How much information about training samples can be gleaned from synthetic data generated by Large Language Models (LLMs)? Overlooking the subtleties of information flow in synthetic data generation pipelines can lead to a false sense of privacy. In this paper, we design membership inference attacks (MIAs) that target data used to fine-tune pre-trained LLMs that are then used to synthesize data, particularly when the adversary does not have access to the fine-tuned model but only to the synthetic data. We show that such data-based MIAs do significantly better than a random guess, meaning that synthetic data leaks information about the training data. Further, we find that canaries crafted to maximize vulnerability to model-based MIAs are sub-optimal for privacy auditing when only synthetic data is released. Such out-of-distribution canaries have limited influence on the model's output when prompted to generate useful, in-distribution synthetic data, which drastically reduces their vulnerability. To tackle this problem, we leverage the mechanics of auto-regressive models to design canaries with an in-distribution prefix and a high-perplexity suffix that leave detectable traces in synthetic data. This enhances the power of data-based MIAs and provides a better assessment of the privacy risks of releasing synthetic data generated by LLMs.
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