Daily Papers

Privacy compliance requires re-identification models to selectively forget individuals while preserving their ability to recognize others. For this, we present MoME, a switchable framework that can adapt pre-trained backbones for privacy compliance, allowing the same model to switch between Full mode for standard inference and Core mode for unlearned inference. MoME splits one backbone into core parameters that preserve retrieval and zero-initialized parasitic parameters that carry the full-data knowledge, and training them under gradient isolation so the core never receives a forget-set gradient. Disabling the branch yields Core, which satisfies a request to delete a person's training data, and enabling it yields Full, which retains what the deleted data taught, so honoring the request is a flag flip rather than a retraining run. We prove Core independent of the forget set up to an audited set of coupling channels and introduce the rank-based Forgetting-Rank statistic to audit that independence in a trained model. On Market-1501, VeRi-776 and RegDB, Core reads at a retrained reference under three membership attacks while retrieving above it, and the retrieval advantage carries to ResNet and CLIP backbones. Code and weights are available at https://github.com/Jingong-Chen/MoME.

Motivated by the EU's "Right To Be Forgotten" regulation, we initiate a study of statistical data deletion problems where users' data are accessible only for a limited period of time. This setting is formulated as an online supervised learning task with constant memory limit. We propose a deletion-aware algorithm FIFD-OLS for the low dimensional case, and witness a catastrophic rank swinging phenomenon due to the data deletion operation, which leads to statistical inefficiency. As a remedy, we propose the FIFD-Adaptive Ridge algorithm with a novel online regularization scheme, that effectively offsets the uncertainty from deletion. In theory, we provide the cumulative regret upper bound for both online forgetting algorithms. In the experiment, we showed FIFD-Adaptive Ridge outperforms the ridge regression algorithm with fixed regularization level, and hopefully sheds some light on more complex statistical models.

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

Machine unlearning, the ability for a machine learning model to forget, is becoming increasingly important to comply with data privacy regulations, as well as to remove harmful, manipulated, or outdated information. The key challenge lies in forgetting specific information while protecting model performance on the remaining data. While current state-of-the-art methods perform well, they typically require some level of retraining over the retained data, in order to protect or restore model performance. This adds computational overhead and mandates that the training data remain available and accessible, which may not be feasible. In contrast, other methods employ a retrain-free paradigm, however, these approaches are prohibitively computationally expensive and do not perform on par with their retrain-based counterparts. We present Selective Synaptic Dampening (SSD), a novel two-step, post hoc, retrain-free approach to machine unlearning which is fast, performant, and does not require long-term storage of the training data. First, SSD uses the Fisher information matrix of the training and forgetting data to select parameters that are disproportionately important to the forget set. Second, SSD induces forgetting by dampening these parameters proportional to their relative importance to the forget set with respect to the wider training data. We evaluate our method against several existing unlearning methods in a range of experiments using ResNet18 and Vision Transformer. Results show that the performance of SSD is competitive with retrain-based post hoc methods, demonstrating the viability of retrain-free post hoc unlearning approaches.

Machine learning systems increasingly face the need to remove the influence of entire data domains, such as toxic language, harmful behavior, or topical content, rather than isolated records. Recent work formalizes this problem as distributional unlearning: selecting a subset of a forget domain whose removal moves the training distribution away from an unwanted population while preserving proximity to the desired one. However, existing analyses often impose parametric assumptions to obtain tractable selection rules. These assumptions may be poorly suited to high-dimensional language-model representations. We introduce Mamushi, a framework for non-parametric distributional unlearning that ranks forget examples using a probabilistic classifier whose Bayes-optimal logit equals the forget-to-retain log-density ratio (up to an additive class-prior constant). We show that thresholding the population log-density ratio yields the optimal fixed-budget selection rule for our removal--preservation objective and establish a non-asymptotic transfer guarantee relating score-estimation and threshold-calibration errors to degradation from the population-optimal selection rule. Our empirical evaluation spans real-world datasets on toxic-language removal and topical-domain removal regimes using different representations, with Mamushi achieving a more favorable removal--preservation trade-off than other baselines. Our work shows that Mamushi can serve as an efficient selection approach for downstream machine unlearning procedures, reducing the number of forget examples required to reach a fixed forgetting target.

In large language model (LLM) unlearning, private information is required to be removed. Task arithmetic unlearns by subtracting a specific task vector (TV)--defined as the parameter difference between a privacy-information-tuned model and the original model. While efficient, it can cause over-forgetting by disrupting parameters essential for retaining other information. Motivated by the observation that each parameter exhibits different importance for forgetting versus retention, we propose a per-parameter task arithmetic (PerTA) mechanism to rescale the TV, allowing per-parameter adjustment. These weights quantify the relative importance of each parameter for forgetting versus retention, estimated via gradients (i.e., PerTA-grad) or the diagonal Fisher information approximation (i.e., PerTA-fisher). Moreover, we discuss the effectiveness of PerTA, extend it to a more general form, and provide further analysis. Extensive experiments demonstrate that PerTA consistently improves upon standard TV, and in many cases surpasses widely used training-based unlearning methods in both forgetting effectiveness and overall model utility. By retaining the efficiency of task arithmetic while mitigating over-forgetting, PerTA offers a principled and practical framework for LLM unlearning.

Broad, open source availability of large pretrained foundation models on the internet through platforms such as HuggingFace has taken the world of practical deep learning by storm. A classical pipeline for neural network training now typically consists of finetuning these pretrained network on a small target dataset instead of training from scratch. In the case of large models this can be done even on modest hardware using a low rank training technique known as Low-Rank Adaptation (LoRA). While Low Rank training has already been studied in the continual learning setting, existing works often consider storing the learned adapter along with the existing model but rarely attempt to modify the weights of the pretrained model by merging the LoRA with the existing weights after finishing the training of each task. In this article we investigate this setting and study the impact of LoRA rank on the forgetting of the pretraining foundation task and on the plasticity and forgetting of subsequent ones. We observe that this rank has an important impact on forgetting of both the pretraining and downstream tasks. We also observe that vision transformers finetuned in that way exhibit a sort of ``contextual'' forgetting, a behaviour that we do not observe for residual networks and that we believe has not been observed yet in previous continual learning works.

The objective of digital forgetting is, given a model with undesirable knowledge or behavior, obtain a new model where the detected issues are no longer present. The motivations for forgetting include privacy protection, copyright protection, elimination of biases and discrimination, and prevention of harmful content generation. Effective digital forgetting has to be effective (meaning how well the new model has forgotten the undesired knowledge/behavior), retain the performance of the original model on the desirable tasks, and be scalable (in particular forgetting has to be more efficient than retraining from scratch on just the tasks/data to be retained). This survey focuses on forgetting in large language models (LLMs). We first provide background on LLMs, including their components, the types of LLMs, and their usual training pipeline. Second, we describe the motivations, types, and desired properties of digital forgetting. Third, we introduce the approaches to digital forgetting in LLMs, among which unlearning methodologies stand out as the state of the art. Fourth, we provide a detailed taxonomy of machine unlearning methods for LLMs, and we survey and compare current approaches. Fifth, we detail datasets, models and metrics used for the evaluation of forgetting, retaining and runtime. Sixth, we discuss challenges in the area. Finally, we provide some concluding remarks.

As Multimodal Large Language Models (MLLMs) develop, their potential security issues have become increasingly prominent. Machine Unlearning (MU), as an effective strategy for forgetting specific knowledge in training data, has been widely used in privacy protection. However, MU for safety in MLLM has yet to be fully explored. To address this issue, we propose SAFEERASER, a safety unlearning benchmark for MLLMs, consisting of 3,000 images and 28.8K VQA pairs. We comprehensively evaluate unlearning methods from two perspectives: forget quality and model utility. Our findings show that existing MU methods struggle to maintain model performance while implementing the forget operation and often suffer from over-forgetting. Hence, we introduce Prompt Decouple (PD) Loss to alleviate over-forgetting through decouple prompt during unlearning process. To quantitatively measure over-forgetting mitigated by PD Loss, we propose a new metric called Safe Answer Refusal Rate (SARR). Experimental results demonstrate that combining PD Loss with existing unlearning methods can effectively prevent over-forgetting and achieve a decrease of 79.5% in the SARR metric of LLaVA-7B and LLaVA-13B, while maintaining forget quality and model utility. Our code and dataset will be released upon acceptance. Warning: This paper contains examples of harmful language and images, and reader discretion is recommended.

We introduce a rank-statistic approximation of f-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter K, we map the mismatch between two univariate distributions μ and ν to a rank histogram on { 0, ldots, K} and measure its deviation from uniformity via a discrete f-divergence, yielding a rank-statistic divergence estimator. We prove that the resulting estimator of the divergence is monotone in K, is always a lower bound of the true f-divergence, and we establish quantitative convergence rates for Ktoinfty under mild regularity of the quantile-domain density ratio. To handle high-dimensional data, we define the sliced rank-statistic f-divergence by averaging the univariate construction over random projections, and we provide convergence results for the sliced limit as well. We also derive finite-sample deviation bounds along with asymptotic normality results for the estimator. Finally, we empirically validate the approach by benchmarking against neural baselines and illustrating its use as a learning objective in generative modeling experiments.

Low-Rank Adaptation (LoRA) methods have emerged as crucial techniques for adapting large pre-trained models to downstream tasks under computational and memory constraints. However, they face a fundamental challenge in balancing task-specific performance gains against catastrophic forgetting of pre-trained knowledge, where existing methods provide inconsistent recommendations. This paper presents a comprehensive analysis of the performance-forgetting trade-offs inherent in low-rank adaptation using principal components as initialization. Our investigation reveals that fine-tuning intermediate components leads to better balance and show more robustness to high learning rates than first (PiSSA) and last (MiLoRA) components in existing work. Building on these findings, we provide a practical approach for initialization of LoRA that offers superior trade-offs. We demonstrate in a thorough empirical study on a variety of computer vision and NLP tasks that our approach improves accuracy and reduces forgetting, also in continual learning scenarios.

