Towards Undistillable Models by Minimizing Conditional Mutual Information

Linfeng Ye, Shayan Mohajer Hamidi, Renhao Tan, EN-HUI YANG

Keywords: Nasty teacher, Knowledge distillation, Intellectual property protection

Abstract: A deep neural network (DNN) is said to be undistillable if used as a black-box input-output teacher, it can not be distilled by knowledge distillation (KD) to train a student model so that the distilled student (called knockoff student) outperforms the student trained alone with label smoothing (LS student) in terms of prediction accuracy. To protect intellectual property of DNNs, it is desirable to build undistillable DNNs. To this end, it is first observed that an undistillable DNN may have the trait that each cluster of its output probability distributions in response to all sample instances with the same label should be highly concentrated to the extent that each cluster corresponding to each label should ideally collapse into one probability distribution. Based on this observation and by measuring the concentration of each cluster in terms of conditional mutual information (CMI), a new training method called CMI minimized (CMIM) method is proposed, which trains a DNN by jointly minimizing the conventional cross entropy (CE) loss and the CMI values of all temperature scaled clusters across the entire temperature spectrum. The resulting CMIM model is shown, by extensive experiments, to be undistillable by all tested KD methods existing in the literature. That is, the knockoff students distilled by these KD methods from the CMIM model underperform the respective LS students. In addition, the CMIM model is also shown to performs better than the model trained with the CE loss alone in terms of their own prediction accuracy.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 1976