  Recent work has shown that Large Language Models (LLMs) can unintentionally
leak sensitive information present in their training data. In this paper, we
present Model Perturbations (MoPe), a new method to identify with high
confidence if a given text is in the training data of a pre-trained language
model, given white-box access to the models parameters. MoPe adds noise to the
model in parameter space and measures the drop in log-likelihood at a given
point $x$, a statistic we show approximates the trace of the Hessian matrix
with respect to model parameters. Across language models ranging from $70$M to
$12$B parameters, we show that MoPe is more effective than existing loss-based
attacks and recently proposed perturbation-based methods. We also examine the
role of training point order and model size in attack success, and empirically
demonstrate that MoPe accurately approximate the trace of the Hessian in
practice. Our results show that the loss of a point alone is insufficient to
determine extractability -- there are training points we can recover using our
method that have average loss. This casts some doubt on prior works that use
the loss of a point as evidence of memorization or unlearning.
