# Robust and Imperceptible Black-box DNN Watermarking Based on Fourier Perturbation Analysis and Frequency Sensitivity Clustering

arXiv: https://arxiv.org/abs/2208.03944 · HTML: https://mlsanity.com/paper/2208.03944/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2022.

## Built on by (most cited first, 5 of 5)

- [Boosting Adversarial Transferability via High-Frequency Augmentation and Hierarchical-Gradient Fusion](https://mlsanity.com/paper/2505.21181/) (2025)
- [Robust and Lossless Fingerprinting of Deep Neural Networks via Pooled Membership Inference](https://mlsanity.com/paper/2209.04113/) (2022)
- [NWaaS: A Non-Intrusive and Privacy-Preserving Watermarking-as-a-Service System with Adaptive Resource Scheduling](https://mlsanity.com/paper/2507.18036/) (2025)
- [An Information Asymmetry Game for Trigger-based DNN Model Watermarking](https://mlsanity.com/paper/2510.14218/) (2025)
- [Rotation, Scale, and Translation Resilient Black-box Fingerprinting for Intellectual Property Protection of EaaS Models](https://mlsanity.com/paper/2510.16706/) (2025)

## Abstract (arXiv)

Recently, more and more attention has been focused on the intellectual property protection of deep neural networks (DNNs), promoting DNN watermarking to become a hot research topic. Compared with embedding watermarks directly into DNN parameters, inserting trigger-set watermarks enables us to verify the ownership without knowing the internal details of the DNN, which is more suitable for application scenarios. The cost is we have to carefully craft the trigger samples. Mainstream methods construct the trigger samples by inserting a noticeable pattern to the clean samples in the spatial domain, which does not consider sample imperceptibility, sample robustness and model robustness, and therefore has limited the watermarking performance and the model generalization. It has motivated the authors in this paper to propose a novel DNN watermarking method based on Fourier perturbation analysis and frequency sensitivity clustering. First, we analyze the perturbation impact of different frequency components of the input sample on the task functionality of the DNN by applying random perturbation. Then, by K-means clustering, we determine the frequency components that result in superior watermarking performance for crafting the trigger samples. Our experiments show that the proposed work not only maintains the performance of the DNN on its original task, but also provides better watermarking performance compared with related works.