Machine unlearning algorithms aim to efficiently remove data from a model without retraining it from scratch, in order to remove corrupted or outdated data or respect a user's "right to be forgotten." Certified machine unlearning is a strong theoretical guarantee based on differential privacy that quantifies the extent to which an algorithm erases data from the model weights. In contrast to existing works in certified unlearning for convex or strongly convex loss functions, or nonconvex objectives with limiting assumptions, we propose the first, first-order, black-box (i.e., can be applied to models pretrained with vanilla gradient descent) algorithm for unlearning on general nonconvex loss functions, which unlearns by "rewinding" to an earlier step during the learning process before performing gradient descent on the loss function of the retained data points. We prove (ϵ,δ) certified unlearning and performance guarantees that establish the privacy-utility-complexity tradeoff of our algorithm, and we prove generalization guarantees for functions that satisfy the Polyak-Lojasiewicz inequality. Finally, we demonstrate the superior performance of our algorithm compared to existing methods, within a new experimental framework that more accurately reflects unlearning user data in practice.

In this work, we first empirically demonstrate the instability and suboptimal performance of existing popular MU methods when deployed in different scenarios. To address this issue, we propose Dual Optimizer (DualOptim), which incorporates adaptive learning rate and decoupled momentum factors. Empirical and theoretical evidence demonstrates that DualOptim contributes to effective and stable unlearning. Through extensive experiments, we show that DualOptim can significantly boost MU efficacy and stability across diverse tasks, including image classification, image generation, and large language models, making it a versatile approach to empower existing MU algorithms.

To address these concerns, unlearning techniques have been developed to remove the influence of specific data without retraining from scratch. However, this paper reveals a critical vulnerability in fine-tuning-based unlearning: a malicious user can craft a manipulated forgetting request that stealthily degrades the model's utility for benign users. We demonstrate this risk through a red-teaming Stealthy Attack (SA), which is inspired by two key limitations of existing unlearning--the inability to constrain the scope of unlearning effect and the failure to distinguish benign tokens from unlearning signals. Prior work has shown that unlearned models tend to memorize forgetting data as unlearning signals, and respond with hallucinations or feigned ignorance when unlearning signals appear in the input. By subtly increasing the presence of common benign tokens in the forgetting data, SA enhances the connection between benign tokens and unlearning signals. As a result, when normal users include such tokens in their prompts, the model exhibits unlearning behaviors, leading to unintended utility degradation. To address this vulnerability, we propose Scope-aware Unlearning (SU), a lightweight enhancement that introduces a scope term into the unlearning objective, encouraging the model to localize the forgetting effect. Our method requires no additional data processing, integrates seamlessly with existing fine-tuning frameworks, and significantly improves robustness against SA.

Machine unlearning is a fundamental mechanism that enforces the right to be forgotten. Existing unlearning studies that rely on label manipulation or task-gradient reversal often deliver limited unlearning effectiveness. Moreover, they can undermine the original learning objective and typically do not guarantee equivalence to standard unlearning by retraining. In this paper, we propose \textbf{ManiF-SMC} (\textbf{Mani}fold \textbf{F}orgetting with \textbf{S}elf \textbf{M}ode \textbf{C}onnectivity), motivated by the observation that a model retrained on the remaining data tends to classify erased samples by their semantic similarity to the retained data. We begin with systematically recasting the approximate unlearning as pushing each erased sample away from its original learned manifold representation centroid toward its nearest semantic neighbors in the retained data. This reformulation aligns unlearning with retraining behavior and operates purely in representation space, reducing reliance on labels and task-specific gradients. To tackle the manifold representation-based unlearning problem, ManiF-SMC encapsulates the unlearning and representation preservation goals in a margin-based triplet loss. Because finding a suitable margin for unlearning is challenging, we propose a self-mode-connectivity module that rapidly reconstructs the local manifold to guide the adaptive margins generation for each unlearning case. Extensive experiments on four representative datasets show that ManiF-SMC achieves unlearning effectiveness comparable to state-of-the-art approximate methods while operating solely within the model's representation space.

Machine unlearning (MU) empowers individuals with the `right to be forgotten' by removing their private or sensitive information encoded in machine learning models. However, it remains uncertain whether MU can be effectively applied to Multimodal Large Language Models (MLLMs), particularly in scenarios of forgetting the leaked visual data of concepts. To overcome the challenge, we propose an efficient method, Single Image Unlearning (SIU), to unlearn the visual recognition of a concept by fine-tuning a single associated image for few steps. SIU consists of two key aspects: (i) Constructing Multifaceted fine-tuning data. We introduce four targets, based on which we construct fine-tuning data for the concepts to be forgotten; (ii) Joint training loss. To synchronously forget the visual recognition of concepts and preserve the utility of MLLMs, we fine-tune MLLMs through a novel Dual Masked KL-divergence Loss combined with Cross Entropy loss. Alongside our method, we establish MMUBench, a new benchmark for MU in MLLMs and introduce a collection of metrics for its evaluation.