Incremental Task learning (ITL) is a category of continual learning that seeks to train a single network for multiple tasks (one after another), where training data for each task is only available during the training of that task. Neural networks tend to forget older tasks when they are trained for the newer tasks; this property is often known as catastrophic forgetting. To address this issue, ITL methods use episodic memory, parameter regularization, masking and pruning, or extensible network structures. In this paper, we propose a new incremental task learning framework based on low-rank factorization. In particular, we represent the network weights for each layer as a linear combination of several rank-1 matrices. To update the network for a new task, we learn a rank-1 (or low-rank) matrix and add that to the weights of every layer. We also introduce an additional selector vector that assigns different weights to the low-rank matrices learned for the previous tasks. We show that our approach performs better than the current state-of-the-art methods in terms of accuracy and forgetting. Our method also offers better memory efficiency compared to episodic memory- and mask-based approaches. Our code will be available at https://github.com/CSIPlab/task-increment-rank-update.git

Catastrophic forgetting remains a central obstacle for continual learning in neural models. Popular approaches -- replay and elastic weight consolidation (EWC) -- have limitations: replay requires a strong generator and is prone to distributional drift, while EWC implicitly assumes a shared optimum across tasks and typically uses a diagonal Fisher approximation. In this work, we study the gradient geometry of diffusion models, which can already produce high-quality replay data. We provide theoretical and empirical evidence that, in the low signal-to-noise ratio (SNR) regime, per-sample gradients become strongly collinear, yielding an empirical Fisher that is effectively rank-1 and aligned with the mean gradient. Leveraging this structure, we propose a rank-1 variant of EWC that is as cheap as the diagonal approximation yet captures the dominant curvature direction. We pair this penalty with a replay-based approach to encourage parameter sharing across tasks while mitigating drift. On class-incremental image generation datasets (MNIST, FashionMNIST, CIFAR-10, ImageNet-1k), our method consistently improves average FID and reduces forgetting relative to replay-only and diagonal-EWC baselines. In particular, forgetting is nearly eliminated on MNIST and FashionMNIST and is more than halved on ImageNet-1k. These results suggest that diffusion models admit an approximately rank-1 Fisher. With a better Fisher estimate, EWC becomes a strong complement to replay: replay encourages parameter sharing across tasks, while EWC effectively constrains replay-induced drift.

Parameter-efficient fine-tuning methods like Low-Rank Adaptation (LoRA) have become the dominant paradigm for adapting large pretrained models. We present a theoretical framework explaining an underexplored property: LoRA's inherent resistance to label noise. Our analysis reveals three key insights. First, we prove that rank-r LoRA cannot memorize all possible label assignments once the sample size exceeds O(r(d+k-r)), limiting its capacity to fit arbitrary noise. Second, we derive an optimal rank balancing approximation bias and noise-induced variance, showing it decreases with noise rate. Third, we establish temporal separation: clean patterns are learned early while noise memorization occurs later. We propose RACT (Rank-Aware Curriculum Training), leveraging rank discrepancy for noise detection. Experiments validate our predictions, with RACT achieving 91.1% F1 for noise detection on AG News while maintaining 91.46% accuracy, competitive with baselines that lack noise detection capability.

Machine unlearning seeks to remove targeted information from trained models without requiring costly retraining. Existing optimization-based methods often degrade unrelated capabilities, while subspace-based approaches rely on computationally expensive singular value decompositions (SVD). We introduce QR-Erase, a subspace-based framework that uses Pivoted QR decomposition to identify and remove task-specific representations directly from model parameters. We further propose Layer-Localized QR-Erase, which restricts updates to layers containing the highest concentration of task-specific information. We show that Pivoted QR provides accurate subspace recovery with bounded error, and that under a mild spectral gap condition, the recovered subspace approaches the optimal SVD solution. Across task-level, cross-lingual, and speech unlearning, QR-Erase achieves a stronger forgetting-retention tradeoff than optimization-based methods while remaining within 5% of SVD across all metrics. Exploiting low-rank and layer-localized structure further improves forgetting (for example, reducing speech forget-set accuracy from 53.1% to 15.7%). These results demonstrate that accurate subspace recovery, rather than optimal reconstruction, is sufficient for effective unlearning and provides an efficient and general alternative to SVD-based methods for modern foundation models.

Attention-based rerankers score each candidate by the attention mass that retrieval heads route to it from the question, but the question, serving as a fixed query, carries limited information for locating relevant evidence. We propose Re^3Rank, a listwise reranker built on reasoning-conditioned retrieval heads (RRHeads). A generator first writes a reasoning trace over the question and the candidates, and a scorer then uses the trace tokens as the attention query of a few selected RRHeads, reading relevance as continuous scores. We present a straight-through estimator to propagate the ranking loss through the discrete trace, so that the generator and the scorer can be trained jointly for ranking. Averaged over 9 benchmarks, Re^3Rank outperforms 11 baseline rerankers: our 4B variant exceeds the strongest baseline by 3.11 NDCG@10 points on average, and even our 0.6B variant surpasses rerankers with up to 32B parameters.

Popular facts are memorised more deeply during pretraining and resist removal longer than rare ones, yet existing LLM unlearning methods apply uniform gradient pressure regardless of training-data frequency. We propose the AdaPop (Adaptive Popularity) method, which combines local token confidence with a per-fact popularity-dependent exponent derived from an external proxy (e.g., Wikidata sitelinks, LLM-as-Judge), and automates the forget-retain balance via a dual-ascent controller that adjusts the retain penalty each epoch. Across three model families and two benchmarks, AdaPop leaks ~5x less forgotten content than competing methods under paraphrased queries and ~1.6x less under adversarial reformulations. We support our analysis with internal metrics: under our method, forget-set hidden states move further from the pre-unlearning model's states than under other methods, while retain-set representations remain close.

Driven by privacy protection laws and regulations, unlearning in Large Language Models (LLMs) is gaining increasing attention. However, current research often neglects the interpretability of the unlearning process, particularly concerning sample-level unlearning difficulty. Existing studies typically assume a uniform unlearning difficulty across samples. This simplification risks attributing the performance of unlearning algorithms to sample selection rather than the algorithm's design, potentially steering the development of LLM unlearning in the wrong direction. Thus, we investigate the relationship between LLM unlearning and sample characteristics, with a focus on unlearning difficulty. Drawing inspiration from neuroscience, we propose a Memory Removal Difficulty (MRD) metric to quantify sample-level unlearning difficulty. Using MRD, we analyze the characteristics of hard-to-unlearn versus easy-to-unlearn samples. Furthermore, we propose an MRD-based weighted sampling method to optimize existing unlearning algorithms, which prioritizes easily forgettable samples, thereby improving unlearning efficiency and effectiveness. We validate the proposed metric and method using public benchmarks and datasets, with results confirming its effectiveness.

Recent unlearning methods for LLMs are vulnerable to relearning attacks: knowledge believed-to-be-unlearned re-emerges by fine-tuning on a small set of (even seemingly-unrelated) examples. We study this phenomenon in a controlled setting for example-level unlearning in vision classifiers. We make the surprising discovery that forget-set accuracy can recover from around 50% post-unlearning to nearly 100% with fine-tuning on just the retain set -- i.e., zero examples of the forget set. We observe this effect across a wide variety of unlearning methods, whereas for a model retrained from scratch excluding the forget set (gold standard), the accuracy remains at 50%. We observe that resistance to relearning attacks can be predicted by weight-space properties, specifically, L_2-distance and linear mode connectivity between the original and the unlearned model. Leveraging this insight, we propose a new class of methods that achieve state-of-the-art resistance to relearning attacks.

A recent study by Feldman (2020) proposed a long-tail theory to explain the memorization behavior of deep learning models. However, memorization has not been empirically verified in the context of NLP, a gap addressed by this work. In this paper, we use three different NLP tasks to check if the long-tail theory holds. Our experiments demonstrate that top-ranked memorized training instances are likely atypical, and removing the top-memorized training instances leads to a more serious drop in test accuracy compared with removing training instances randomly. Furthermore, we develop an attribution method to better understand why a training instance is memorized. We empirically show that our memorization attribution method is faithful, and share our interesting finding that the top-memorized parts of a training instance tend to be features negatively correlated with the class label.

State-of-the-art results on image recognition tasks are achieved using over-parameterized learning algorithms that (nearly) perfectly fit the training set and are known to fit well even random labels. This tendency to memorize the labels of the training data is not explained by existing theoretical analyses. Memorization of the training data also presents significant privacy risks when the training data contains sensitive personal information and thus it is important to understand whether such memorization is necessary for accurate learning. We provide the first conceptual explanation and a theoretical model for this phenomenon. Specifically, we demonstrate that for natural data distributions memorization of labels is necessary for achieving close-to-optimal generalization error. Crucially, even labels of outliers and noisy labels need to be memorized. The model is motivated and supported by the results of several recent empirical works. In our model, data is sampled from a mixture of subpopulations and our results show that memorization is necessary whenever the distribution of subpopulation frequencies is long-tailed. Image and text data is known to be long-tailed and therefore our results establish a formal link between these empirical phenomena. Our results allow to quantify the cost of limiting memorization in learning and explain the disparate effects that privacy and model compression have on different subgroups.

