@inproceedings{zhou-etal-2026-geometric,
title = "Geometric-disentanglement Unlearning",
author = "Zhou, Duo and
Zhang, Yuji and
Wei, Tianxin and
Qiu, Ruizhong and
Yang, Ke and
Lin, Xiao and
Qian, Cheng and
He, Jingrui and
Tong, Hanghang and
Zhai, ChengXiang and
Ji, Heng and
Zhang, Huan",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.2517/",
pages = "57231--57255",
ISBN = "979-8-89176-459-0",
abstract = "Machine unlearning aims to remove specified training data while preserving retained behavior, but gradient-based updates often induce a forgetting-retention tradeoff. This motivates our first-principles objective: optimize forgetting while keeping the retaining loss locally unchanged, formalized as retain invariance. We prove an equivalence under optimizer-induced geometry: the retain loss is locally invariant if and only if the update is orthogonal to the subspace spanned by retain gradients. Crucially, this geometry differs from Euclidean geometry because optimizer preconditioning rescales raw gradients before parameter updates. Based on this characterization, we propose Geometric-disentanglement Unlearning (GU), a plug-and-play projection module that filters any candidate forget update without modifying the underlying unlearning objective. GU projects the candidate update under the optimizer-induced metric to enforce first-order retain invariance and, under a trust-region constraint, gives the steepest forget direction among retain-preserving updates. Across 72 TOFU configurations, GU improves or preserves retain-set Extraction Strength in 91.7{\%} and model utility in 86.1{\%}, with gains transferring to MUSE and WMDP. Optimizer-metric GU outperforms its Euclidean counterpart on all four metrics, while running $5.1\times$ faster than the per-sample-QR baseline. Code is available at https://github.com/Lemutisme/Geometric-Unlearning."
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<abstract>Machine unlearning aims to remove specified training data while preserving retained behavior, but gradient-based updates often induce a forgetting-retention tradeoff. This motivates our first-principles objective: optimize forgetting while keeping the retaining loss locally unchanged, formalized as retain invariance. We prove an equivalence under optimizer-induced geometry: the retain loss is locally invariant if and only if the update is orthogonal to the subspace spanned by retain gradients. Crucially, this geometry differs from Euclidean geometry because optimizer preconditioning rescales raw gradients before parameter updates. Based on this characterization, we propose Geometric-disentanglement Unlearning (GU), a plug-and-play projection module that filters any candidate forget update without modifying the underlying unlearning objective. GU projects the candidate update under the optimizer-induced metric to enforce first-order retain invariance and, under a trust-region constraint, gives the steepest forget direction among retain-preserving updates. Across 72 TOFU configurations, GU improves or preserves retain-set Extraction Strength in 91.7% and model utility in 86.1%, with gains transferring to MUSE and WMDP. Optimizer-metric GU outperforms its Euclidean counterpart on all four metrics, while running 5.1\times faster than the per-sample-QR baseline. Code is available at https://github.com/Lemutisme/Geometric-Unlearning.</abstract>
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%0 Conference Proceedings
%T Geometric-disentanglement Unlearning
%A Zhou, Duo
%A Zhang, Yuji
%A Wei, Tianxin
%A Qiu, Ruizhong
%A Yang, Ke
%A Lin, Xiao
%A Qian, Cheng
%A He, Jingrui
%A Tong, Hanghang
%A Zhai, ChengXiang
%A Ji, Heng
%A Zhang, Huan
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F zhou-etal-2026-geometric
%X Machine unlearning aims to remove specified training data while preserving retained behavior, but gradient-based updates often induce a forgetting-retention tradeoff. This motivates our first-principles objective: optimize forgetting while keeping the retaining loss locally unchanged, formalized as retain invariance. We prove an equivalence under optimizer-induced geometry: the retain loss is locally invariant if and only if the update is orthogonal to the subspace spanned by retain gradients. Crucially, this geometry differs from Euclidean geometry because optimizer preconditioning rescales raw gradients before parameter updates. Based on this characterization, we propose Geometric-disentanglement Unlearning (GU), a plug-and-play projection module that filters any candidate forget update without modifying the underlying unlearning objective. GU projects the candidate update under the optimizer-induced metric to enforce first-order retain invariance and, under a trust-region constraint, gives the steepest forget direction among retain-preserving updates. Across 72 TOFU configurations, GU improves or preserves retain-set Extraction Strength in 91.7% and model utility in 86.1%, with gains transferring to MUSE and WMDP. Optimizer-metric GU outperforms its Euclidean counterpart on all four metrics, while running 5.1\times faster than the per-sample-QR baseline. Code is available at https://github.com/Lemutisme/Geometric-Unlearning.
%U https://aclanthology.org/2026.emnlp-main.2517/
%P 57231-57255
Markdown (Informal)
[Geometric-disentanglement Unlearning](https://aclanthology.org/2026.emnlp-main.2517/) (Zhou et al., EMNLP 2026)
ACL
- Duo Zhou, Yuji Zhang, Tianxin Wei, Ruizhong Qiu, Ke Yang, Xiao Lin, Cheng Qian, Jingrui He, Hanghang Tong, ChengXiang Zhai, Heng Ji, and Huan Zhang. 2026. Geometric-disentanglement Unlearning. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 57231–57255, Budapest, Hungary. Association for Computational Linguistics.