Quantifying Cross-Domain Knowledge Distillation in the Presence of Domain Shift

Xiangchao Li, Xiao Han, Qing Yang, Xin Tong
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:67268-67304, 2026.

Abstract

This paper presents a theoretical investigation into the generalization capabilities of cross-domain knowledge distillation. Utilizing a high-dimensional asymptotic analysis of a linear teacher–student model, we characterize the excess risk while accounting for both model and covariate shifts. Our results provide a formal guarantee for the efficacy of distillation: even when the source and target domains differ substantially, there still may exist a regime where the student model achieves superior generalization ability over the student-only baseline. Moreover, we identify a crossed double descent phenomenon: the excess risk can vary non-monotonically with the teacher’s and student’s dimension-to-sample-size ratios. These results provide rigorous insight into when and why distillation helps across domains.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-li26bd, title = {Quantifying Cross-Domain Knowledge Distillation in the Presence of Domain Shift}, author = {Li, Xiangchao and Han, Xiao and Yang, Qing and Tong, Xin}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {67268--67304}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/li26bd/li26bd.pdf}, url = {https://proceedings.mlr.press/v306/li26bd.html}, abstract = {This paper presents a theoretical investigation into the generalization capabilities of cross-domain knowledge distillation. Utilizing a high-dimensional asymptotic analysis of a linear teacher–student model, we characterize the excess risk while accounting for both model and covariate shifts. Our results provide a formal guarantee for the efficacy of distillation: even when the source and target domains differ substantially, there still may exist a regime where the student model achieves superior generalization ability over the student-only baseline. Moreover, we identify a crossed double descent phenomenon: the excess risk can vary non-monotonically with the teacher’s and student’s dimension-to-sample-size ratios. These results provide rigorous insight into when and why distillation helps across domains.} }
Endnote
%0 Conference Paper %T Quantifying Cross-Domain Knowledge Distillation in the Presence of Domain Shift %A Xiangchao Li %A Xiao Han %A Qing Yang %A Xin Tong %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-li26bd %I PMLR %P 67268--67304 %U https://proceedings.mlr.press/v306/li26bd.html %V 306 %X This paper presents a theoretical investigation into the generalization capabilities of cross-domain knowledge distillation. Utilizing a high-dimensional asymptotic analysis of a linear teacher–student model, we characterize the excess risk while accounting for both model and covariate shifts. Our results provide a formal guarantee for the efficacy of distillation: even when the source and target domains differ substantially, there still may exist a regime where the student model achieves superior generalization ability over the student-only baseline. Moreover, we identify a crossed double descent phenomenon: the excess risk can vary non-monotonically with the teacher’s and student’s dimension-to-sample-size ratios. These results provide rigorous insight into when and why distillation helps across domains.
APA
Li, X., Han, X., Yang, Q. & Tong, X.. (2026). Quantifying Cross-Domain Knowledge Distillation in the Presence of Domain Shift. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:67268-67304 Available from https://proceedings.mlr.press/v306/li26bd.html.

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