提出首个形式化验证的模型版权保护方案，解决现有方法易被伪造的问题。

The great economic values of deep neural networks (DNNs) urge AI enterprises to protect their intellectual property (IP) for these models. Recently, proof-of-training (PoT) has been proposed as a promising solution to DNN IP protection, through which AI enterprises can utilize the record of DNN training process as their ownership proof. To prevent attackers from forging ownership proof, a secure PoT scheme should be able to distinguish honest training records from those forged by attackers. Although existing PoT schemes provide various distinction criteria, these criteria are based on intuitions or observations. The effectiveness of these criteria lacks clear and comprehensive analysis, resulting in existing schemes initially deemed secure being swiftly compromised by simple ideas. In this paper, we make the first move to identify distinction criteria in the style of formal methods, so that their effectiveness can be explicitly demonstrated. Specifically, we conduct systematic modeling to cover a wide range of attacks and then theoretically analyze the distinctions between honest and forged training records. The analysis results not only induce a universal distinction criterion, but also provide detailed reasoning to demonstrate its effectiveness in defending against attacks covered by our model. Guided by the criterion, we propose a generic PoT construction that can be instantiated into concrete schemes. This construction sheds light on the realization that trajectory matching algorithms, previously employed in data distillation, possess significant advantages in PoT construction. Experimental results demonstrate that our scheme can resist attacks that have compromised existing PoT schemes, which corroborates its superiority in security.