Machine unlearning evaluation is structurally skewed: Why-type questions, which probe causal and relational knowledge, comprise less than 0.06% of CounterFact, 0.6% of ZSRE, and less than 1.3% of TOFU, MUSE, and WMDP-Cyber. This near-zero representation means that methods that fail on causal knowledge can score highly in aggregate, and this failure is undetectable without balanced evaluation. We present 5WBENCH, a balanced 5,000-sample benchmark with 1,000 examples per 5W category (Who, What, When, Where, Why), making causal unlearning failures quantifiable for the first time. Using 5WBENCH, we show that no existing baseline simultaneously achieves high forgetting and high retention on Why-type questions: aggressive forgetting degrades retained knowledge, while conservative methods fail to forget causal facts. Why-type difficulty stems from multi-hop reasoning chains (44% of Why entries vs. less than or equal to 2% for others) and gradient dilution over 40.1-token answer spans. We present MAAT (Multi-phase Adapter-Aware Targeted Unlearning), a three-phase framework operating on LoRA adapter weights, combining gradient-projected ascent, SVD rank-dimension pruning, task vector negation, and hybrid KL-hidden-state retain repair. MAAT is the first method to simultaneously achieve high forgetting and high retention on Why-type causal knowledge, reaching a new operating point on the forget-retain Pareto frontier. We make our code publicly available.

As machine learning systems increasingly rely on data subject to privacy regulation, selectively unlearning specific information from trained models has become essential. In image classification, this involves removing the influence of particular training samples, semantic classes, or visual styles without full retraining. We introduce Forget-Aligned Model Reconstruction (FAMR), a theoretically grounded and computationally efficient framework for post-hoc unlearning in deep image classifiers. FAMR frames forgetting as a constrained optimization problem that minimizes a uniform-prediction loss on the forget set while anchoring model parameters to their original values via an ell_2 penalty. A theoretical analysis links FAMR's solution to influence-function-based retraining approximations, with bounds on parameter and output deviation. Empirical results on class forgetting tasks using CIFAR-10 and ImageNet-100 demonstrate FAMR's effectiveness, with strong performance retention and minimal computational overhead. The framework generalizes naturally to concept and style erasure, offering a scalable and certifiable route to efficient post-hoc forgetting in vision models.

Machine unlearning aims to remove knowledge of the specific training data in a well-trained model. Currently, machine unlearning methods typically handle all forgetting data in a single batch, removing the corresponding knowledge all at once upon request. However, in practical scenarios, requests for data removal often arise in a streaming manner rather than in a single batch, leading to reduced efficiency and effectiveness in existing methods. Such challenges of streaming forgetting have not been the focus of much research. In this paper, to address the challenges of performance maintenance, efficiency, and data access brought about by streaming unlearning requests, we introduce a streaming unlearning paradigm, formalizing the unlearning as a distribution shift problem. We then estimate the altered distribution and propose a novel streaming unlearning algorithm to achieve efficient streaming forgetting without requiring access to the original training data. Theoretical analyses confirm an O(T + V_T) error bound on the streaming unlearning regret, where V_T represents the cumulative total variation in the optimal solution over T learning rounds. This theoretical guarantee is achieved under mild conditions without the strong restriction of convex loss function. Experiments across various models and datasets validate the performance of our proposed method.

Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank approximation and its application in adaptation can sometimes be obscure, leaving practitioners and researchers with questions about its true capabilities and limitations. This paper seeks to clarify low-rank approximation and adaptation by offering a comprehensive guide that reveals their inner workings and explains their utility in a clear and accessible way. Our focus here is to develop a solid intuition for how low-rank approximation and adaptation operate, and why they are so effective. We begin with basic concepts and gradually build up to the mathematical underpinnings, ensuring that readers of all backgrounds can gain a deeper understanding of low-rank approximation and adaptation. We strive to strike a balance between informal explanations and rigorous mathematics, ensuring that both newcomers and experienced experts can benefit from this survey. Additionally, we introduce new low-rank decomposition and adaptation algorithms that have not yet been explored in the field, hoping that future researchers will investigate their potential applicability.

Catastrophic forgetting is a problem faced by many machine learning models and algorithms. When trained on one task, then trained on a second task, many machine learning models "forget" how to perform the first task. This is widely believed to be a serious problem for neural networks. Here, we investigate the extent to which the catastrophic forgetting problem occurs for modern neural networks, comparing both established and recent gradient-based training algorithms and activation functions. We also examine the effect of the relationship between the first task and the second task on catastrophic forgetting. We find that it is always best to train using the dropout algorithm--the dropout algorithm is consistently best at adapting to the new task, remembering the old task, and has the best tradeoff curve between these two extremes. We find that different tasks and relationships between tasks result in very different rankings of activation function performance. This suggests the choice of activation function should always be cross-validated.

Machine unlearning aims to make a model forget specific data, yet unlearned LLMs often fail to stay unlearned: brief fine-tuning can revive removed knowledge. Existing robustness predictors rely on global weight-space displacement, but distance alone can be misleading when random or destructive updates collapse performance. We argue that relearning robustness depends on update structure: robust unlearning should affect forget-critical weights while sparing retain-critical ones. We introduce the Forget-Retain Alignment Gap (FRAG), a training-free predictor that scores an update's forget-retain alignment without running a relearning attack, and separates selective from dense updates more reliably than global distance. Building on the forget-critical, retain-sparing principle, Forget-Retain Pruning (FRP) improves relearning robustness. Our results suggest that weight selectivity better explains robustness than distance alone. Code is available at https://github.com/Yi1-Chen/FRAG.

Where an LLM sits in an agent memory pipeline -- between the recall plane that retrieves stored facts (extensively benchmarked) and the control plane that mutates them via supersede, release, purge (largely untested) -- shapes which forgetting failure modes the system recovers. Comparing thirteen system configurations on a 385-case adversarial surface, we observe three placement regimes with partly complementary coverage: deterministic primitives suffice for lexical/temporal categories but fail canonicalization (5% on identifier-obfuscation, 0% on cross-lingual); inscribe-time LLM recovers canonicalization (100%) but cannot help intent-aware deletion (0% on prefix-collision and compound-fact); a mutation-time hook recovers intent-aware deletion (78-85%) and brightens nearly all categories simultaneously (91.7-93.2% overall, $0.17 per 385-case run, 2.3s/case mutation latency vs. 64-191ms/case deterministic, recall path unchanged). We expose the trade-off via ForgetEval, a 1000-case templated suite plus a 385-case adversarial layer (132 hand-crafted + 253 LLM-drafted oracle-validated) scored by deterministic substring match, paired with a six-method Adapter Protocol with honest N/A scoring that lets heterogeneous memory stores enter in 130 lines. Admission is corroborated by 10-annotator IAA (Fleiss' kappa = 0.958) and a 77-case external-authored subset (four blind contributors) that replicates the canonicalization asymmetry and amplifies the joint-placement lift (+27.8 pt). Production failures are predominantly forgetting failures rather than recall failures, yet existing benchmarks measure only recall. ForgetEval and all adapters are released under MIT.

Machine unlearning for large language models (LLMs) aims to selectively remove memorized content such as private data, copyrighted text, or hazardous knowledge, without costly full retraining. Most existing methods require a retain set of curated examples to prevent catastrophic degradation of general model utility, creating an extra data dependency that complicates deployment. We propose SHRED (Self-distillation via High-surprisal-only Retain-set-free Entropy Demotion), a retain-set-free unlearning method built on a key insight: not all tokens within a forget set instance carry memorized information equally. High-information tokens concentrate the model's memorized knowledge, while low-information tokens reflect general language competence. SHRED operates in two stages. (1) Selection: We perform a forward pass on a forget set instance, collect per-token autoregressive probabilities, and select the bottom (lowest probability, highest Shannon information) as forget positions; the remaining positions are retained as benign anchors. (2) Training: We construct modified KL targets that demote the memorized token's logit at forget positions while preserving the original distribution at benign positions. The model is then trained via a single top KL self-distillation objective that simultaneously drives forgetting and utility preservation. We evaluate SHRED across four standard unlearning benchmarks and demonstrate that it establishes a new Pareto-optimal trade-off between forget efficacy and model utility, outperforming retain-set-dependent methods. Our analysis shows that SHRED is robust against relearning attacks and membership-inference attacks, and it maintains stable utility even after many sequential unlearning runs.

We analyze continual learning on a sequence of separable linear classification tasks with binary labels. We show theoretically that learning with weak regularization reduces to solving a sequential max-margin problem, corresponding to a special case of the Projection Onto Convex Sets (POCS) framework. We then develop upper bounds on the forgetting and other quantities of interest under various settings with recurring tasks, including cyclic and random orderings of tasks. We discuss several practical implications to popular training practices like regularization scheduling and weighting. We point out several theoretical differences between our continual classification setting and a recently studied continual regression setting.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

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 capable despite explicit forget instructions. These results expose a clear gap between prompt-level suppression and true visual concept erasure.

LLMs cannot forget the way we delete a file. Strangely, we are asked to remove something that was never put anywhere in particular. What the model took from a piece of text is now smeared across billions of weights. Existing methods rewrite all of them to change one thing, and none of them say which part produced that change. To address this, we introduce Causal Routing for Unlearning (CRU) by asking where the concept is expressed in the model and suppressing only that part. One untrained forward pass over the forget set ranks neurons by how their activations vary. Then, small routing modules on those neurons gate and suppress only the concepts that need to be forgotten. In CRU, the base model is frozen, and any change in behavior is caused only by the gated neurons; hence, why the routing is causal. Due to our parameter efficiency (only ~0.01% as many parameters as the base model), unlearning a concept costs 14 GiB, whereas the baselines require 71 GiB. On TOFU, CRU is indistinguishable from the retained model (p > 0.05, KS test) and is never Pareto-dominated, whereas every compared baseline matches its forgetting on the larger-forget batches only by collapsing utility. On RWKU, it achieves an adversarial-probe recall of 0.052, compared to 0.250 for the strongest baseline, meaning the knowledge is gone, not merely harder to reach. Thus, deciding on the intervention at query time, rather than fixing it beforehand, is the axis along which we argue that unlearning should proceed.

