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    <abstract>Machine unlearning in Large Language Models (LLMs) faces a critical trade-off between erasing target knowledge and preserving general utility. We propose SAUL (Sharpness-Aware Augmented-Lagrangian Unlearning), which formulates unlearning as a constrained minimization problem following the principle of “forget enough, but no more than necessary.” At its core, SAUL formulates forgetting as an explicit constraint with a prescribed satisfaction criterion, whereas prior unlearning methods typically specify the desired level of forgetting implicitly through optimization objectives. An augmented Lagrangian controller adaptively adjusts forget-side pressure according to constraint violation and can eventually deactivate the forget-side update as the prescribed criterion remains satisfied. Sharpness-aware updates on both retain and forget objectives, together with a dual-optimizer design that maintains role-separated states, further stabilize the resulting unlearning dynamics. We evaluate SAUL on the TOFU, WMDP, and MUSE benchmarks, demonstrating favorable forgetting–utility trade-offs over representative sharpness- and perturbation-based baselines under benchmark-specific forgetting criteria. Beyond the complete SAUL framework, we further show on TOFU and WMDP that applying the augmented-Lagrangian controller as a drop-in modifier to representative baselines improves their post-forgetting utility, demonstrating the practical value of explicit forgetting control.</abstract>
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%0 Conference Proceedings
%T SAUL: Sharpness-Aware Augmented-Lagrangian Unlearning
%A Choi, Jaewan
%A Yang, Junyoung
%A Park, Sangdon
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F choi-etal-2026-saul
%X Machine unlearning in Large Language Models (LLMs) faces a critical trade-off between erasing target knowledge and preserving general utility. We propose SAUL (Sharpness-Aware Augmented-Lagrangian Unlearning), which formulates unlearning as a constrained minimization problem following the principle of “forget enough, but no more than necessary.” At its core, SAUL formulates forgetting as an explicit constraint with a prescribed satisfaction criterion, whereas prior unlearning methods typically specify the desired level of forgetting implicitly through optimization objectives. An augmented Lagrangian controller adaptively adjusts forget-side pressure according to constraint violation and can eventually deactivate the forget-side update as the prescribed criterion remains satisfied. Sharpness-aware updates on both retain and forget objectives, together with a dual-optimizer design that maintains role-separated states, further stabilize the resulting unlearning dynamics. We evaluate SAUL on the TOFU, WMDP, and MUSE benchmarks, demonstrating favorable forgetting–utility trade-offs over representative sharpness- and perturbation-based baselines under benchmark-specific forgetting criteria. Beyond the complete SAUL framework, we further show on TOFU and WMDP that applying the augmented-Lagrangian controller as a drop-in modifier to representative baselines improves their post-forgetting utility, demonstrating the practical value of explicit forgetting control.
%R 10.18653/2026.findings-emnlp.1559
%U https://aclanthology.org/2026.findings-emnlp.1559/
%U https://doi.org/10.18653/2026.findings-emnlp.1559
%P 33202-33230

Markdown (Informal)

[SAUL: Sharpness-Aware Augmented-Lagrangian Unlearning](https://aclanthology.org/2026.findings-emnlp.1559/) (Choi et al., Findings 2026)

• SAUL: Sharpness-Aware Augmented-Lagrangian Unlearning (Choi et al., Findings 2026)

ACL

• Jaewan Choi, Junyoung Yang, and Sangdon Park. 2026. SAUL: Sharpness-Aware Augmented-Lagrangian Unlearning. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 33202–33230, Budapest, Hungary. Association for Computational Linguistics.