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Machine unlearning in LLMs is the targeted removal of specific knowledge while preserving all other capabilities, critical for privacy and safety. Yet existing benchmarks measure it unreliably. They miss knowledge that resurfaces under paraphrased or indirect queries, a failure we call under-forgetting, and lack the semantic, syntactic, and lexical probes needed to verify that unrelated knowledge is preserved, a failure we call over-forgetting. Both failures reflect an asymmetric generalization problem. Forget evaluation must cover diverse query formulations of the same target facts, testing whether forgetting holds beyond exact training prompts. Retain evaluation must probe a far larger and implicitly defined set, namely every fact disjoint from the forget target. The retain set thus defines the effective forget set, yet current datasets provide no fine-grained annotation of this forget-retain boundary. We address this with SUITE, an evaluation protocol and training corpus that captures forget-retain structure for real-world factual domains. Methods trained on SUITE improve substantially, showing that training data is as important as algorithmic design. Building on the obtained in

Machine unlearning (MU) is commonly judged by output forgetting, such as low forget-set accuracy or reduced logit-level membership inference. But if output-level success can coexist with retraining-inconsistent residuals in representation space, what kind of forgetting are current evaluations actually certifying? We study this question through retraining-consistent representation forgetting, using the retrained model (i.e., trained from scratch without the forget data) as an operational reference for correct forgetting. Across multiple unlearning methods, datasets, and models, our theoretical analysis and empirical results show that standard output-level evaluation can systematically overestimate the success of unlearning. Under this stronger lens, current methods often appear forgotten at the output layer while exhibiting a structured mismatch relative to retraining. They partially align with retraining on forget samples, remain more inconsistent on retain samples, and leave residual discrepancy concentrated along retraining-related directions rather than diffuse in representation space. This structured mismatch is characterized by forget/retain asymmetry, directional mismatch, an

A fundamental challenge in developing general learning algorithms is their tendency to forget past knowledge as they adapt to new data. Addressing this problem requires a principled understanding of forgetting. Yet, despite decades of study, no unified definition has emerged that offers insight into the underlying dynamics of learning. We propose an algorithm- and task-agnostic theory that characterises forgetting as a lack of self-consistency in a learner's predictive distribution, manifesting as a loss of predictive information. Our theory naturally yields a general measure of an algorithm's propensity to forget, proves that exact Bayesian inference allows for adaptation without forgetting, and provides a tautological explanation for why generative models forget when trained on their own synthetic outputs. To validate these claims, we design a comprehensive set of experiments that span classification, regression, generative modelling, and reinforcement learning. We demonstrate that forgetting is present across all deep learning settings and plays a significant role in determining learning efficiency. Together, these results establish a principled understanding of forgetting and l

In machine unlearning, $(\varepsilon,δ)-$unlearning is a popular framework that provides formal guarantees on the effectiveness of the removal of a subset of training data, the forget set, from a trained model. For strongly convex objectives, existing first-order methods achieve $(\varepsilon,δ)-$unlearning, but they only use the forget set to calibrate injected noise, never as a direct optimization signal. In contrast, efficient empirical heuristics often exploit the forget samples (e.g., via gradient ascent) but come with no formal unlearning guarantees. We bridge this gap by presenting the Variance-Reduced Unlearning (VRU) algorithm. To the best of our knowledge, VRU is the first first-order algorithm that directly includes forget set gradients in its update rule, while provably satisfying ($(\varepsilon,δ)-$unlearning. We establish the convergence of VRU and show that incorporating the forget set yields strictly improved rates, i.e. a better dependence on the achieved error compared to existing first-order $(\varepsilon,δ)-$unlearning methods. Moreover, we prove that, in a low-error regime, VRU asymptotically outperforms any first-order method that ignores the forget set.Experi

Machine unlearning, which enables a model to forget specific data, is crucial for ensuring data privacy and model reliability. However, its effectiveness can be severely undermined in real-world scenarios where models learn unintended biases from spurious correlations within the data. This paper investigates the unique challenges of unlearning from such biased models. We identify a novel phenomenon we term ``shortcut unlearning," where models exhibit an ``easy to learn, yet hard to forget" tendency. Specifically, models struggle to forget easily-learned, bias-aligned samples; instead of forgetting the class attribute, they unlearn the bias attribute, which can paradoxically improve accuracy on the class intended to be forgotten. To address this, we propose CUPID, a new unlearning framework inspired by the observation that samples with different biases exhibit distinct loss landscape sharpness. Our method first partitions the forget set into causal- and bias-approximated subsets based on sample sharpness, then disentangles model parameters into causal and bias pathways, and finally performs a targeted update by routing refined causal and bias gradients to their respective pathways.

