# Watermarking Kolmogorov-Arnold Networks for Emerging Networked Applications via Activation Perturbation

arXiv: https://arxiv.org/abs/2508.06676 · HTML: https://mlsanity.com/paper/2508.06676/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Builds on (most cited first, 10 of 10)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Turning Your Weakness Into a Strength: Watermarking Deep Neural Networks by Backdooring](https://mlsanity.com/paper/1802.04633/) (2018)
- [Embedding Watermarks into Deep Neural Networks](https://mlsanity.com/paper/1701.04082/) (2017)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [How to Prove Your Model Belongs to You: A Blind-Watermark based Framework to Protect Intellectual Property of DNN](https://mlsanity.com/paper/1903.01743/) (2019)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)

## Abstract (arXiv)

With the increasing importance of protecting intellectual property in machine learning, watermarking techniques have gained significant attention. As advanced models are increasingly deployed in domains such as social network analysis, the need for robust model protection becomes even more critical. While existing watermarking methods have demonstrated effectiveness for conventional deep neural networks, they often fail to adapt to the novel architecture, Kolmogorov-Arnold Networks (KAN), which feature learnable activation functions. KAN holds strong potential for modeling complex relationships in network-structured data. However, their unique design also introduces new challenges for watermarking. Therefore, we propose a novel watermarking method, Discrete Cosine Transform-based Activation Watermarking (DCT-AW), tailored for KAN. Leveraging the learnable activation functions of KAN, our method embeds watermarks by perturbing activation outputs using discrete cosine transform, ensuring compatibility with diverse tasks and achieving task independence. Experimental results demonstrate that DCT-AW has a small impact on model performance and provides superior robustness against various watermark removal attacks, including fine-tuning, pruning, and retraining after pruning.