Machine Unlearning is rising as a new field, driven by the pressing necessity of ensuring privacy in modern artificial intelligence models. This technique primarily aims to eradicate any residual influence of a specific subset of data from the knowledge acquired by a neural model during its training. This work introduces a novel unlearning algorithm, denoted as Distance-based Unlearning via Centroid Kinematics (DUCK), which employs metric learning to guide the removal of samples matching the nearest incorrect centroid in the embedding space. Evaluation of the algorithm's performance is conducted across various benchmark datasets in two distinct scenarios, class removal, and homogeneous sampling removal, obtaining state-of-the-art performance. We also introduce a novel metric, called Adaptive Unlearning Score (AUS), encompassing not only the efficacy of the unlearning process in forgetting target data but also quantifying the performance loss relative to the original model. Additionally, we conducted a thorough investigation of the unlearning mechanism in DUCK, examining its impact on the organization of the feature space and employing explainable AI techniques for deeper insights.

Machine unlearning (MU) aims to remove the influence of specific training data while preserving model utility. As the name suggests, MU can be viewed as the inverse of learning, using gradient-based updates to reduce the influence of a forget-set by counteracting the previously learned behavior. Recently, Muon, a gradient descent variant, has been introduced. Muon applies spectral magnitude normalization to encourage exploration of rare directions and demonstrates promising performance. Inspired by Muon, we adopt the spectral view for unlearning and propose Spectral Saliency Unlearning (SSU). SSU thresholds weak singular components and updates only those directions supported by a confident unlearning signal. We further provide theoretical justification for this thresholding approach from the perspective of the forgetting-retention trade-off. Experiments across image classifiers, diffusion models, and LLMs demonstrate SSU's effectiveness.

High-dimensional mean testing is challenging under strong dependence and heavy tails, since classical Hotelling statistics are ill posed and regularized versions based on sample moments remain sensitive to outliers. This paper develops a robust regularized Hotelling framework for one-sample mean inference under elliptical distributions. The proposed HRST statistic combines a Hettmansperger-Randles spatial location estimator with the inverse of a trace-normalized shrinkage Tyler scatter matrix, and calibrates the resulting quadratic form through ridge-resolvent random-matrix theory rather than sparse covariance or precision-matrix assumptions. In the regime p/nto yin(0,infty), allowing a vanishing lower bulk edge and finite-rank diverging spikes, we establish feasible asymptotic normality for each shrinkage level, derive local-alternative distributions with explicit noncentrality parameters, and prove joint Gaussian limits over finite shrinkage grids. These results justify an adaptive Cauchy combination test across shrinkage levels. Simulations and a paired tumor-normal gene-expression study show that HRST maintains size and improves robustness under heavy-tailed distributions while retaining power under strong correlation.

Advances in Multimodal Large Language Models (MLLMs) intensify concerns about data privacy, making Machine Unlearning (MU), the selective removal of learned information, a critical necessity. However, existing MU benchmarks for MLLMs are limited by a lack of image diversity, potential inaccuracies, and insufficient evaluation scenarios, which fail to capture the complexity of real-world applications. To facilitate the development of MLLMs unlearning and alleviate the aforementioned limitations, we introduce OFFSIDE, a novel benchmark for evaluating misinformation unlearning in MLLMs based on football transfer rumors. This manually curated dataset contains 15.68K records for 80 players, providing a comprehensive framework with four test sets to assess forgetting efficacy, generalization, utility, and robustness. OFFSIDE supports advanced settings like selective unlearning and corrective relearning, and crucially, unimodal unlearning (forgetting only text data). Our extensive evaluation of multiple baselines reveals key findings: (1) Unimodal methods (erasing text-based knowledge) fail on multimodal rumors; (2) Unlearning efficacy is largely driven by catastrophic forgetting; (3) All methods struggle with "visual rumors" (rumors appear in the image); (4) The unlearned rumors can be easily recovered and (5) All methods are vulnerable to prompt attacks. These results expose significant vulnerabilities in current approaches, highlighting the need for more robust multimodal unlearning solutions. The code is available at https://github.com/zh121800/OFFSIDE{https://github.com/zh121800/OFFSIDE}.

The growing computational demands posed by increasingly number of neural network's parameters necessitate low-memory-consumption training approaches. Previous memory reduction techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, suffer from the limitation of low rank and saddle point issues, particularly during intensive tasks like pre-training. In this paper, we propose Sparse Spectral Training (SST), an advanced training methodology that updates all singular values and selectively updates singular vectors of network weights, thereby optimizing resource usage while closely approximating full-rank training. SST refines the training process by employing a targeted updating strategy for singular vectors, which is determined by a multinomial sampling method weighted by the significance of the singular values, ensuring both high performance and memory reduction. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, including natural language generation, machine translation, node classification and link prediction, SST demonstrates its capability to outperform existing memory reduction training methods and is comparable with full-rank training in some cases. On OPT-125M, with rank equating to 8.3% of embedding dimension, SST reduces the perplexity gap to full-rank training by 67.6%, demonstrating a significant reduction of the performance loss with prevalent low-rank methods. This approach offers a strong alternative to traditional training techniques, paving the way for more efficient and scalable neural network training solutions.

Understanding memorisation in language models has practical and societal implications, e.g., studying models' training dynamics or preventing copyright infringements. Prior work defines memorisation as the causal effect of training with an instance on the model's ability to predict that instance. This definition relies on a counterfactual: the ability to observe what would have happened had the model not seen that instance. Existing methods struggle to provide computationally efficient and accurate estimates of this counterfactual. Further, they often estimate memorisation for a model architecture rather than for a specific model instance. This paper fills an important gap in the literature, proposing a new, principled, and efficient method to estimate memorisation based on the difference-in-differences design from econometrics. Using this method, we characterise a model's memorisation profile--its memorisation trends across training--by only observing its behaviour on a small set of instances throughout training. In experiments with the Pythia model suite, we find that memorisation (i) is stronger and more persistent in larger models, (ii) is determined by data order and learning rate, and (iii) has stable trends across model sizes, thus making memorisation in larger models predictable from smaller ones.

Unlearning in large language models (LLMs) aims to remove specified data, but its efficacy is typically assessed with task-level metrics like accuracy and perplexity. We demonstrate that these metrics are often misleading, as models can appear to forget while their original behavior is easily restored through minimal fine-tuning. This phenomenon of reversibility suggests that information is merely suppressed, not genuinely erased. To address this critical evaluation gap, we introduce a representation-level analysis framework. Our toolkit comprises PCA-based similarity and shift, centered kernel alignment (CKA), and Fisher information, complemented by a summary metric, the mean PCA distance, to measure representational drift. Applying this framework across six unlearning methods, three data domains, and two LLMs, we identify four distinct forgetting regimes based on their reversibility and catastrophicity. Our analysis reveals that achieving the ideal state--irreversible, non-catastrophic forgetting--is exceptionally challenging. By probing the limits of unlearning, we identify a case of seemingly irreversible, targeted forgetting, offering new insights for designing more robust erasure algorithms. Our findings expose a fundamental gap in current evaluation practices and establish a representation-level foundation for trustworthy unlearning.

Machine unlearning is an emerging paradigm to remove the influence of specific training data (i.e., the forget set) from a model while preserving its knowledge of the rest of the data (i.e., the retain set). Previous approaches assume the forget data to be uniformly distributed from all training datapoints. However, if the data to unlearn is dominant in one group, we empirically show that performance for this group degrades, leading to fairness issues. This work tackles the overlooked problem of non-uniformly distributed forget sets, which we call group-robust machine unlearning, by presenting a simple, effective strategy that mitigates the performance loss in dominant groups via sample distribution reweighting. Moreover, we present MIU (Mutual Information-aware Machine Unlearning), the first approach for group robustness in approximate machine unlearning. MIU minimizes the mutual information between model features and group information, achieving unlearning while reducing performance degradation in the dominant group of the forget set. Additionally, MIU exploits sample distribution reweighting and mutual information calibration with the original model to preserve group robustness. We conduct experiments on three datasets and show that MIU outperforms standard methods, achieving unlearning without compromising model robustness. Source code available at https://github.com/tdemin16/group-robust_machine_unlearning.

The leakage of benchmark data into the training data has emerged as a significant challenge for evaluating the capabilities of large language models (LLMs). In this work, we challenge the common assumption that small-scale contamination renders benchmark evaluations invalid. First, we experimentally quantify the magnitude of benchmark overfitting based on scaling along three dimensions: The number of model parameters (up to 1.6B), the number of times an example is seen (up to 144), and the number of training tokens (up to 40B). If model and data follow the Chinchilla scaling laws, minor contamination indeed leads to overfitting. At the same time, even 144 times of contamination can be forgotten if the training data is scaled beyond five times Chinchilla, a regime characteristic of many modern LLMs. Continual pre-training of OLMo-7B corroborates these results. Next, we study the impact of the weight decay parameter on example forgetting, showing that empirical forgetting occurs faster than the cumulative weight decay. This allows us to gauge the degree of example forgetting in large-scale training runs, indicating that many LLMs, including Lllama 3 405B, have forgotten the data seen at the beginning of training.

