An Information Asymmetry Game for Trigger-based DNN Model Watermarking

TL;DR

This work addresses the protection of DNN intellectual property via trigger-based watermarking under pruning-based removal. It formulates a static information-asymmetric game where the defender holds private watermark knowledge and the attacker observes only the watermarked model, and it derives a closed-form attacker optimum $k^{\ast}$ together with an exponential bound on post-attack watermark reliability $\text{WSR}_{\text{post}}$. Theoretical results align with CIFAR-10 experiments showing that sparse watermarking preserves $\text{ACC}$ while resisting pruning-driven watermark decay, with $\text{WSR}_{\text{post}}$ obeying $\text{WSR}_{\text{post}} \le \text{WSR}_{0} \exp(-a k)+\varepsilon_{\text{res}}(\delta)$. The findings offer principled design guidance for robust watermarking schemes in model copyright protection and extend to practical considerations of attacker resources and information asymmetry in DNN security.

Abstract

As a valuable digital product, deep neural networks (DNNs) face increasingly severe threats to the intellectual property, making it necessary to develop effective technical measures to protect them. Trigger-based watermarking methods achieve copyright protection by embedding triggers into the host DNNs. However, the attacker may remove the watermark by pruning or fine-tuning. We model this interaction as a game under conditions of information asymmetry, namely, the defender embeds a secret watermark with private knowledge, while the attacker can only access the watermarked model and seek removal. We define strategies, costs, and utilities for both players, derive the attacker's optimal pruning budget, and establish an exponential lower bound on the accuracy of watermark detection after attack. Experimental results demonstrate the feasibility of the watermarked model, and indicate that sparse watermarking can resist removal with negligible accuracy loss. This study highlights the effectiveness of game-theoretic analysis in guiding the design of robust watermarking schemes for model copyright protection.

Figures (2)

• Figure 1: Original and trigger-based samples used for watermark embedding. The trigger is a $5\times5$ square placed at the bottom-right corner of the image.
• Figure 2: ACC and WSR under different pruning budgets $k$ on CIFAR-10 with watermark embedding.