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A Survey of Zero-Knowledge Proof Based Verifiable Machine Learning
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Machine learning is increasingly deployed through outsourced and cloud-based pipelines, which improve accessibility but also raise concerns about computational integrity, data privacy, and model confidentiality. Zero-knowledge proofs (ZKPs) provide a compelling foundation for verifiable machine learning because they allow one party to certify that a training, testing, or inference result was produced by the claimed computation without revealing sensitive data or proprietary model parameters. Despite rapid progress in zero-knowledge machine learning (ZKML), the literature remains fragmented across different cryptographic settings, ML tasks, and system objectives. This survey presents a comprehensive review of ZKML research published from June 2017 to August 2025. We first introduce the basic ZKP formulations underlying ZKML and organize existing studies into three core tasks: verifiable training, verifiable testing, and verifiable inference. We then synthesize representative systems, compare their design choices, and analyze the main implementation bottlenecks, including limited circuit expressiveness, high proving cost, and deployment complexity. In addition, we summarize major techniques for improving generality and efficiency, review emerging commercial efforts, and discuss promising future directions. By consolidating the design space of ZKML, this survey aims to provide a structured reference for researchers and practitioners working on trustworthy and privacy-preserving machine learning.
Forward citations
Cited by 5 Pith papers
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ZKP Security Tools and Verification: Coverage, Effectiveness, Adoption, and Challenges
Six Circom-focused ZKP tools detect 45.7% of 70 real bugs in isolation but only 19.6% on full codebases; formal verification is mostly constraint-soundness, and practitioners still run human-led workflows with heavy LLM use.
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\texttt{Range-Arithmetic}: Verifiable Deep Learning Inference on an Untrusted Party
Range-Arithmetic verifies outsourced DNN inference by checking matrix multiplication with sum-check and handling fixed-point rounding and ReLU with Bulletproofs range proofs, achieving logarithmic communication and qu...
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AVEC: Bootstrapping Privacy for Local LLMs
AVEC is a proposed framework for per-query differential privacy budgeting, entity-level randomized response, and hash-based verification when delegating LLM queries to a remote model.
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Embodied AI: Emerging Risks and Opportunities for Policy Action
A policy analysis arguing that embodied AI risks are real, under-covered by current US/EU/UK frameworks, and best handled through certification, benchmarks, clarified liability, and economic adaptation.
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Engineering Trustworthy Machine-Learning Operations with Zero-Knowledge Proofs
A systematic review of 57 ZKP-for-ML papers concludes that inference verification dominates the field and that research is converging toward a unified ZKMLOps framework for trustworthy, auditable AI.
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