Due to growing privacy concerns, machine unlearning, which aims at enabling machine learning models to ``forget" specific training data, has received increasing attention. Among existing methods, influence-based unlearning has emerged as a prominent approach due to its ability to estimate the impact of individual training samples on model parameters without retraining. However, this approach suffers from prohibitive computational overhead arising from the necessity to compute the Hessian matrix and its inverse across all training samples and parameters, rendering it impractical for large-scale models and scenarios involving frequent data deletion requests. This highlights the difficulty of forgetting. Inspired by cognitive science, which suggests that memorizing is easier than forgetting, this paper establishes a theoretical link between memorizing (incremental learning) and forgetting (unlearning). This connection allows machine unlearning to be addressed from the perspective of incremental learning. Unlike the time-consuming Hessian computations in unlearning (forgetting), incremental learning (memorizing) typically relies on more efficient gradient optimization, which supports the aforementioned cognitive theory. Based on this connection, we introduce the Influence Approximation Unlearning (IAU) algorithm for efficient machine unlearning from the incremental perspective. Extensive empirical evaluations demonstrate that IAU achieves a superior balance among removal guarantee, unlearning efficiency, and comparable model utility, while outperforming state-of-the-art methods across diverse datasets and model architectures. Our code is available at https://github.com/Lolo1222/IAU.

When language models (LMs) are trained to forget (or "unlearn'') a skill, how precisely does their behavior change? We study the behavior of transformer LMs in which tasks have been forgotten via fine-tuning on randomized labels. Such LMs learn to generate near-random predictions for individual examples in the "training'' set used for forgetting. Across tasks, however, LMs exhibit extreme variability in whether LM predictions change on examples outside the training set. In some tasks (like entailment classification), forgetting generalizes robustly, and causes models to produce uninformative predictions on new task instances; in other tasks (like physical commonsense reasoning and scientific question answering) forgetting affects only the training examples, and models continue to perform the "forgotten'' task accurately even for examples very similar to those that appeared in the training set. Dataset difficulty is not predictive of whether a behavior can be forgotten; instead, generalization in forgetting is (weakly) predicted by the confidence of LMs' initial task predictions and the variability of LM representations of training data, with low confidence and low variability both associated with greater generalization. Perhaps most surprisingly, random-label forgetting appears to be somewhat insensitive to the contents of the training set: for example, models trained on science questions with random labels continue to answer other science questions accurately, but begin to produce random labels on entailment classification tasks. Finally, we show that even generalizable forgetting is shallow: linear probes trained on LMs' representations can still perform tasks reliably after forgetting. Our results highlight the difficulty and unpredictability of performing targeted skill removal from models via fine-tuning.

Many approximate machine unlearning methods demonstrate strong logit-level forgetting -- such as near-zero accuracy on the forget set -- yet continue to preserve substantial information within their internal feature representations. We refer to this discrepancy as superficial forgetting. Recent studies indicate that most existing unlearning approaches primarily alter the final classifier, leaving intermediate representations largely unchanged and highly similar to those of the original model. To address this limitation, we introduce the Erase at the Core (EC), a framework designed to enforce forgetting throughout the entire network hierarchy. EC integrates multi-layer contrastive unlearning on the forget set with retain set preservation through deeply supervised learning. Concretely, EC attaches auxiliary modules to intermediate layers and applies both contrastive unlearning and cross-entropy losses at each supervision point, with layer-wise weighted losses. Experimental results show that EC not only achieves effective logit-level forgetting, but also substantially reduces representational similarity to the original model across intermediate layers. Furthermore, EC is model-agnostic and can be incorporated as a plug-in module into existing unlearning methods, improving representation-level forgetting while maintaining performance on the retain set.

Machine unlearning is a process to remove specific data points from a trained model while maintaining the performance on retain data, addressing privacy or legal requirements. Despite its importance, existing unlearning evaluations tend to focus on logit-based metrics (i.e., accuracy) under small-scale scenarios. We observe that this could lead to a false sense of security in unlearning approaches under real-world scenarios. In this paper, we conduct a new comprehensive evaluation that employs representation-based evaluations of the unlearned model under large-scale scenarios to verify whether the unlearning approaches genuinely eliminate the targeted forget data from the model's representation perspective. Our analysis reveals that current state-of-the-art unlearning approaches either completely degrade the representational quality of the unlearned model or merely modify the classifier (i.e., the last layer), thereby achieving superior logit-based evaluation metrics while maintaining significant representational similarity to the original model. Furthermore, we introduce a rigorous unlearning evaluation setup, in which the forgetting classes exhibit semantic similarity to downstream task classes, necessitating that feature representations diverge significantly from those of the original model, thus enabling a more rigorous evaluation from a representation perspective. We hope our benchmark serves as a standardized protocol for evaluating unlearning algorithms under realistic conditions.

Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU's superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.

Diffusion models have shown strong performance in generating high-quality tabular data, but they carry privacy risks by reproducing exact training samples. While prior work focuses on dataset-level augmentation to reduce memorization, little is known about which individual samples contribute most. We present the first data-centric study of memorization dynamics in tabular diffusion models. We quantify memorization for each real sample based on how many generated samples are flagged as replicas, using a relative distance ratio. Our empirical analysis reveals a heavy-tailed distribution of memorization counts: a small subset of samples contributes disproportionately to leakage, confirmed via sample-removal experiments. To understand this, we divide real samples into top- and non-top-memorized groups and analyze their training-time behaviors. We track when each sample is first memorized and monitor per-epoch memorization intensity (AUC). Memorized samples are memorized slightly earlier and show stronger signals in early training. Based on these insights, we propose DynamicCut, a two-stage, model-agnostic mitigation method: (a) rank samples by epoch-wise intensity, (b) prune a tunable top fraction, and (c) retrain on the filtered dataset. Across multiple tabular datasets and models, DynamicCut reduces memorization with minimal impact on data diversity and downstream performance. It also complements augmentation-based defenses. Furthermore, DynamicCut enables cross-model transferability: high-ranked samples identified from one model (e.g., a diffusion model) are also effective for reducing memorization when removed from others, such as GANs and VAEs.

Although Multimodal Large Language Models (MLLMs) have achieved remarkable progress across many domains, their training on large-scale multimodal datasets raises serious privacy concerns, making effective machine unlearning increasingly necessary. However, existing benchmarks mainly focus on static or short-sequence settings, offering limited support for evaluating continual privacy deletion requests in realistic deployments. To bridge this gap, we introduce ICU-Bench, a continual multimodal unlearning benchmark built on privacy-critical document data. ICU-Bench contains 1,000 privacy-sensitive profiles from two document domains, medical reports and labor contracts, with 9,500 images, 16,000 question-answer pairs, and 100 forget tasks. Additionally, new continual unlearning metrics are introduced, facilitating a comprehensive analysis of forgetting effectiveness, historical forgetting preservation, retained utility, and stability throughout the continual unlearning process. Through extensive experiments with representative unlearning methods on ICU-Bench, we show that existing methods generally struggle in continual settings and exhibit clear limitations in balancing forgetting quality, utility preservation, and scalability over long task sequences. These findings highlight the need for multimodal unlearning methods explicitly designed for continual privacy deletion.

Learning to rank is a key component of many e-commerce search engines. In learning to rank, one is interested in optimising the global ordering of a list of items according to their utility for users.Popular approaches learn a scoring function that scores items individually (i.e. without the context of other items in the list) by optimising a pointwise, pairwise or listwise loss. The list is then sorted in the descending order of the scores. Possible interactions between items present in the same list are taken into account in the training phase at the loss level. However, during inference, items are scored individually, and possible interactions between them are not considered. In this paper, we propose a context-aware neural network model that learns item scores by applying a self-attention mechanism. The relevance of a given item is thus determined in the context of all other items present in the list, both in training and in inference. We empirically demonstrate significant performance gains of self-attention based neural architecture over Multi-LayerPerceptron baselines, in particular on a dataset coming from search logs of a large scale e-commerce marketplace, Allegro.pl. This effect is consistent across popular pointwise, pairwise and listwise losses.Finally, we report new state-of-the-art results on MSLR-WEB30K, the learning to rank benchmark.

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

Recently, the pretrain-finetune paradigm has become a cornerstone in various deep learning areas. While in general the pre-trained model would promote both effectiveness and efficiency of downstream tasks fine-tuning, studies have shown that not all knowledge acquired during pre-training is beneficial. Some of the knowledge may actually bring detrimental effects to the fine-tuning tasks, which is also known as negative transfer. To address this problem, graceful forgetting has emerged as a promising approach. The core principle of graceful forgetting is to enhance the learning plasticity of the target task by selectively discarding irrelevant knowledge. However, this approach remains underexplored in the context of generative language models, and it is often challenging to migrate existing forgetting algorithms to these models due to architecture incompatibility. To bridge this gap, in this paper we propose a novel framework, Learning With Forgetting (LWF), to achieve graceful forgetting in generative language models. With Fisher Information Matrix weighting the intended parameter updates, LWF computes forgetting confidence to evaluate self-generated knowledge regarding the forgetting task, and consequently, knowledge with high confidence is periodically unlearned during fine-tuning. Our experiments demonstrate that, although thoroughly uncovering the mechanisms of knowledge interaction remains challenging in pre-trained language models, applying graceful forgetting can contribute to enhanced fine-tuning performance.

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. Extensive experiments on biased datasets including Waterbirds, BAR, and Biased NICO++ demonstrate that our method achieves state-of-the-art forgetting performance and effectively mitigates the shortcut unlearning problem.

Machine unlearning aims to remove targeted information from large language models, but existing evaluations often measure forgetting only on a designated benchmark distribution. We argue that such behavioral forgetting is an insufficient standard for privacy-oriented unlearning, and that evaluation should instead test whether forgetting persists across the access paths through which the same information may be recovered. We demonstrate this with a controlled case study of cross-lingual querying: across multiple multilingual model families, forgetting varies substantially when semantically equivalent information is queried in different languages and scripts. A single access path is therefore enough to expose a real gap between behavioral forgetting and information inaccessibility, motivating broader evaluation of access-path generalization and adversarial recoverability alongside in-distribution forgetting.

