We propose DualOptim+, a novel optimization framework for improving machine unlearning in large language models. It introduces a base state to capture common representations shared by forgetting and retaining objectives and delta states to preserve objective-specific residuals. This architecture allows the optimizer to adaptively bridge shared and decoupled states based on the directional conflict between forgetting and retaining gradients. We further introduce DualOptim+ 8bit, a quantized variant that reduces memory overhead without compromising performance. Extensive experiments across fictitious and real-world unlearning, safety alignment, and multi-task learning tasks demonstrate that DualOptim+ consistently achieves a superior trade-off between different objectives. Codes are available at https://github.com/CityU-MLO/DualOptimPlus.
@article{arxiv.2605.21539,
title = {DualOptim+: Bridging Shared and Decoupled Optimizer States for Better Machine Unlearning in Large Language Models},
author = {Xuyang Zhong and Qizhang Li and Yiwen Guo and Chen Liu},
journal= {arXiv preprint arXiv:2605.21539},
year = {2026}
}