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This paper presents a comprehensive survey of zero-knowledge proof-based verifiable machine learning (ZKP-VML) technology. We first analyze the potential verifiability issues that may exist in different machine learning scenarios. Subsequently, we provide a formal definition of ZKP-VML. We then conduct a detailed analysis and classification of existing works based on their technical approaches. Finally, we discuss the key challenges and future directions in the field of ZKP-based VML.