Training machine learning models requires the storage of large datasets, which often contain sensitive or private data. Storing data is associated with a number of potential risks which increase over time, such as database breaches and malicious adversaries. Machine unlearning is the study of methods to efficiently remove the influence of training data subsets from previously-trained models. Existing unlearning methods typically require direct access to the "forget set" -- the data to be forgotten-and organisations must retain this data for unlearning rather than deleting it immediately upon request, increasing risks associated with the forget set. We introduce partially-blind unlearning -- utilizing auxiliary information to unlearn without explicit access to the forget set. We also propose a practical framework Reload, a partially-blind method based on gradient optimization and structured weight sparsification to operationalize partially-blind unlearning. We show that Reload efficiently unlearns, approximating models retrained from scratch, and outperforms several forget set-dependent approaches. On language models, Reload unlearns entities using <0.025% of the retain set and &

Custom Diffusion Models (CDMs) have gained significant attention due to their remarkable ability to personalize generative processes. However, existing CDMs suffer from catastrophic forgetting when continuously learning new concepts. Most prior works attempt to mitigate this issue under the sequential learning setting with a fixed order of concept inflow and neglect inter-concept interactions. In this paper, we propose a novel framework - Forget Less by Learning Together (FL2T) - that enables concurrent and order-agnostic concept learning while addressing catastrophic forgetting. Specifically, we introduce a set-invariant inter-concept learning module where proxies guide feature selection across concepts, facilitating improved knowledge retention and transfer. By leveraging inter-concept guidance, our approach preserves old concepts while efficiently incorporating new ones. Extensive experiments, across three datasets, demonstrates that our method significantly improves concept retention and mitigates catastrophic forgetting, highlighting the effectiveness of inter-concept catalytic behavior in incremental concept learning of ten tasks with at least 2% gain on average CLIP Image Al

Continual learning is a long-standing challenge in robot policy learning, where a policy must acquire new skills over time without catastrophically forgetting previously learned ones. While prior work has extensively studied continual learning in relatively small behavior cloning (BC) policy models trained from scratch, its behavior in modern large-scale pretrained Vision-Language-Action (VLA) models remains underexplored. In this work, we found that pretrained VLAs are remarkably resistant to forgetting compared with smaller policy models trained from scratch. Simple Experience Replay (ER) works surprisingly well on VLAs, sometimes achieving zero forgetting even with a small replay data size. Our analysis reveals that pretraining plays a critical role in downstream continual learning performance: large pretrained models mitigate forgetting with a small replay buffer size while maintaining strong forward learning capabilities. Furthermore, we found that VLAs can retain relevant knowledge from prior tasks despite performance degradation during learning new tasks. This knowledge retention enables rapid recovery of seemingly forgotten skills through finetuning. Together, these insight

Reinforcement learning (RL) agents can forget tasks they have previously been trained on. There is a rich body of work on such forgetting effects in humans. Therefore we look for commonalities in the forgetting behavior of humans and RL agents across tasks and test the viability of forgetting prevention measures from learning theory in RL. We find that in many cases, RL agents exhibit forgetting curves similar to those of humans. Methods like Leitner or SuperMemo have been shown to be effective at counteracting human forgetting, but we demonstrate they do not transfer as well to RL. We identify a likely cause: asymmetrical learning and retention patterns between tasks that cannot be captured by retention-based or performance-based curriculum strategies.

