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

Large language models deployed in sensitive applications increasingly require the ability to unlearn specific knowledge, such as user requests, copyrighted materials, or outdated information, without retraining from scratch to ensure regulatory compliance, user privacy, and safety. This task, known as machine unlearning, aims to remove the influence of targeted data (forgetting) while maintaining performance on the remaining data (retention). A common approach is to formulate this as a multi-objective problem and reduce it to a single-objective problem via scalarization, where forgetting and retention losses are combined using a weighted sum. However, this often results in unstable training dynamics and degraded model utility due to conflicting gradient directions. To address these challenges, we propose OFMU, a penalty-based bi-level optimization framework that explicitly prioritizes forgetting while preserving retention through a hierarchical structure. Our method enforces forgetting via an inner maximization step that incorporates a similarity-aware penalty to decorrelate the gradients of the forget and retention objectives, and restores utility through an outer minimization step. To ensure scalability, we develop a two-loop algorithm with provable convergence guarantees under both convex and non-convex regimes. We further provide a rigorous theoretical analysis of convergence rates and show that our approach achieves better trade-offs between forgetting efficacy and model utility compared to prior methods. Extensive experiments across vision and language benchmarks demonstrate that OFMU consistently outperforms existing unlearning methods in both forgetting efficacy and retained utility.

Machine unlearning has become a critical capability for safely removing specific, sensitive knowledge from large language models (LLMs). Current state-of-the-art approaches primarily rely on iterative, training-time unlearning via fine-tuning. However, even when utilizing parameter-efficient dimensionality reduction techniques like LoRA, gradient-based optimization remains computationally expensive and lacks explicit analytical formulations. It can also leave the targeted knowledge merely hidden rather than removed, to the point that simply quantizing the unlearned model restores much of what it was supposed to have erased. To resolve this, we propose a novel one-shot unlearning approach, abandoning iterative optimization in favor of a direct, exact analytical solution. We frame the unlearning process as a ridge-regularized least-squares optimization problem, deriving a closed-form additive update for targeted weight matrices. This update forces the selected layer to suppress unwanted content while strictly preserving its behavior on retained data. Computed from gradient-free forward passes alone, with no backpropagation and no iteration to convergence, GROM applies the weight edit in mere seconds, which makes it orders of magnitude faster than traditional fine-tuning. Extensive evaluations demonstrate that GROM achieves state-of-the-art forgetting-utility trade-offs on TOFU-5%, TOFU-10%, MUSE-Books, MUSE-News and WMDP, significantly reducing computational overhead without sacrificing overall model performance. Because the update removes the targeted content from the weights instead of masking it, GROM also withstands the low-bit quantization attack that recovers much of the content a gradient-based baseline had appeared to forget. Our code is publicly available at https://github.com/Batorskq/GROM.

Large language models inevitably retain sensitive information, defined as inputs that may induce harmful generations, due to training on massive web corpora, raising concerns for privacy and safety. Existing machine unlearning methods primarily rely on retraining or aggressive fine-tuning, which are either computationally expensive or prone to degrading related knowledge and overall model utility. In this work, we reformulate machine unlearning as a precise knowledge re-mapping problem via model editing. We propose ZeroUnlearn, a few-shot unlearning framework. It overwrites sensitive inputs by mapping them to a neutral target state and removing their original representations. ZeroUnlearn enforces representational orthogonality through a multiplicative parameter update with a closed-form solution, enabling efficient and targeted unlearning. We further extend ZeroUnlearn to a gradient-based variant for multi-sample unlearning. Experiments demonstrate that our approach outperforms existing baselines while preserving general model utility. Our code is available at the github: https://github.com/XMUDeepLIT/ZeroUnlearn.