Design and Evaluation of a Geometric Algebra-Based Graph Neural Network for Molecular Property Prediction

Kasper Helverskov Petersen, Mikkel N. Schmidt
Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL), PMLR 307:328-344, 2026.

Abstract

Geometric Algebra (GA) provides a unified framework for representing scalars, vectors, and higher-dimensional geometric elements, along with the geometric product, an operation that mixes information across these components in an equivariant manner. While GA has recently attracted attention in deep learning, its potential for molecular property prediction remains underexplored. We introduce GA-GNN, a novel equivariant graph neural network that extends message passing architectures from separate scalar and vector features to multivector representations, and employs sequences of geometric product layers as the core update mechanism. Evaluated on the QM9 benchmark, GA-GNN achieves competitive performance with the recent state-of-the-art while demonstrating that GA-based representations can simplify architecture design. These results highlight the potential of GA for building expressive equivariant message passing networks for molecular property prediction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v307-petersen26a, title = {Design and Evaluation of a Geometric Algebra-Based Graph Neural Network for Molecular Property Prediction}, author = {Petersen, Kasper Helverskov and Schmidt, Mikkel N.}, booktitle = {Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL)}, pages = {328--344}, year = {2026}, editor = {Kim, Hyeongji and Ramírez Rivera, Adín and Ricaud, Benjamin}, volume = {307}, series = {Proceedings of Machine Learning Research}, month = {06--08 Jan}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v307/main/assets/petersen26a/petersen26a.pdf}, url = {https://proceedings.mlr.press/v307/petersen26a.html}, abstract = {Geometric Algebra (GA) provides a unified framework for representing scalars, vectors, and higher-dimensional geometric elements, along with the geometric product, an operation that mixes information across these components in an equivariant manner. While GA has recently attracted attention in deep learning, its potential for molecular property prediction remains underexplored. We introduce GA-GNN, a novel equivariant graph neural network that extends message passing architectures from separate scalar and vector features to multivector representations, and employs sequences of geometric product layers as the core update mechanism. Evaluated on the QM9 benchmark, GA-GNN achieves competitive performance with the recent state-of-the-art while demonstrating that GA-based representations can simplify architecture design. These results highlight the potential of GA for building expressive equivariant message passing networks for molecular property prediction.} }
Endnote
%0 Conference Paper %T Design and Evaluation of a Geometric Algebra-Based Graph Neural Network for Molecular Property Prediction %A Kasper Helverskov Petersen %A Mikkel N. Schmidt %B Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL) %C Proceedings of Machine Learning Research %D 2026 %E Hyeongji Kim %E Adín Ramírez Rivera %E Benjamin Ricaud %F pmlr-v307-petersen26a %I PMLR %P 328--344 %U https://proceedings.mlr.press/v307/petersen26a.html %V 307 %X Geometric Algebra (GA) provides a unified framework for representing scalars, vectors, and higher-dimensional geometric elements, along with the geometric product, an operation that mixes information across these components in an equivariant manner. While GA has recently attracted attention in deep learning, its potential for molecular property prediction remains underexplored. We introduce GA-GNN, a novel equivariant graph neural network that extends message passing architectures from separate scalar and vector features to multivector representations, and employs sequences of geometric product layers as the core update mechanism. Evaluated on the QM9 benchmark, GA-GNN achieves competitive performance with the recent state-of-the-art while demonstrating that GA-based representations can simplify architecture design. These results highlight the potential of GA for building expressive equivariant message passing networks for molecular property prediction.
APA
Petersen, K.H. & Schmidt, M.N.. (2026). Design and Evaluation of a Geometric Algebra-Based Graph Neural Network for Molecular Property Prediction. Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL), in Proceedings of Machine Learning Research 307:328-344 Available from https://proceedings.mlr.press/v307/petersen26a.html.

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