Machine unlearning aims to remove the influence of selected training examples without full retraining. Standard evaluations often summarize unlearning quality with aggregate metrics, such as accuracy- and forgetting-based scores, which can hide localized failures. We study this failure mode at the example level by comparing the predictions of an unlearned model to those of the model retrained after deletion. We show that this pointwise discrepancy can be highly non-uniform: for gradient-ascent and random-labeling methods, with and without retain-set fine-tuning, it grows with geometric proximity to the forget set. We call this phenomenon localized collateral forgetting. Our analysis identifies a mechanism behind the effect: surrogate targets used during unlearning can be inconsistent with the local prediction structure induced by retraining, and this inconsistency propagates through shared representations to nearby examples. Motivated by this mechanism, we propose Local Teacher Distillation, a simple mitigation strategy that replaces random targets with soft labels from a small teacher trained only on retained neighbors of the forget set. On CIFAR-100 partial-class deletion, this l

VLMs trained on web-scale data retain sensitive and copyrighted visual concepts that deployment may require removing. Training-based unlearning methods share a structural flaw: fine-tuning on a narrow forget set degrades general capabilities before unlearning begins, making it impossible to attribute subsequent performance drops to the unlearning procedure itself. Training-free approaches sidestep this by suppressing concepts through prompts or system instructions, but no rigorous benchmark exists for evaluating them on visual tasks. We introduce VLM-UnBench, the first benchmark for training-free visual concept unlearning in VLMs. It covers four forgetting levels, 7 source datasets, and 11 concept axes, and pairs a three-level probe taxonomy with five evaluation conditions to separate genuine forgetting from instruction compliance. Across 8 evaluation settings and 13 VLM configurations, realistic unlearning prompts leave forget accuracy near the no-instruction baseline; meaningful reductions appear only under oracle conditions that disclose the target concept to the model. Object and scene concepts are the most resistant to suppression, and stronger instruction-tuned models remain

Large language models (LLMs) exhibit remarkable generative capabilities but raise ethical and security concerns by memorizing sensitive data, reinforcing biases, and producing harmful content. These risks have spurred interest in LLM unlearning, the task of removing knowledge associated with undesirable data from pre-trained models. However, most existing methods assume access to clean, well-defined forget data samples, whereas real-world forget data could often be low-quality, synthetically rewritten, or watermarked, casting doubt on the reliability of unlearning. This work presents the first study of unlearning under perturbed or low-fidelity forget data, referred to as noisy forget sets. By systematically benchmarking state-of-the-art LLM unlearning methods, RMU and NPO, on such noisy forget sets, we find that unlearning remains surprisingly robust to perturbations, provided that core semantic signals are preserved. To explain this robustness, we propose a saliency-based interpretation: key semantic components that drive forgetting remain consistently influential despite substantial variation in surface form. This suggests that unlearning algorithms are primarily guided by deep

Machine unlearning seeks to remove the influence of particular data or class from trained models to meet privacy, legal, or ethical requirements. Existing unlearning methods tend to forget shallowly: phenomenon of an unlearned model pretend to forget by adjusting only the model response, while its internal representations retain information sufficiently to restore the forgotten data or behavior. We empirically confirm the widespread shallowness by reverting the forgetting effect of various unlearning methods via training-free performance recovery attack and gradient-inversion-based data reconstruction attack. To address this vulnerability fundamentally, we define a theoretical criterion of ``deep forgetting'' based on one-point-contraction of feature representations of data to forget. We also propose an efficient approximation algorithm, and use it to construct a novel general-purpose unlearning algorithm: One-Point-Contraction (OPC). Empirical evaluations on image classification unlearning benchmarks show that OPC achieves not only effective unlearning performance but also superior resilience against both performance recovery attack and gradient-inversion attack. The distinctive u

Neural Machine Translation (NMT) models can be specialized by domain adaptation, often involving fine-tuning on a dataset of interest. This process risks catastrophic forgetting: rapid loss of generic translation quality. Forgetting has been widely observed, with many mitigation methods proposed. However, the causes of forgetting and the relationship between forgetting and adaptation data are under-explored. This paper takes a novel approach to understanding catastrophic forgetting during NMT adaptation by investigating the impact of the data. We provide a first investigation of what is forgotten, and why. We examine the relationship between forgetting and the in-domain data, and show that the amount and type of forgetting is linked to that data's target vocabulary coverage. Our findings pave the way toward better informed NMT domain adaptation.

