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Fundamental questions on robustness and accuracy for classical and quantum learning algorithms

arXiv Quantum Physics
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⚡ Quantum Brief
Nana Liu’s February 2026 study examines the inherent tension between accuracy and robustness in classical and quantum machine learning models under noise and adversarial attacks, proposing refined definitions for both metrics. The paper introduces "corrupted-instance robustness accuracy" and "prediction-change robustness," differentiating them from traditional measures to better capture real-world performance under perturbations. Through theoretical analysis, Liu identifies conditions where accuracy-robustness trade-offs emerge—and scenarios where they can be avoided—highlighting dependencies on model bias, noise types, and perturbation relevance. Key implications include challenges posed by "incompatible noise" and adversarial quantum perturbations, suggesting these may fundamentally limit certain learning algorithms’ reliability in noisy environments. Future work is proposed to frame these problems using dynamical systems theory, potentially offering new tools to analyze stability and generalization in quantum and classical learning frameworks.
Fundamental questions on robustness and accuracy for classical and quantum learning algorithms

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Quantum Physics arXiv:2602.15079 (quant-ph) [Submitted on 16 Feb 2026] Title:Fundamental questions on robustness and accuracy for classical and quantum learning algorithms Authors:Nana Liu View a PDF of the paper titled Fundamental questions on robustness and accuracy for classical and quantum learning algorithms, by Nana Liu View PDF HTML (experimental) Abstract:This chapter introduces and investigates some fundamental questions on the relationship between accuracy and robustness in both classical and quantum classification algorithms under noisy and adversarial conditions. We introduce and clarify various definitions of robustness and accuracy, including corrupted-instance robustness accuracy and prediction-change robustness, distinguishing them from conventional accuracy and robustness measures. Through theoretical analysis and toy models, we establish conditions under which trade-offs between accuracy and robustness accuracy arise and identify scenarios where such trade-offs can be avoided. The framework developed highlights the nuanced interplay between model bias, noise characteristics, and perturbation types, including relevant and irrelevant perturbations. We explore the implications of some of these results for incompatible noise, adversarial quantum perturbations, the no free lunch theorem, and suggest future methods to examine these problems from the lens of dynamical systems. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2602.15079 [quant-ph] (or arXiv:2602.15079v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.15079 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nana Liu [view email] [v1] Mon, 16 Feb 2026 08:12:57 UTC (34 KB) Full-text links: Access Paper: View a PDF of the paper titled Fundamental questions on robustness and accuracy for classical and quantum learning algorithms, by Nana LiuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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Source: arXiv Quantum Physics