English

Collaborative Threshold Watermarking

Machine Learning 2026-05-29 v2

Abstract

In federated learning (FL), KK 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 KK grows, or give any individual client the ability to verify and potentially remove the watermark. We introduce (t,K)(t,K)-threshold watermarking: clients collaboratively embed a shared watermark during training, while only coalitions of at least tt clients can reconstruct the watermark key and verify a suspect model. We secret-share the watermark key τ\tau so that coalitions of fewer than tt clients cannot reconstruct it, and verification can be performed without revealing τ\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=128K=128) with minimal accuracy loss and stays above the detection threshold (z4z\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.

Keywords

Cite

@article{arxiv.2602.10765,
  title  = {Collaborative Threshold Watermarking},
  author = {Tameem Bakr and Anish Ambreth and Nils Lukas},
  journal= {arXiv preprint arXiv:2602.10765},
  year   = {2026}
}
R2 v1 2026-07-01T10:31:44.146Z