# Near-Tie Restriction

The authors revisit a watermark-distillation protocol for LLM fingerprinting, show that its utility evaluation understates text-quality degradation in open-ended generation, and propose near-tie restriction, which uses top-1-relative logit gaps to confine the watermark bias to tokens close to the base model's top prediction; across Llama-3.2-3B, Qwen-2.5-3B, Llama-3.1-8B, and Gemma-9B, this improves detection-quality frontiers under sampling, system prompts, quantization, pruning, and fine-tuning, preserves higher text quality across query budgets, and further improves existing schemes when combined with them.

The authors revisit a watermark-distillation protocol for LLM fingerprinting, show that its utility evaluation understates text-quality degradation in open-ended generation, and propose near-tie restriction, which uses top-1-relative logit gaps to confine the watermark bias to tokens close to the base model's top prediction; across Llama-3.2-3B, Qwen-2.5-3B, Llama-3.1-8B, and Gemma-9B, this improves detection-quality frontiers under sampling, system prompts, quantization, pruning, and fine-tuning, preserves higher text quality across query budgets, and further improves existing schemes when combined with them.