We analyze the layerwise effective dimension (rank of the feature matrix) in fully-connected ReLU networks of finite width. Specifically, for a fixed batch of m inputs and random Gaussian weights, we derive closed-form expressions for the expected rank of the \mtimes n hidden activation matrices. Our main result shows that E[EDim(ell)]=m[1-(1-2/pi)^ell]+O(e^{-c m}) so that the rank deficit decays geometrically with ratio 1-2 / pi approx 0.3634. We also prove a sub-Gaussian concentration bound, and identify the "revival" depths at which the expected rank attains local maxima. In particular, these peaks occur at depths ell_k^*approx(k+1/2)pi/log(1/rho) with height approx (1-e^{-pi/2}) m approx 0.79m. We further show that this oscillatory rank behavior is a finite-width phenomenon: under orthogonal weight initialization or strong negative-slope leaky-ReLU, the rank remains (nearly) full. These results provide a precise characterization of how random ReLU layers alternately collapse and partially revive the subspace of input variations, adding nuance to prior work on expressivity of deep networks.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

Machine unlearning aims to remove the influence of targeted training data from a model while preserving its remaining capabilities, but evaluating whether such information has truly become inaccessible remains challenging. Existing benchmarks primarily assess unlearning under clean, non-adversarial queries, leaving open whether information that appears forgotten can still be recovered through strategic prompting. We address this gap through a unified evaluation of prompt-based and fine-tuning-based unlearning methods on TOFU using Llama-3.2-3B-Instruct, followed by an adversarial robustness evaluation of methods that perform strongly under standard metrics. We introduce Attack Success Rate (ASR), an LLM-as-judge metric that measures the fraction of adversarial responses whose leakage score exceeds 0.2, and evaluate recovery across eight attack suites. Our results reveal a substantial gap between clean-query forgetting and adversarial robustness. Although several fine-tuning-based methods achieve Forget Quality above 0.91, targeted information remains recoverable with ASRs between 72.8% and 84.3%, close to the 87.5% ASR of the unprotected base model. In contrast, clean multilingual reformulations yield only 2.95% measured leakage. A manual audit further finds agreement between binary ASR decisions and human factual assessments in seven of ten cases, indicating that ASR provides a useful, though imperfect, signal of behavioral recoverability. These findings show that strong standard-metric performance alone is insufficient to establish robustness after unlearning and motivate adversarial stress-testing as a complementary component of unlearning evaluation.

Memorization, or the tendency of large language models (LLMs) to output entire sequences from their training data verbatim, is a key concern for safely deploying language models. In particular, it is vital to minimize a model's memorization of sensitive datapoints such as those containing personal identifiable information (PII). The prevalence of such undesirable memorization can pose issues for model trainers, and may even require discarding an otherwise functional model. We therefore seek to predict which sequences will be memorized before a large model's full train-time by extrapolating the memorization behavior of lower-compute trial runs. We measure memorization of the Pythia model suite and plot scaling laws for forecasting memorization, allowing us to provide equi-compute recommendations to maximize the reliability (recall) of such predictions. We additionally provide further novel discoveries on the distribution of memorization scores across models and data. We release all code and data necessary to reproduce the results in this paper at https://github.com/EleutherAI/pythia

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 insights, we introduce JensUn++, an unlearning algorithm that achieves the best forget-retain utility trade-off across three LLMs, in both sequential and joint unlearning settings. Code and datasets are available at https://amitpeleg.github.io/forget-narrowly-retain-broadly

Parameter regularization or allocation methods are effective in overcoming catastrophic forgetting in lifelong learning. However, they solve all tasks in a sequence uniformly and ignore the differences in the learning difficulty of different tasks. So parameter regularization methods face significant forgetting when learning a new task very different from learned tasks, and parameter allocation methods face unnecessary parameter overhead when learning simple tasks. In this paper, we propose the Parameter Allocation & Regularization (PAR), which adaptively select an appropriate strategy for each task from parameter allocation and regularization based on its learning difficulty. A task is easy for a model that has learned tasks related to it and vice versa. We propose a divergence estimation method based on the Nearest-Prototype distance to measure the task relatedness using only features of the new task. Moreover, we propose a time-efficient relatedness-aware sampling-based architecture search strategy to reduce the parameter overhead for allocation. Experimental results on multiple benchmarks demonstrate that, compared with SOTAs, our method is scalable and significantly reduces the model's redundancy while improving the model's performance. Further qualitative analysis indicates that PAR obtains reasonable task-relatedness.

Large language models can memorize private or harmful information, motivating machine unlearning methods that remove targeted knowledge while preserving other capabilities. However, existing evaluations rely primarily on behavioral benchmarks, which assess whether a model appears to forget but provide limited insight into how unlearning changes the model or affects related knowledge. We introduce TRIAGE (Tripartite Representation-internal Introspection for Adjacency Gap Evaluation), a benchmark-agnostic evaluation framework for characterizing these changes. TRIAGE uses diagonal approximations of the Fisher information and Hessian to measure changes in parameter sensitivity and local curvature, and utilizes a Forget / Adjacent-Retain / Generic-Retain partition to quantify an adjacency gap in semantically related knowledge. Based on the magnitude and distribution of these changes, TRIAGE further classifies each algorithm's update as no-op, partially localized, collateral dominant, or globally destructive. Across 12 unlearning methods, four language models, and the WMDP, TOFU, and MUSE benchmarks, we find that methods with similar behavioral forgetting can produce substantially different internal changes and patterns of collateral damage. These signatures also vary across models and benchmarks, indicating that the effects of unlearning are not determined solely by the unlearning algorithm. TRIAGE can be applied alongside existing unlearning benchmarks to complement behavioral evaluation with a model-internal view of how unlearning reshapes the model's parameter space and affects retained knowledge.

We introduce a new analytical framework to quantify the changes in a machine learning algorithm's output distribution following the inclusion of a few data points in its training set, a notion we define as leave-one-out distinguishability (LOOD). This problem is key to measuring data **memorization** and **information leakage** in machine learning, and the **influence** of training data points on model predictions. We illustrate how our method broadens and refines existing empirical measures of memorization and privacy risks associated with training data. We use Gaussian processes to model the randomness of machine learning algorithms, and validate LOOD with extensive empirical analysis of information leakage using membership inference attacks. Our theoretical framework enables us to investigate the causes of information leakage and where the leakage is high. For example, we analyze the influence of activation functions, on data memorization. Additionally, our method allows us to optimize queries that disclose the most significant information about the training data in the leave-one-out setting. We illustrate how optimal queries can be used for accurate **reconstruction** of training data.

Most work on sequential learning assumes a fixed set of actions that are available all the time. However, in practice, actions can consist of picking subsets of readings from sensors that may break from time to time, road segments that can be blocked or goods that are out of stock. In this paper we study learning algorithms that are able to deal with stochastic availability of such unreliable composite actions. We propose and analyze algorithms based on the Follow-The-Perturbed-Leader prediction method for several learning settings differing in the feedback provided to the learner. Our algorithms rely on a novel loss estimation technique that we call Counting Asleep Times. We deliver regret bounds for our algorithms for the previously studied full information and (semi-)bandit settings, as well as a natural middle point between the two that we call the restricted information setting. A special consequence of our results is a significant improvement of the best known performance guarantees achieved by an efficient algorithm for the sleeping bandit problem with stochastic availability. Finally, we evaluate our algorithms empirically and show their improvement over the known approaches.

The rise of the phenomenon of the "right to be forgotten" has prompted research on machine unlearning, which grants data owners the right to actively withdraw data that has been used for model training, and requires the elimination of the contribution of that data to the model. A simple method to achieve this is to use the remaining data to retrain the model, but this is not acceptable for other data owners who continue to participate in training. Existing machine unlearning methods have been found to be ineffective in quickly removing knowledge from deep learning models. This paper proposes using a stochastic network as a teacher to expedite the mitigation of the influence caused by forgotten data on the model. We performed experiments on three datasets, and the findings demonstrate that our approach can efficiently mitigate the influence of target data on the model within a single epoch. This allows for one-time erasure and reconstruction of the model, and the reconstruction model achieves the same performance as the retrained model.

The machine learning community is increasingly recognizing the importance of fostering trust and safety in modern generative AI (GenAI) models. We posit machine unlearning (MU) as a crucial foundation for developing safe, secure, and trustworthy GenAI models. Traditional MU methods often rely on stringent assumptions and require access to real data. This paper introduces Score Forgetting Distillation (SFD), an innovative MU approach that promotes the forgetting of undesirable information in diffusion models by aligning the conditional scores of "unsafe" classes or concepts with those of "safe" ones. To eliminate the need for real data, our SFD framework incorporates a score-based MU loss into the score distillation objective of a pretrained diffusion model. This serves as a regularization term that preserves desired generation capabilities while enabling the production of synthetic data through a one-step generator. Our experiments on pretrained label-conditional and text-to-image diffusion models demonstrate that our method effectively accelerates the forgetting of target classes or concepts during generation, while preserving the quality of other classes or concepts. This unlearned and distilled diffusion not only pioneers a novel concept in MU but also accelerates the generation speed of diffusion models. Our experiments and studies on a range of diffusion models and datasets confirm that our approach is generalizable, effective, and advantageous for MU in diffusion models. (Warning: This paper contains sexually explicit imagery, discussions of pornography, racially-charged terminology, and other content that some readers may find disturbing, distressing, and/or offensive.)

