Motivated by liability and intellectual property concerns over open-weight models we consider the following problem: given the weights of two models, can we test whether they were trained independently—i.e., from independent random initializations? We consider two settings: constrained and unconstrained. In the constrained setting, we make assumptions about model architecture and training and propose statistical tests that yield exact p-values with respect to the null hypothesis that the models are trained from independent random initializations. We compute the p-values by simulating exchangeable copies of each model under our assumptions and comparing various similarity measures between the original two models versus these copies. We report p-values on pairs of 21 open-weight models (210 total pairs) and find we correctly identify all pairs of non-independent models. In the unconstrained setting we make none of the prior assumptions and allow for adversarial evasion attacks that do not change model output. We thus propose a new test which matches hidden activations between two models, which is robust to these transformations and to changes in model architecture and can also identify specific non-independent components of models. Though we no longer obtain exact p-values from this test, empirically we find it reliably distinguishes non-independent models like a p-value. Notably, we can use the test to identify specific parts of one model that are derived from another (e.g., how Llama 3.1-8B was pruned to initialize Llama 3.2-3B, or shared layers between Mistral-7B and StripedHyena-7B), and it is even robust to retraining individual layers of either model from scratch.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice’s model to produce text. Can Alice prove that Bob is using her model, either by querying Bob’s derivative model (query setting) or from the text alone ( observational setting)? We formulate this question as an independence testing problem—in which the null hypothesis is that Bob’s model or text is independent of Alice’s randomized training run—and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice’s model using test statistics that capture correlation between Bob’s model or text and the ordering of training examples in Alice’s training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice’s training data. In the query setting, we directly estimate (via prompting) the likelihood Bob’s model gives to Alice’s training examples and their training order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model’s training data order, achieving a p-value on the order of at most $1 \times 10^{-8}$ in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob’s text overlapping with spans of Alice’s training examples and 2) the likelihood of Bob’s text with respect to different versions of Alice’s model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob’s text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.