WF-Bench: A Benchmark for Neural-Network WaveFunction Expressivity and Scaling Laws

Lixing Zhang, Guijing Duan, Di Luo
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:155152-155167, 2026.

Abstract

We present a comprehensive benchmarking dataset and empirical scaling law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many body target wavefunctions. The dataset, WF-Bench, spans multiple distinct regimes of strongly correlated quantum matter, including topological states, Wigner crystals, and superconducting wavefunctions, providing a diverse and challenging test bed for neural network wavefunction expressivity. We introduce a systematic and reproducible benchmarking protocol for target wavefunction matching, enabling consistent performance evaluation across different neural network wavefunction architectures. By using wavefunction fidelity as the uniform metric, we discover empirical scaling laws that characterize how representability depends on system size and key model parameters, including number of determinant and model depth. By applying our benchmark protocol on Psiformer and Ferminet, we show that WF-Bench establishes a unified dataset driven framework for evaluating and comparing neural network wavefunctions and for guiding the design of future architectures.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-zhang26am, title = {{WF}-Bench: A Benchmark for Neural-Network {W}ave{F}unction Expressivity and Scaling Laws}, author = {Zhang, Lixing and Duan, Guijing and Luo, Di}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {155152--155167}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/zhang26am/zhang26am.pdf}, url = {https://proceedings.mlr.press/v306/zhang26am.html}, abstract = {We present a comprehensive benchmarking dataset and empirical scaling law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many body target wavefunctions. The dataset, WF-Bench, spans multiple distinct regimes of strongly correlated quantum matter, including topological states, Wigner crystals, and superconducting wavefunctions, providing a diverse and challenging test bed for neural network wavefunction expressivity. We introduce a systematic and reproducible benchmarking protocol for target wavefunction matching, enabling consistent performance evaluation across different neural network wavefunction architectures. By using wavefunction fidelity as the uniform metric, we discover empirical scaling laws that characterize how representability depends on system size and key model parameters, including number of determinant and model depth. By applying our benchmark protocol on Psiformer and Ferminet, we show that WF-Bench establishes a unified dataset driven framework for evaluating and comparing neural network wavefunctions and for guiding the design of future architectures.} }
Endnote
%0 Conference Paper %T WF-Bench: A Benchmark for Neural-Network WaveFunction Expressivity and Scaling Laws %A Lixing Zhang %A Guijing Duan %A Di Luo %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-zhang26am %I PMLR %P 155152--155167 %U https://proceedings.mlr.press/v306/zhang26am.html %V 306 %X We present a comprehensive benchmarking dataset and empirical scaling law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many body target wavefunctions. The dataset, WF-Bench, spans multiple distinct regimes of strongly correlated quantum matter, including topological states, Wigner crystals, and superconducting wavefunctions, providing a diverse and challenging test bed for neural network wavefunction expressivity. We introduce a systematic and reproducible benchmarking protocol for target wavefunction matching, enabling consistent performance evaluation across different neural network wavefunction architectures. By using wavefunction fidelity as the uniform metric, we discover empirical scaling laws that characterize how representability depends on system size and key model parameters, including number of determinant and model depth. By applying our benchmark protocol on Psiformer and Ferminet, we show that WF-Bench establishes a unified dataset driven framework for evaluating and comparing neural network wavefunctions and for guiding the design of future architectures.
APA
Zhang, L., Duan, G. & Luo, D.. (2026). WF-Bench: A Benchmark for Neural-Network WaveFunction Expressivity and Scaling Laws. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:155152-155167 Available from https://proceedings.mlr.press/v306/zhang26am.html.

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