Collaborative Threshold Watermarking

Tameem Bakr, Anish Ambreth, Nils Lukas
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:5675-5698, 2026.

Abstract

In federated learning (FL), $K$ clients jointly train a model without sharing raw data. Because each participant invests data and compute, clients need mechanisms to later prove the provenance of a jointly trained model. Model watermarking embeds a hidden signal in the weights, but naive approaches either do not scale with many clients as per-client watermarks dilute as $K$ grows, or give any individual client the ability to verify and potentially remove the watermark. We introduce $(t,K)$-threshold watermarking: clients collaboratively embed a shared watermark during training, while only coalitions of at least $t$ clients can reconstruct the watermark key and verify a suspect model. We secret-share the watermark key $\tau$ so that coalitions of fewer than $t$ clients cannot reconstruct it, and verification can be performed without revealing $\tau$ in the clear. We instantiate our protocol in the white-box setting and evaluate it on image classification tasks on both IID and non-IID partitions, as well as language models fine-tuning setting. Our watermark remains detectable at scale ($K=128$) with minimal accuracy loss and stays above the detection threshold ($z\ge 4$) under attacks including adaptive fine-tuning using up to 20% of the training data. Code is available at https://github.com/tameemalaa/collaborative-threshold-watermark.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-bakr26a, title = {Collaborative Threshold Watermarking}, author = {Bakr, Tameem and Ambreth, Anish and Lukas, Nils}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {5675--5698}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/bakr26a/bakr26a.pdf}, url = {https://proceedings.mlr.press/v306/bakr26a.html}, abstract = {In federated learning (FL), $K$ clients jointly train a model without sharing raw data. Because each participant invests data and compute, clients need mechanisms to later prove the provenance of a jointly trained model. Model watermarking embeds a hidden signal in the weights, but naive approaches either do not scale with many clients as per-client watermarks dilute as $K$ grows, or give any individual client the ability to verify and potentially remove the watermark. We introduce $(t,K)$-threshold watermarking: clients collaboratively embed a shared watermark during training, while only coalitions of at least $t$ clients can reconstruct the watermark key and verify a suspect model. We secret-share the watermark key $\tau$ so that coalitions of fewer than $t$ clients cannot reconstruct it, and verification can be performed without revealing $\tau$ in the clear. We instantiate our protocol in the white-box setting and evaluate it on image classification tasks on both IID and non-IID partitions, as well as language models fine-tuning setting. Our watermark remains detectable at scale ($K=128$) with minimal accuracy loss and stays above the detection threshold ($z\ge 4$) under attacks including adaptive fine-tuning using up to 20% of the training data. Code is available at https://github.com/tameemalaa/collaborative-threshold-watermark.} }
Endnote
%0 Conference Paper %T Collaborative Threshold Watermarking %A Tameem Bakr %A Anish Ambreth %A Nils Lukas %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-bakr26a %I PMLR %P 5675--5698 %U https://proceedings.mlr.press/v306/bakr26a.html %V 306 %X In federated learning (FL), $K$ clients jointly train a model without sharing raw data. Because each participant invests data and compute, clients need mechanisms to later prove the provenance of a jointly trained model. Model watermarking embeds a hidden signal in the weights, but naive approaches either do not scale with many clients as per-client watermarks dilute as $K$ grows, or give any individual client the ability to verify and potentially remove the watermark. We introduce $(t,K)$-threshold watermarking: clients collaboratively embed a shared watermark during training, while only coalitions of at least $t$ clients can reconstruct the watermark key and verify a suspect model. We secret-share the watermark key $\tau$ so that coalitions of fewer than $t$ clients cannot reconstruct it, and verification can be performed without revealing $\tau$ in the clear. We instantiate our protocol in the white-box setting and evaluate it on image classification tasks on both IID and non-IID partitions, as well as language models fine-tuning setting. Our watermark remains detectable at scale ($K=128$) with minimal accuracy loss and stays above the detection threshold ($z\ge 4$) under attacks including adaptive fine-tuning using up to 20% of the training data. Code is available at https://github.com/tameemalaa/collaborative-threshold-watermark.
APA
Bakr, T., Ambreth, A. & Lukas, N.. (2026). Collaborative Threshold Watermarking. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:5675-5698 Available from https://proceedings.mlr.press/v306/bakr26a.html.

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