HEDP: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning

Yu Feng, Zhen Tian, Haoran Luo, Xie Yu, Diancheng Cheng, Haoyue Zheng, Shuai Lyu, Ping Zong, Lianyuan Li, Xin Ge, Yifan Zhu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:30426-30438, 2026.

Abstract

Domain Incremental Learning is a critical scenario that requires models to continuously adapt to new data domains without retraining. However, domain shifts often cause severe performance degradation. To address this, we propose Hybrid Energy-Distance Prompt, a domain-incremental framework inspired by Helmholtz free energy. HEDP introduces an energy regularization loss to enhance the separability of domain representations and a hybrid energy-distance weighted mechanism that fuses energy-based and distance-based cues to improve domain selection and generalization. Experiments on multiple benchmarks, including CORe50, show that HEDP achieves superior performance on unseen domains with a 2.57% accuracy gain, effectively mitigating catastrophic forgetting and enhancing open-world adaptability. Our code is available at https://github.com/dannis97500/HEDP.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-feng26r, title = {{HEDP}: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning}, author = {Feng, Yu and Tian, Zhen and Luo, Haoran and Yu, Xie and Cheng, Diancheng and Zheng, Haoyue and Lyu, Shuai and Zong, Ping and Li, Lianyuan and Ge, Xin and Zhu, Yifan}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {30426--30438}, 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/feng26r/feng26r.pdf}, url = {https://proceedings.mlr.press/v306/feng26r.html}, abstract = {Domain Incremental Learning is a critical scenario that requires models to continuously adapt to new data domains without retraining. However, domain shifts often cause severe performance degradation. To address this, we propose Hybrid Energy-Distance Prompt, a domain-incremental framework inspired by Helmholtz free energy. HEDP introduces an energy regularization loss to enhance the separability of domain representations and a hybrid energy-distance weighted mechanism that fuses energy-based and distance-based cues to improve domain selection and generalization. Experiments on multiple benchmarks, including CORe50, show that HEDP achieves superior performance on unseen domains with a 2.57% accuracy gain, effectively mitigating catastrophic forgetting and enhancing open-world adaptability. Our code is available at https://github.com/dannis97500/HEDP.} }
Endnote
%0 Conference Paper %T HEDP: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning %A Yu Feng %A Zhen Tian %A Haoran Luo %A Xie Yu %A Diancheng Cheng %A Haoyue Zheng %A Shuai Lyu %A Ping Zong %A Lianyuan Li %A Xin Ge %A Yifan Zhu %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-feng26r %I PMLR %P 30426--30438 %U https://proceedings.mlr.press/v306/feng26r.html %V 306 %X Domain Incremental Learning is a critical scenario that requires models to continuously adapt to new data domains without retraining. However, domain shifts often cause severe performance degradation. To address this, we propose Hybrid Energy-Distance Prompt, a domain-incremental framework inspired by Helmholtz free energy. HEDP introduces an energy regularization loss to enhance the separability of domain representations and a hybrid energy-distance weighted mechanism that fuses energy-based and distance-based cues to improve domain selection and generalization. Experiments on multiple benchmarks, including CORe50, show that HEDP achieves superior performance on unseen domains with a 2.57% accuracy gain, effectively mitigating catastrophic forgetting and enhancing open-world adaptability. Our code is available at https://github.com/dannis97500/HEDP.
APA
Feng, Y., Tian, Z., Luo, H., Yu, X., Cheng, D., Zheng, H., Lyu, S., Zong, P., Li, L., Ge, X. & Zhu, Y.. (2026). HEDP: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:30426-30438 Available from https://proceedings.mlr.press/v306/feng26r.html.

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