Machine unlearning has raised significant interest with the adoption of laws ensuring the "right to be forgotten".

Driven by the right to be forgotten (RTBF), machine unlearning has become an essential requirement for privacy-preserving machine learning. However, its realization in decentralized federated learning (DFL) remains largely unexplored. In DFL, clients exchange local updates only with neighbors, causing model information to propagate and mix across the network. As a result, when a client requests data deletion, its influence is implicitly embedded throughout the system, making removal difficult without centralized coordination. We propose a novel certified unlearning framework for DFL based on Newton-style updates. Our approach first quantifies how a client's data influence propagates during training. Leveraging curvature information of the loss with respect to the target data, we then construct corrective updates using Newton-style approximations. To ensure scalability, we approximate second-order information via Fisher information matrices. The resulting updates are perturbed with calibrated noise and broadcast through the network to eliminate residual influence across clients. We theoretically prove that our approach satisfies the formal definition of certified unlearning, ensuring that the unlearned model is difficult to distinguish from a retrained model without the deleted data. We also establish utility bounds showing that the unlearned model remains close to retraining from scratch. Extensive experiments across diverse decentralized settings demonstrate the effectiveness and efficiency of our framework.

Machine unlearning (MU) seeks to remove the influence of specified data from a trained model in response to privacy requests or data poisoning. While certified unlearning has been analyzed in centralized and server-orchestrated federated settings (via guarantees analogous to differential privacy, DP), the decentralized setting -- where peers communicate without a coordinator remains underexplored. We study certified unlearning in decentralized networks with fixed topologies and propose RR-DU, a random-walk procedure that performs one projected gradient ascent step on the forget set at the unlearning client and a geometrically distributed number of projected descent steps on the retained data elsewhere, combined with subsampled Gaussian noise and projection onto a trust region around the original model. We provide (i) convergence guarantees in the convex case and stationarity guarantees in the nonconvex case, (ii) $(\varepsilon,δ)$ network-unlearning certificates on client views via subsampled Gaussian Rényi DP (RDP) with segment-level subsampling, and (iii) deletion-capacity bounds that scale with the forget-to-local data ratio and quantify the effect of decentralization (network mixing and randomized subsampling) on the privacy-utility trade-off. Empirically, on image benchmarks (MNIST, CIFAR-10), RR-DU matches a given $(\varepsilon,δ)$ while achieving higher test accuracy than decentralized DP baselines and reducing forget accuracy to random guessing ($\approx 10\%$).

Graph neural networks (GNNs) are increasingly used to model complex patterns in graph-structured data. However, enabling them to "forget" designated information remains challenging, especially under privacy regulations such as the GDPR. Existing unlearning methods largely optimize for efficiency and scalability, yet they offer little transparency, and the black-box nature of GNNs makes it difficult to verify whether forgetting has truly occurred. We propose an explainability-driven verifier for GNN unlearning that snapshots the model before and after deletion, using attribution shifts and localized structural changes (for example, graph edit distance) as transparent evidence. The verifier uses five explainability metrics: residual attribution, heatmap shift, explainability score deviation, graph edit distance, and a diagnostic graph rule shift. We evaluate two backbones (GCN, GAT) and four unlearning strategies (Retrain, GraphEditor, GNNDelete, IDEA) across five benchmarks (Cora, Citeseer, Pubmed, Coauthor-CS, Coauthor-Physics). Results show that Retrain and GNNDelete achieve near-complete forgetting, GraphEditor provides partial erasure, and IDEA leaves residual signals. These explanation deltas provide the primary, human-readable evidence of forgetting; we also report membership-inference ROC-AUC as a complementary, graph-wide privacy signal.

Large language models (LLMs) possess vast knowledge acquired from extensive training corpora, but they often cannot remove specific pieces of information when needed, which makes it hard to handle privacy, bias mitigation, and knowledge correction. Traditional model unlearning approaches require computationally expensive fine-tuning or direct weight editing, making them impractical for real-world deployment. In this work, we introduce LoRA-based Unlearning with Negative Examples (LUNE), a lightweight framework that performs negative-only unlearning by updating only low-rank adapters while freezing the backbone, thereby localizing edits and avoiding disruptive global changes. Leveraging Low-Rank Adaptation (LoRA), LUNE targets intermediate representations to suppress (or replace) requested knowledge with an order-of-magnitude lower compute and memory than full fine-tuning or direct weight editing. Extensive experiments on multiple factual unlearning tasks show that LUNE: (I) achieves effectiveness comparable to full fine-tuning and memory-editing methods, and (II) reduces computational cost by about an order of magnitude.