Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction
Abstract
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.
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BibTeX
@misc{ren2026mathematical,
title = {{Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction}},
author = {Yiming Ren and Xiang Liu and Mustafa Hajij and Pietro Liò and Guo-Wei Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07712},
eprint = {2610.07712},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07712},
}
RIS
TY - UNPB
TI - Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction
AU - Yiming Ren
AU - Xiang Liu
AU - Mustafa Hajij
AU - Pietro Liò
AU - Guo-Wei Wei
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07712
UR - https://arxiv.org/abs/2610.07712
AB - 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.
ER -