Machine unlearning seeks to remove the influence of specific training data from a model, a need driven by privacy regulations and robustness concerns. Existing approaches typically modify model parameters, but such updates can be unstable, computationally costly, and limited by local approximations. We introduce Representation Unlearning, a framework that performs unlearning directly in the model's representation space. Instead of modifying model parameters, we learn a transformation over representations that imposes an information bottleneck: maximizing mutual information with retained data while suppressing information about data to be forgotten. We derive variational surrogates that make this objective tractable and show how they can be instantiated in two practical regimes: when both retain and forget data are available, and in a zero-shot setting where only forget data can be accessed. Experiments across several benchmarks demonstrate that Representation Unlearning achieves more reliable forgetting, better utility retention, and greater computational efficiency than parameter-centric baselines.

The rapid development of large language models (LLMs) has raised concerns on the use of inappropriate data for training, which has led to a growing interest in LLM unlearning. Many existing LLM unlearning approaches rely on optimizing prediction loss(es), such as maximizing the loss on the forget set, but often face critical issues like over-forgetting and poor model utility. To address them, this paper novelly frames the optimization objective for LLM unlearning as one of zeroing out data attribution instead. In particular, we propose the first LLM unlearning framework based on data attribution rewards called DareU that performs reinforcement learning to update the LLM by reducing the attribution score of its generated responses (i.e., de-attributing) to the forget data owners. Empirical evaluation using an LLM classifier as an efficient approximation of attribution shows that DareU outperforms existing baselines by achieving effective unlearning while balancing forget quality and model utility well.

Neural operators perform well on structured domains, yet their behaviour on irregular geometries remains poorly understood. We show that this limitation is not merely an encoding issue, but a depth-wise failure mode inherent to deep operator architectures. We formalise the Geometric Forgetting Hypothesis: due to the Markovian structure of operator layers and their reliance on global mixing mechanisms, neural operators progressively lose access to domain geometry as depth increases. Using layer-wise geometric probing, we demonstrate that both spectral and attention-based operators systematically lose geometric fidelity. We show that this geometric forgetting degrades accuracy, stability, and generalisation. To counteract it, we introduce a lightweight geometry memory injection mechanism that restores geometric constraints at intermediate depths with minimal architectural overhead. This simple intervention consistently mitigates forgetting and exposes a geometric shortcut instability in transformer-based operators, revealing that geometric retention is a structural requirement rather than a design choice.

Forgetting a subset in machine unlearning is rarely an isolated task. Often, retained samples that are closely related to the forget set can be unintentionally affected, particularly when they share correlated features from pretraining or exhibit strong semantic similarities. To address this challenge, we propose a novel two-phase optimization framework specifically designed to handle such retai-forget entanglements. In the first phase, an augmented Lagrangian method increases the loss on the forget set while preserving accuracy on less-related retained samples. The second phase applies a gradient projection step, regularized by the Wasserstein-2 distance, to mitigate performance degradation on semantically related retained samples without compromising the unlearning objective. We validate our approach through comprehensive experiments on multiple unlearning tasks, standard benchmark datasets, and diverse neural architectures, demonstrating that it achieves effective and reliable unlearning while outperforming existing baselines in both accuracy retention and removal fidelity.

Privacy preservation in AI is crucial, especially in healthcare, where models rely on sensitive patient data. In the emerging field of machine unlearning, existing methodologies struggle to remove patient data from trained multimodal architectures, which are widely used in healthcare. We propose Forget-MI, a novel machine unlearning method for multimodal medical data, by establishing loss functions and perturbation techniques. Our approach unlearns unimodal and joint representations of the data requested to be forgotten while preserving knowledge from the remaining data and maintaining comparable performance to the original model. We evaluate our results using performance on the forget dataset, performance on the test dataset, and Membership Inference Attack (MIA), which measures the attacker's ability to distinguish the forget dataset from the training dataset. Our model outperforms the existing approaches that aim to reduce MIA and the performance on the forget dataset while keeping an equivalent performance on the test set. Specifically, our approach reduces MIA by 0.202 and decreases AUC and F1 scores on the forget set by 0.221 and 0.305, respectively. Additionally, our perform