FissionGuard: Testing Local Watermark Proportions with FDR Control

2026-10-08

AI Summary

This study addresses the failure of inference and loss of false discovery rate (FDR) control caused by evidence reuse in local text watermark detection. To overcome these issues, this work proposes FissionGuard, a framework that leverages data fission to decouple alarm and verification statistics. By integrating partial conjunction testing with online multiple hypothesis testing, it enables sequential auditing of local watermark channels. Notably, this paper provides the first finite-sample theoretical guarantees for FDR control under permissible dependence conditions. Experimental evaluations on both synthetic streams and large language model-generated texts demonstrate that the proposed method substantially improves watermark coverage while strictly maintaining the empirical FDR below the target threshold.

Abstract

A watermark detector can flag a text even when only a small fraction of its tokens are watermarked. We study sequential auditing to identify local passages whose watermark proportions exceed a prespecified threshold. Each alarm fixes a candidate passage's endpoint, while its start is chosen from earlier tokens. Reusing the same evidence to locate and test a passage can invalidate inference. We propose FissionGuard, which uses data fission to construct an alarm value and a validation value from each token-level $p$-value. The alarm values guide alarms and localization. The validation values yield passage-level $p$-values through partial conjunction, excluding as many of the strongest signals as the proportion null allows. These $p$-values are used to test the corresponding hypotheses at levels assigned by an online multiple-testing procedure. Under the stated watermark generation model, allowing dependence among token-level $p$-values at watermarked positions, we prove finite-sample false discovery rate (FDR) control among reported passages at every fixed finite horizon. We also derive a finite-sample lower bound on power for testing nonnull candidates. Experiments on synthetic streams and Mistral and Qwen generations across four marking layouts show gains in watermarked-token coverage over sample splitting, with empirical FDR below the target.

Problem

• watermark detection
• sequential auditing
• false discovery rate control
• local watermark proportion
• data fission

Innovation

• Data Fission
• False Discovery Rate Control
• Sequential Auditing
• Partial Conjunction
• Watermark Detection