations, which may capture only selected aspects of complex three-dimensional structure. Here, we introduce mathematical invariant-enabled topological neural networks (MITNNs), a framework that represents complex structures through multiple complementary mathematical views and integrates them with topological neural architectures. MITNNs combine multiscale invariants from topology, spectral theory, commutative algebra, differential geometry, and discrete curvature, capturing complementary structural information from the same system. Systematic invariant-subset, architecture-subset, and ensemble analyses show that predictive performance depends on how mathematical representations and neural architectures are paired, with selected combinations outperforming individual models and the aggregation of all available components. Across protein-ligand binding, metal-organic framework properties, mutation-induced protein solubility, and molecular toxicity prediction, MITNN consistently outperforms existing methods. These results establish MITNN as a mathematically multimodal framework for scientific machine learning.
