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A survey of zero-knowledge proof based verifiable machine learning.

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Title: A survey of zero-knowledge proof based verifiable machine learning.
Authors: Peng, Zhizhi1 (AUTHOR) p1878575@163.com, Zhao, Chonghe2 (AUTHOR) chonghe.zhao@gzhu.edu.cn, Wang, Taotao1 (AUTHOR) ttwang@szu.edu.cn, Liao, Guofu1 (AUTHOR) liaoguofu2022@email.szu.edu.cn, Lin, Zibin1 (AUTHOR) linaacc9595@gmail.com, Liu, Yifeng3 (AUTHOR) 13539213368@163.com, Cao, Bin4 (AUTHOR) caobin@bupt.edu.cn, Shi, Long5 (AUTHOR) slong1007@gmail.com, Yang, Qing1 (AUTHOR) yang.qing@szu.edu.cn, Zhang, Shengli1 (AUTHOR) zsl@szu.edu.cn
Source: Artificial Intelligence Review. Jul2026, Vol. 59 Issue 7, p1-51. 51p.
Subjects: Cryptography, Machine learning, Cloud computing, Data privacy
Abstract: As machine learning technologies advance rapidly across various domains, concerns over data privacy and model security have grown significantly. These challenges are particularly pronounced when models are trained and deployed on cloud platforms or third-party servers due to the computational resource limitations of users' end devices. In response, zero-knowledge proof (ZKP) technology has emerged as a promising solution, enabling effective validation of model performance and authenticity in both training and inference processes without disclosing sensitive data. Thus, ZKP ensures the verifiability and security of machine learning models, making it a valuable tool for privacy-preserving AI. Although some research has explored the verifiable machine learning solutions that exploit ZKP, a comprehensive survey and summary of these efforts remains absent. This survey paper aims to bridge this gap by reviewing and analyzing all the existing Zero-Knowledge Machine Learning (ZKML) research from June 2017 to August 2025. We begin by introducing the concept of ZKML and outlining its ZKP algorithmic setups under three key categories: verifiable training, verifiable inference, and verifiable testing. Next, we provide a comprehensive categorization of existing ZKML research within these categories and analyze the works in detail. Furthermore, we explore the implementation challenges faced in this field and discuss the improvement works to address these obstacles. Additionally, we highlight several commercial applications of ZKML technology. Finally, we propose promising directions for future advancements in this domain. [ABSTRACT FROM AUTHOR]
Copyright of Artificial Intelligence Review is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A survey of zero-knowledge proof based verifiable machine learning.
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  Data: <searchLink fieldCode="AR" term="%22Peng%2C+Zhizhi%22">Peng, Zhizhi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> p1878575@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Chonghe%22">Zhao, Chonghe</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> chonghe.zhao@gzhu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Taotao%22">Wang, Taotao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ttwang@szu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liao%2C+Guofu%22">Liao, Guofu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> liaoguofu2022@email.szu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lin%2C+Zibin%22">Lin, Zibin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> linaacc9595@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Yifeng%22">Liu, Yifeng</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> 13539213368@163.com</i><br /><searchLink fieldCode="AR" term="%22Cao%2C+Bin%22">Cao, Bin</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> caobin@bupt.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Shi%2C+Long%22">Shi, Long</searchLink><relatesTo>5</relatesTo> (AUTHOR)<i> slong1007@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Qing%22">Yang, Qing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yang.qing@szu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Shengli%22">Zhang, Shengli</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zsl@szu.edu.cn</i>
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  Data: <searchLink fieldCode="DE" term="%22Cryptography%22">Cryptography</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Cloud+computing%22">Cloud computing</searchLink><br /><searchLink fieldCode="DE" term="%22Data+privacy%22">Data privacy</searchLink>
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  Data: As machine learning technologies advance rapidly across various domains, concerns over data privacy and model security have grown significantly. These challenges are particularly pronounced when models are trained and deployed on cloud platforms or third-party servers due to the computational resource limitations of users' end devices. In response, zero-knowledge proof (ZKP) technology has emerged as a promising solution, enabling effective validation of model performance and authenticity in both training and inference processes without disclosing sensitive data. Thus, ZKP ensures the verifiability and security of machine learning models, making it a valuable tool for privacy-preserving AI. Although some research has explored the verifiable machine learning solutions that exploit ZKP, a comprehensive survey and summary of these efforts remains absent. This survey paper aims to bridge this gap by reviewing and analyzing all the existing Zero-Knowledge Machine Learning (ZKML) research from June 2017 to August 2025. We begin by introducing the concept of ZKML and outlining its ZKP algorithmic setups under three key categories: verifiable training, verifiable inference, and verifiable testing. Next, we provide a comprehensive categorization of existing ZKML research within these categories and analyze the works in detail. Furthermore, we explore the implementation challenges faced in this field and discuss the improvement works to address these obstacles. Additionally, we highlight several commercial applications of ZKML technology. Finally, we propose promising directions for future advancements in this domain. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Artificial Intelligence Review is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Machine learning
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      – SubjectFull: Cloud computing
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      – SubjectFull: Data privacy
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              Text: Jul2026
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