Independence Tests for Language Models

Sally Zhu, Ahmed M Ahmed, Rohith Kuditipudi, Percy Liang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:79673-79698, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhu25a, title = {Independence Tests for Language Models}, author = {Zhu, Sally and Ahmed, Ahmed M and Kuditipudi, Rohith and Liang, Percy}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {79673--79698}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhu25a/zhu25a.pdf}, url = {https://proceedings.mlr.press/v267/zhu25a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Independence Tests for Language Models %A Sally Zhu %A Ahmed M Ahmed %A Rohith Kuditipudi %A Percy Liang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhu25a %I PMLR %P 79673--79698 %U https://proceedings.mlr.press/v267/zhu25a.html %V 267 %X 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.
APA
Zhu, S., Ahmed, A.M., Kuditipudi, R. & Liang, P.. (2025). Independence Tests for Language Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:79673-79698 Available from https://proceedings.mlr.press/v267/zhu25a.html.

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