With the implementation of personal data privacy regulations, the field of machine learning (ML) faces the challenge of the "right to be forgotten". Machine unlearning has emerged to address this issue, aiming to delete data and reduce its impact on models according to user requests. Despite the widespread interest in machine unlearning, comprehensive surveys on its latest advancements, especially in the field of Large Language Models (LLMs) is lacking. This survey aims to fill this gap by providing an in-depth exploration of machine unlearning, including the definition, classification and evaluation criteria, as well as challenges in different environments and their solutions. Specifically, this paper categorizes and investigates unlearning on both traditional models and LLMs, and proposes methods for evaluating the effectiveness and efficiency of unlearning, and standards for performance measurement. This paper reveals the limitations of current unlearning techniques and emphasizes the importance of a comprehensive unlearning evaluation to avoid arbitrary forgetting. This survey not only summarizes the key concepts of unlearning technology but also points out its prominent issues and feasible directions for future research, providing valuable guidance for scholars in the field.

While Large Vision-Language Models (LVLMs) offer powerful capabilities, they pose privacy risks by unintentionally memorizing sensitive personal information. Current unlearning benchmarks attempt to mitigate this using fictitious identities but overlook a critical stage 1 failure: models fail to effectively memorize target information initially, rendering subsequent unlearning evaluations unreliable. Diagnosing under-memorization and the multi-hop curse as root causes, we introduce ReMem, a Reliable Multi-hop and Multi-image Memorization Benchmark. ReMem ensures robust foundational learning through principled data scaling, reasoning-aware QA pairs, and diverse visual contexts. Additionally, we propose a novel Exposure metric to quantify the depth of information erasure from the model's internal probability distribution. Extensive experiments demonstrate that ReMem provides a rigorous and trustworthy framework for diagnosing both learning and unlearning behaviors in LVLMs.

Large Language Models (LLMs) often memorize sensitive or harmful information, necessitating effective machine unlearning techniques. While existing parameter-efficient unlearning methods have shown promise, they still struggle with the forget-retain trade-off. This can be attributed to their reliance on parameter importance metrics to identify parameters that are important exclusively for the forget set, which is fundamentally limited by the superposition phenomenon. Due to the polysemantic nature of LLM parameters, such an importance metric may struggle to disentangle parameters associated with the forget and retain sets. In this work, we propose Representation-Guided Low-rank Unlearning (REGLU), a novel approach that leverages the geometric properties of representation spaces to achieve robust and precise unlearning. First, we develop a representation-guided initialization for LoRA that identifies the optimal subspace for selective forgetting. Second, we introduce a regularization loss that constrains the outputs of the LoRA update to lie in the orthogonal complement of the retain set's representation subspace, thereby minimizing interference with the model's performance on the retain set. We evaluate REGLU on the TOFU and WMDP benchmarks across multiple models. Our results demonstrate that REGLU consistently outperforms state-of-the-art baselines, achieving superior unlearning quality while maintaining higher model utility.

Continual Test-Time Adaptation (CTTA) aims to adapt a pretrained model to ever-changing environments during the test time under continuous domain shifts. Most existing CTTA approaches are based on the Mean Teacher (MT) structure, which contains a student and a teacher model, where the student is updated using the pseudo-labels from the teacher model, and the teacher is then updated by exponential moving average strategy. However, these methods update the MT model indiscriminately on all parameters of the model. That is, some critical parameters involving sharing knowledge across different domains may be erased, intensifying error accumulation and catastrophic forgetting. In this paper, we introduce Parameter-Selective Mean Teacher (PSMT) method, which is capable of effectively updating the critical parameters within the MT network under domain shifts. First, we introduce a selective distillation mechanism in the student model, which utilizes past knowledge to regularize novel knowledge, thereby mitigating the impact of error accumulation. Second, to avoid catastrophic forgetting, in the teacher model, we create a mask through Fisher information to selectively update parameters via exponential moving average, with preservation measures applied to crucial parameters. Extensive experimental results verify that PSMT outperforms state-of-the-art methods across multiple benchmark datasets. Our code is available at https://github.com/JiaxuTian/PSMT.

LoRA-based continual learning methods mitigate catastrophic forgetting through various mechanisms, yet nearly all complement these with small learning rates as a heuristic to restrict gradient scaling magnitude. Such fixed heuristics lack theoretical guidance on how the strength of this restriction should evolve as tasks accumulate. We reveal that even under directional constraints such as nullspace projection, finite-precision updates inevitably leak into the subspace of accumulated prior knowledge along multiple directions. While small learning rates attenuate such leakage, they cannot prevent the accumulated forgetting from intensifying as the effective rank of historical knowledge grows. We show that the optimal magnitude restriction should adaptively increase with this effective rank to balance stability and plasticity, i.e., preservation of previous knowledge and acquisition of new task information. Under an anisotropic leakage model, we derive a pacing law s^*=R/c that characterizes the optimal scaling of gradient steps, i.e., the magnitude restriction itself, where R is the effective rank of past updates. Based on this insight, we propose PaLoRA, which compresses historical knowledge via adaptive SVD truncation, projects gradients onto the nullspace of prior tasks, and applies rank-aware adaptive pacing. Experiments demonstrate consistent improvements over prior methods, with particularly strong performance in long-horizon settings, achieving substantial gains of 4% accuracy on challenging 50-task ImageNet-A and ImageNet-R benchmarks.

The rehearsal strategy is widely used to alleviate the catastrophic forgetting problem in class incremental learning (CIL) by preserving limited exemplars from previous tasks. With imbalanced sample numbers between old and new classes, the classifier learning can be biased. Existing CIL methods exploit the long-tailed (LT) recognition techniques, e.g., the adjusted losses and the data re-sampling methods, to handle the data imbalance issue within each increment task. In this work, the dynamic nature of data imbalance in CIL is shown and a novel Dynamic Residual Classifier (DRC) is proposed to handle this challenging scenario. Specifically, DRC is built upon a recent advance residual classifier with the branch layer merging to handle the model-growing problem. Moreover, DRC is compatible with different CIL pipelines and substantially improves them. Combining DRC with the model adaptation and fusion (MAF) pipeline, this method achieves state-of-the-art results on both the conventional CIL and the LT-CIL benchmarks. Extensive experiments are also conducted for a detailed analysis. The code is publicly available.

The development of state-of-the-art systems in different applied areas of machine learning (ML) is driven by benchmarks, which have shaped the paradigm of evaluating generalisation capabilities from multiple perspectives. Although the paradigm is shifting towards more fine-grained evaluation across diverse tasks, the delicate question of how to aggregate the performances has received particular interest in the community. In general, benchmarks follow the unspoken utilitarian principles, where the systems are ranked based on their mean average score over task-specific metrics. Such aggregation procedure has been viewed as a sub-optimal evaluation protocol, which may have created the illusion of progress. This paper proposes Vote'n'Rank, a framework for ranking systems in multi-task benchmarks under the principles of the social choice theory. We demonstrate that our approach can be efficiently utilised to draw new insights on benchmarking in several ML sub-fields and identify the best-performing systems in research and development case studies. The Vote'n'Rank's procedures are more robust than the mean average while being able to handle missing performance scores and determine conditions under which the system becomes the winner.

Iterative self-training (self-distillation) repeatedly refits a model on pseudo-labels generated by its own predictions. We study this procedure in overparameterized linear regression: an initial estimator is trained on noisy labels, and each subsequent iterate is trained on fresh covariates with noiseless pseudo-labels from the previous model. In the high-dimensional regime, we derive deterministic-equivalent recursions for the prediction risk and effective noise across iterations, and prove that the empirical quantities concentrate sharply around these limits. The recursion separates two competing forces: a systematic component that grows with iteration due to progressive signal forgetting, and a stochastic component that decays due to denoising via repeated data-dependent projections. Their interaction yields a U-shaped test-risk curve and an optimal early-stopping time. In spiked covariance models, iteration further acts as an iteration-dependent spectral filter that preserves strong eigendirections while suppressing weaker ones, inducing an implicit form of soft feature selection distinct from ridge regression. Finally, we propose an iterated generalized cross-validation criterion and prove its uniform consistency for estimating the risk along the self-training trajectory, enabling fully data-driven selection of the stopping time and regularization. Experiments on synthetic covariances validate the theory and illustrate the predicted denoising-forgetting trade-off.

Machine unlearning aims to remove the influence of specific training data from a model without requiring full retraining. This capability is crucial for ensuring privacy, safety, and regulatory compliance. Therefore, verifying whether a model has truly forgotten target data is essential for maintaining reliability and trustworthiness. However, existing evaluation methods often assess forgetting at the level of individual inputs. This approach may overlook residual influence present in semantically similar examples. Such influence can compromise privacy and lead to indirect information leakage. We propose REMIND (Residual Memorization In Neighborhood Dynamics), a novel evaluation method aiming to detect the subtle remaining influence of unlearned data and classify whether the data has been effectively forgotten. REMIND analyzes the model's loss over small input variations and reveals patterns unnoticed by single-point evaluations. We show that unlearned data yield flatter, less steep loss landscapes, while retained or unrelated data exhibit sharper, more volatile patterns. REMIND requires only query-based access, outperforms existing methods under similar constraints, and demonstrates robustness across different models, datasets, and paraphrased inputs, making it practical for real-world deployment. By providing a more sensitive and interpretable measure of unlearning effectiveness, REMIND provides a reliable framework to assess unlearning in language models. As a result, REMIND offers a novel perspective on memorization and unlearning.

Continual learning treats degradation on previously seen data as evidence of failure, a convention inherited from settings with a stationary prediction target, where a correct label remains correct indefinitely. World models do not satisfy this condition. Their prediction target is the environment, which changes, so knowledge that was accurate when acquired may later become false, and discarding it is required behavior rather than a defect. Non-stationary ground truth is well studied in the concept drift literature and in the temporal factuality of language models, but has not been formulated for world models, which are distinctive in that they also encode knowledge that must never be revised. We argue that continual world models require retention stratified by invariance timescale, separating invariants such as physics and object permanence, which must never be revised, from instance-level facts that should be revised as soon as the environment changes. Standard forgetting metrics cannot distinguish a world model that has correctly revised outdated knowledge from one that has suffered catastrophic forgetting, and consequently rank a frozen model highest, while existing physical-reasoning benchmarks evaluate only frozen checkpoints. We propose differential retention, which reports invariant regression testing across the adaptation stream jointly with revision latency, without aggregation.

