A cross-domain empirical benchmark of quantum-inspired and classical optimization algorithms for machine learning

Abstract

Quantum-inspired (QI) optimizers are increasingly proposed as alternatives to classical gradient-based training, yet are frequently benchmarked through classical stand-ins rather than themselves. Across tabular, vision, and language tasks we evaluate three classes: direct implementations of published update rules (Spall’s SPSA; quantum-behaved particle swarm optimization, QPSO, adapted to stochastic minibatches), a documented classical analog of quantum natural gradient (an NGD-style diagonal second-moment preconditioner), and the hyperparameter-control configurations under which such methods are often reported. The gap between these classes is our central result: on the tabular benchmark the hyperparameter control trains with the classical baselines while the direct algorithms fall \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document}10–24 points below it, and on CIFAR-10/ResNet18, where v1’s “SPSA” arm was a learning-rate-scaled Adam, Adam itself stands \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document}59 points above genuine SPSA. The QPSO adaptation stays at chance on LSTM tasks a legacy “QPSO” proxy solves at 79–81%, at 18–38\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} Adam’s cost there and up to 74\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} on the small CV model. A seed-paired \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 2$$\end{document} factorial on RoBERTa identifies the smaller learning rate as the dominant observed component of the earlier “QNG advantage” (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+0.50$$\end{document} points at the dataset level); with only three datasets, modified Hartung–Knapp uncertainty spans zero. The configured NGD arm shows no detectable advantage over a learning-rate-matched AdamW (descriptive pooled \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p{=}0.23$$\end{document}) at 6–\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7\%$$\end{document} extra cost, and on ResNet18 its trained endpoints have larger dominant-curvature estimates than the Adam family’s. Headline comparisons use five seeds, paired tests, Holm correction, and stated detection limits. We conclude with an auditing taxonomy (direct algorithm / analog / hyperparameter control): within the arms, protocols, and scales evaluated, no advantage attributable to a QI mechanism is detected after these controls.