Continual Learning through Control Minimization

Sander De Haan, Yassine Taoudi-Benchekroun, Pau Vilimelis Aceituno, Benjamin F Grewe
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:23316-23351, 2026.

Abstract

Catastrophic forgetting remains a fundamental challenge for neural networks when tasks are trained sequentially. In this work, we reformulate continual learning as a control problem where learning and preservation signals compete within neural activity dynamics. We convert regularization penalties into preservation signals that protect prior-task representations. Learning then proceeds by minimizing the control effort required to integrate new tasks while competing with the preservation of prior tasks. At equilibrium, the neural activities produce weight updates that implicitly encode the full prior-task curvature, a property we term the continual-natural gradient, requiring no explicit curvature storage. Experiments confirm that our learning framework recovers true prior-task curvature and enables task discrimination, outperforming existing methods on standard benchmarks without replay.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-de-haan26a, title = {Continual Learning through Control Minimization}, author = {De Haan, Sander and Taoudi-Benchekroun, Yassine and Vilimelis Aceituno, Pau and Grewe, Benjamin F}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {23316--23351}, 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/de-haan26a/de-haan26a.pdf}, url = {https://proceedings.mlr.press/v306/de-haan26a.html}, abstract = {Catastrophic forgetting remains a fundamental challenge for neural networks when tasks are trained sequentially. In this work, we reformulate continual learning as a control problem where learning and preservation signals compete within neural activity dynamics. We convert regularization penalties into preservation signals that protect prior-task representations. Learning then proceeds by minimizing the control effort required to integrate new tasks while competing with the preservation of prior tasks. At equilibrium, the neural activities produce weight updates that implicitly encode the full prior-task curvature, a property we term the continual-natural gradient, requiring no explicit curvature storage. Experiments confirm that our learning framework recovers true prior-task curvature and enables task discrimination, outperforming existing methods on standard benchmarks without replay.} }
Endnote
%0 Conference Paper %T Continual Learning through Control Minimization %A Sander De Haan %A Yassine Taoudi-Benchekroun %A Pau Vilimelis Aceituno %A Benjamin F Grewe %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-de-haan26a %I PMLR %P 23316--23351 %U https://proceedings.mlr.press/v306/de-haan26a.html %V 306 %X Catastrophic forgetting remains a fundamental challenge for neural networks when tasks are trained sequentially. In this work, we reformulate continual learning as a control problem where learning and preservation signals compete within neural activity dynamics. We convert regularization penalties into preservation signals that protect prior-task representations. Learning then proceeds by minimizing the control effort required to integrate new tasks while competing with the preservation of prior tasks. At equilibrium, the neural activities produce weight updates that implicitly encode the full prior-task curvature, a property we term the continual-natural gradient, requiring no explicit curvature storage. Experiments confirm that our learning framework recovers true prior-task curvature and enables task discrimination, outperforming existing methods on standard benchmarks without replay.
APA
De Haan, S., Taoudi-Benchekroun, Y., Vilimelis Aceituno, P. & Grewe, B.F.. (2026). Continual Learning through Control Minimization. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:23316-23351 Available from https://proceedings.mlr.press/v306/de-haan26a.html.

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