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 remain 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 December 2024. 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.
View on arXiv@article{peng2025_2502.18535,
title={ A Survey of Zero-Knowledge Proof Based Verifiable Machine Learning },
author={ Zhizhi Peng and Taotao Wang and Chonghe Zhao and Guofu Liao and Zibin Lin and Yifeng Liu and Bin Cao and Long Shi and Qing Yang and Shengli Zhang },
journal={arXiv preprint arXiv:2502.18535},
year={ 2025 }
}