Diagonal Symmetrization of Neural Network Solvers for the Many-Electron Schrödinger Equation

Kevin Han Huang, Ni Zhan, Elif Ertekin, Peter Orbanz, Ryan P Adams
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:26077-26105, 2025.

Abstract

Incorporating group symmetries into neural networks has been a cornerstone of success in many AI-for-science applications. Diagonal groups of isometries, which describe the invariance under a simultaneous movement of multiple objects, arise naturally in many-body quantum problems. Despite their importance, diagonal groups have received relatively little attention, as they lack a natural choice of invariant maps except in special cases. We study different ways of incorporating diagonal invariance in neural network ansatze trained via variational Monte Carlo methods, and consider specifically data augmentation, group averaging and canonicalization. We show that, contrary to standard ML setups, in-training symmetrization destabilizes training and can lead to worse performance. Our theoretical and numerical results indicate that this unexpected behavior may arise from a unique computational-statistical tradeoff not found in standard ML analyses of symmetrization. Meanwhile, we demonstrate that post hoc averaging is less sensitive to such tradeoffs and emerges as a simple, flexible and effective method for improving neural network solvers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-huang25at, title = {Diagonal Symmetrization of Neural Network Solvers for the Many-Electron Schrödinger Equation}, author = {Huang, Kevin Han and Zhan, Ni and Ertekin, Elif and Orbanz, Peter and Adams, Ryan P}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {26077--26105}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/huang25at/huang25at.pdf}, url = {https://proceedings.mlr.press/v267/huang25at.html}, abstract = {Incorporating group symmetries into neural networks has been a cornerstone of success in many AI-for-science applications. Diagonal groups of isometries, which describe the invariance under a simultaneous movement of multiple objects, arise naturally in many-body quantum problems. Despite their importance, diagonal groups have received relatively little attention, as they lack a natural choice of invariant maps except in special cases. We study different ways of incorporating diagonal invariance in neural network ansatze trained via variational Monte Carlo methods, and consider specifically data augmentation, group averaging and canonicalization. We show that, contrary to standard ML setups, in-training symmetrization destabilizes training and can lead to worse performance. Our theoretical and numerical results indicate that this unexpected behavior may arise from a unique computational-statistical tradeoff not found in standard ML analyses of symmetrization. Meanwhile, we demonstrate that post hoc averaging is less sensitive to such tradeoffs and emerges as a simple, flexible and effective method for improving neural network solvers.} }
Endnote
%0 Conference Paper %T Diagonal Symmetrization of Neural Network Solvers for the Many-Electron Schrödinger Equation %A Kevin Han Huang %A Ni Zhan %A Elif Ertekin %A Peter Orbanz %A Ryan P Adams %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-huang25at %I PMLR %P 26077--26105 %U https://proceedings.mlr.press/v267/huang25at.html %V 267 %X Incorporating group symmetries into neural networks has been a cornerstone of success in many AI-for-science applications. Diagonal groups of isometries, which describe the invariance under a simultaneous movement of multiple objects, arise naturally in many-body quantum problems. Despite their importance, diagonal groups have received relatively little attention, as they lack a natural choice of invariant maps except in special cases. We study different ways of incorporating diagonal invariance in neural network ansatze trained via variational Monte Carlo methods, and consider specifically data augmentation, group averaging and canonicalization. We show that, contrary to standard ML setups, in-training symmetrization destabilizes training and can lead to worse performance. Our theoretical and numerical results indicate that this unexpected behavior may arise from a unique computational-statistical tradeoff not found in standard ML analyses of symmetrization. Meanwhile, we demonstrate that post hoc averaging is less sensitive to such tradeoffs and emerges as a simple, flexible and effective method for improving neural network solvers.
APA
Huang, K.H., Zhan, N., Ertekin, E., Orbanz, P. & Adams, R.P.. (2025). Diagonal Symmetrization of Neural Network Solvers for the Many-Electron Schrödinger Equation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:26077-26105 Available from https://proceedings.mlr.press/v267/huang25at.html.

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