Abstract As artificial intelligence (AI) systems become increasingly integrated into critical applications, ensuring trust in their outputs has emerged as a central challenge. Verifiable machine learning (ML) is one approach to addressing this challenge, providing guarantees that results are both correct and reproducible. Existing paradigms, however, provide only partial solutions: zero-knowledge ML (ZKML) achieves strong cryptographic assurances but suffers from limited scalability and high resource costs, while optimistic ML (OPML) supports a wider range of models but relies on economic incentives and long dispute periods. In this work, we propose zk-OPML, a novel hybrid framework that integrates optimistic verification with zero-knowledge proofs (ZKPs). The approach decomposes ML inference into operator-level computations, selectively generating ZKPs for isolated ONNX operators, while retaining the scalability of the optimistic paradigm. We present a prototype implementation and evaluate its performance by benchmarking it against ZKML and OPML. Our results show that zk-OPML achieves faster verification for more complex inference tasks and scales more effectively to larger models, while avoiding the excessive costs of end-to-end ZKML. The modular design of zk-OPML further enables future extensions with the latest advances in the field of ZK.
Keršič et al. (2026) studied this question.