Abstract: Machine learning often involves high costs related to data collection and model training,which raises concerns for mo-del owners about unauthorized replication or misuse,potentially infringing on their intellectual property(IP).Consequently,the protection of intellectual property in machine learning models has become a pressing issue.In response,researchers have introduced the concept of model watermarking.Similar to how digital watermarking embeds identifiable marks into images,model watermarking involves embedding unique identifiers into machine learning models to facilitate copyright verification.However,exis-ting watermarking techniques face several limitations in practical applications.Firstly,embedding watermarks inevitably affects model performance to some degree.Secondly,watermarks can be removed through techniques such as model fine-tuning.To address these challenges,this paper proposes a novel neural network watermarking scheme,employing a regional and staged embedding approach.This method not only aims to minimize the impact on model performance but also seeks to enhance the robustness of the watermark itself.Experiments conducted on the MNIST,CIFAR-10,and CIFAR-100 datasets validate the effectiveness of the proposed scheme.The results demonstrate that this watermarking approach maintains a high watermark retention rate while having minimal impact on model performance.Compared to existing baseline watermarking schemes,this method achieves performance improvements of up to 18 percentage points.Additionally,the proposed scheme exhibits strong robustness against attacks such as fine-tuning and remains unaffected by model pruning operations.Even if adversaries attempt to completely remove the watermark,they would have to significantly degrade the model’s performance as a trade-off.

Key words: Deep neural network, Model watermarking, Copyright verification, Artificial intelligence security, Watermark robustness, Model performance