DualOptim+: Bridging Shared and Decoupled Optimizer States for Better Machine Unlearning in Large Language Models

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, real-world, and safety alignment tasks demonstrate that DualOptim+ consistently achieves a superior trade-off between forgetting efficacy and model utility.