MathAgent: Multi-Agent Optimization of Mathematical Invariants for Molecular Property Prediction
Abstract
Mathematical invariants provide complementary representations of molecular structure, but their predictive utility can vary across datasets and prediction tasks. For a new dataset, appropriate construction of invariant representations from algebraic topology, differential geometry, topological spectral theory, and commutative algebra is a challenging task, particularly when evaluating multiple representations is computationally expensive. We develop a Mathematical Agentic Model (MathAgent) to automatically optimize invariant representations in molecular property prediction. The framework combines dataset-aware representation design, low-cost candidate screening, and progressive evaluation. Language-model reasoning supports task interpretation, strategy proposal, and workflow coordination, while scientific computations and numerical decisions are carried out by deterministic tools. We evaluate MathAgent on protein--ligand binding-affinity and quantitative toxicity prediction tasks. Different datasets favor different combinations of mathematical invariants, demonstrating the need for dataset-adaptive representation selection rather than a fixed universal representation. Objective-conditioned executions further show that the framework can adjust its evaluation strategy according to user-specified goals. MathAgent therefore provides a systematic, evidence-driven, and traceable approach for optimizing mathematical invariant representations and reducing reliance on manual configuration and/or experimentation in molecular property prediction.
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BibTeX
@misc{ren2026mathagent,
title = {{MathAgent: Multi-Agent Optimization of Mathematical Invariants for Molecular Property Prediction}},
author = {Yiming Ren and Josh V. Vermaas and Guo-Wei Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03992},
eprint = {2610.03992},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03992},
}
RIS
TY - UNPB
TI - MathAgent: Multi-Agent Optimization of Mathematical Invariants for Molecular Property Prediction
AU - Yiming Ren
AU - Josh V. Vermaas
AU - Guo-Wei Wei
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03992
UR - https://arxiv.org/abs/2610.03992
AB - Mathematical invariants provide complementary representations of molecular structure, but their predictive utility can vary across datasets and prediction tasks. For a new dataset, appropriate construction of invariant representations from algebraic topology, differential geometry, topological spectral theory, and commutative algebra is a challenging task, particularly when evaluating multiple representations is computationally expensive. We develop a Mathematical Agentic Model (MathAgent) to automatically optimize invariant representations in molecular property prediction. The framework combines dataset-aware representation design, low-cost candidate screening, and progressive evaluation. Language-model reasoning supports task interpretation, strategy proposal, and workflow coordination, while scientific computations and numerical decisions are carried out by deterministic tools. We evaluate MathAgent on protein--ligand binding-affinity and quantitative toxicity prediction tasks. Different datasets favor different combinations of mathematical invariants, demonstrating the need for dataset-adaptive representation selection rather than a fixed universal representation. Objective-conditioned executions further show that the framework can adjust its evaluation strategy according to user-specified goals. MathAgent therefore provides a systematic, evidence-driven, and traceable approach for optimizing mathematical invariant representations and reducing reliance on manual configuration and/or experimentation in molecular property prediction.
ER -