Protecting the copyright of large language models (LLMs) has become crucial due to their resource-intensive training and accompanying carefully designed licenses. However, identifying the original base model of an LLM is challenging due to potential parameter alterations. In this study, we introduce a human-readable fingerprint for LLMs that uniquely identifies the base model without exposing model parameters or interfering with training. We first observe that the vector direction of LLM parameters remains stable after the model has converged during pretraining, showing negligible perturbations through subsequent training steps, including continued pretraining, supervised fine-tuning (SFT), and RLHF, which makes it a sufficient condition to identify the base model. The necessity is validated by continuing to train an LLM with an extra term to drive away the model parameters' direction and the model becomes damaged. However, this direction is vulnerable to simple attacks like dimension permutation or matrix rotation, which significantly change it without affecting performance. To address this, leveraging the Transformer structure, we systematically analyze potential attacks and define three invariant terms that identify an LLM's base model. We make these invariant terms human-readable by mapping them to a Gaussian vector using a convolutional encoder and then converting it into a natural image with StyleGAN2. Our method generates a dog image as an identity fingerprint for an LLM, where the dog's appearance strongly indicates the LLM's base model. The fingerprint provides intuitive information for qualitative discrimination, while the invariant terms can be employed for quantitative and precise verification. Experimental results across various LLMs demonstrate the effectiveness of our method.
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