With privacy legislation empowering the users with the right to be forgotten, it has become essential to make a model amenable for forgetting some of its training data. However, existing unlearning methods in the machine learning context can not be directly applied in the context of distributed settings like federated learning due to the differences in learning protocol and the presence of multiple actors. In this paper, we tackle the problem of federated unlearning for the case of erasing a client by removing the influence of their entire local data from the trained global model. To erase a client, we propose to first perform local unlearning at the client to be erased, and then use the locally unlearned model as the initialization to run very few rounds of federated learning between the server and the remaining clients to obtain the unlearned global model. We empirically evaluate our unlearning method by employing multiple performance measures on three datasets, and demonstrate that our unlearning method achieves comparable performance as the gold standard unlearning method of federated retraining from scratch, while being significantly efficient. Unlike prior works, our unlearning method neither requires global access to the data used for training nor the history of the parameter updates to be stored by the server or any of the clients.

Large language models (LLMs) demonstrate impressive capabilities across diverse tasks but raise concerns about privacy, copyright, and harmful materials. Existing LLM unlearning methods rarely consider the continual and high-volume nature of real-world deletion requests, which can cause utility degradation and catastrophic forgetting as requests accumulate. To address this challenge, we introduce \fit, a framework for continual unlearning that handles large numbers of deletion requests while maintaining robustness against both catastrophic forgetting and post-unlearning recovery. \fit mitigates degradation through rigorous data Filtering, Importance-aware updates, and Targeted layer attribution, enabling stable performance across long sequences of unlearning operations and achieving a favorable balance between forgetting effectiveness and utility retention. To support realistic evaluation, we present PCH, a benchmark covering Personal information, Copyright, and Harmful content in sequential deletion scenarios, along with two symmetric metrics, Forget Degree (F.D.) and Retain Utility (R.U.), which jointly assess forgetting quality and utility preservation. Extensive experiments on four open-source LLMs with hundreds of deletion requests show that \fit achieves the strongest trade-off between F.D. and R.U., surpasses existing methods on MMLU, CommonsenseQA, and GSM8K, and remains resistant against both relearning and quantization recovery attacks.

A ranker plays an indispensable role in the de facto 'retrieval & rerank' pipeline, but its training still lags behind -- learning from moderate negatives or/and serving as an auxiliary module for a retriever. In this work, we first identify two major barriers to a robust ranker, i.e., inherent label noises caused by a well-trained retriever and non-ideal negatives sampled for a high-capable ranker. Thereby, we propose multiple retrievers as negative generators improve the ranker's robustness, where i) involving extensive out-of-distribution label noises renders the ranker against each noise distribution, and ii) diverse hard negatives from a joint distribution are relatively close to the ranker's negative distribution, leading to more challenging thus effective training. To evaluate our robust ranker (dubbed R^2anker), we conduct experiments in various settings on the popular passage retrieval benchmark, including BM25-reranking, full-ranking, retriever distillation, etc. The empirical results verify the new state-of-the-art effectiveness of our model.

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 unlearning performance of OPC arises from the deep feature forgetting enforced by its theoretical foundation, and recaps the need for improved robustness of machine unlearning methods.

The trustworthy machine learning (ML) community is increasingly recognizing the crucial need for models capable of selectively 'unlearning' data points after training. This leads to the problem of machine unlearning (MU), aiming to eliminate the influence of chosen data points on model performance, while still maintaining the model's utility post-unlearning. Despite various MU methods for data influence erasure, evaluations have largely focused on random data forgetting, ignoring the vital inquiry into which subset should be chosen to truly gauge the authenticity of unlearning performance. To tackle this issue, we introduce a new evaluative angle for MU from an adversarial viewpoint. We propose identifying the data subset that presents the most significant challenge for influence erasure, i.e., pinpointing the worst-case forget set. Utilizing a bi-level optimization principle, we amplify unlearning challenges at the upper optimization level to emulate worst-case scenarios, while simultaneously engaging in standard training and unlearning at the lower level, achieving a balance between data influence erasure and model utility. Our proposal offers a worst-case evaluation of MU's resilience and effectiveness. Through extensive experiments across different datasets (including CIFAR-10, 100, CelebA, Tiny ImageNet, and ImageNet) and models (including both image classifiers and generative models), we expose critical pros and cons in existing (approximate) unlearning strategies. Our results illuminate the complex challenges of MU in practice, guiding the future development of more accurate and robust unlearning algorithms. The code is available at https://github.com/OPTML-Group/Unlearn-WorstCase.

We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison counts have traditionally been used to gauge efficiency, our analysis reveals that expensive LLM inferences overturn these predictions; accordingly, our framework encourages strategies such as batching and caching to mitigate inference costs. We show that algorithms optimal in the classical setting can lose efficiency when LLM inferences dominate the cost under certain optimizations.

Online continual learning aims to continuously train neural networks from a continuous data stream with a single pass-through data. As the most effective approach, the rehearsal-based methods replay part of previous data. Commonly used predictors in existing methods tend to generate biased dot-product logits that prefer to the classes of current data, which is known as a bias issue and a phenomenon of forgetting. Many approaches have been proposed to overcome the forgetting problem by correcting the bias; however, they still need to be improved in online fashion. In this paper, we try to address the bias issue by a more straightforward and more efficient method. By decomposing the dot-product logits into an angle factor and a norm factor, we empirically find that the bias problem mainly occurs in the angle factor, which can be used to learn novel knowledge as cosine logits. On the contrary, the norm factor abandoned by existing methods helps remember historical knowledge. Based on this observation, we intuitively propose to leverage the norm factor to balance the new and old knowledge for addressing the bias. To this end, we develop a heuristic approach called unbias experience replay (UER). UER learns current samples only by the angle factor and further replays previous samples by both the norm and angle factors. Extensive experiments on three datasets show that UER achieves superior performance over various state-of-the-art methods. The code is in https://github.com/FelixHuiweiLin/UER.

Analytic continual learning has emerged as a strong exemplar-free alternative to gradient-based class-incremental learning because it replaces iterative optimization with closed-form ridge updates. Yet the usual forgetting narrative, centered on stochastic gradient overwriting, does not explain why analytic methods still drift on old classes despite exact recursive solvers. We identify the culprit as spectral interference: the joint ridge classifier for all tasks shares the inverse autocorrelation operator (R+λI)^{-1}, so incoming task samples that load onto old dominant eigendirections dilute the spectrum and perturb old-class logits even when old labels are never revisited. Based on this view, we propose SPARCL, a spectral partitioned analytic continual learner that decomposes the running autocorrelation into a high-energy core and a residual complement, freezes old-class classifier components in the core subspace, and updates only the residual block through recursive least squares with an optional residual random-projection expansion. This yields a simple closed-form update with a provable invariance guarantee for the core contribution of old logits. Across CIFAR-100, CUB-200, ImageNet-R, and ImageNet-A under a frozen ViT-B/16 protocol, SPARCL closes most of the gap from classical analytic learners to strong representation matchers, while remaining complementary to sparse feature-decorrelation approaches such as Fly-CL.

Unlearning concerns the task of removing the influence of a sensitive portion of the training data, such as protected, copyrighted or private text, from a model without retraining it from scratch. While unlearning requests happen continuously during a model's lifetime, the vast majority of LLM unlearning methods are ill-suited for iterated removal, yielding steep decay in forgetting and utility upon sequential unlearning. This decay stems from interference between successive updates, as each new deletion can undo earlier ones or push the model further along directions already degraded by them. To address this, we introduce Continual Orthogonal Projection (COP), a gradient-projection scheme that restricts each update to the orthogonal complement of activation subspaces cached from prior forget sets. This approach provably guarantees first-order non-interference with earlier deletions. COP stores only a low-rank basis per layer, requiring neither past gradients nor previous forget sets, and plugs into unlearning methods that update the model through gradient steps on a differentiable loss without modifying its objective. Experiments on standard LLM unlearning benchmarks (TOFU and RWKU) show that COP preserves utility across sequential requests without weakening forgetting, preventing the collapse of standard objectives and forgetting more effectively than continual-specific baselines.

As pretrained models are increasingly shared on the web, ensuring that models can forget or delete sensitive, copyrighted, or private information upon request has become crucial. Machine unlearning has been proposed to address this challenge. However, current evaluations for unlearning methods rely on output-based metrics, which cannot verify whether information is completely deleted or merely suppressed at the representation level, where suppression is insufficient for true unlearning. To address this gap, we propose a novel restoration-based analysis framework that uses Sparse Autoencoders to identify class-specific expert features in intermediate layers and applies inference-time steering to quantitatively distinguish between suppression and deletion. Applying our framework to 12 major unlearning methods in image classification tasks, we find that most methods achieve high restoration rates of unlearned information, indicating that they only suppress information at the decision-boundary level, while preserving semantic features in intermediate representations. Notably, even retraining from pretrained checkpoints shows high restoration, revealing that robust semantic features inherited from pretraining are not removed by retraining. These results demonstrate that representation-level retention poses significant risks overlooked by output-based metrics, highlighting the need for new unlearning evaluation criteria. We propose new evaluation guidelines that prioritize representation-level verification, especially for privacy-critical applications in the era of pre-trained models.

Although Large Language Models (LLMs) have demonstrated impressive capabilities across a wide range of tasks, growing concerns have emerged over the misuse of sensitive, copyrighted, or harmful data during training. 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. Extensive experiments validate the effectiveness of both SA and SU.

Machine unlearning has emerged as a new paradigm to deliberately forget data samples from a given model in order to adhere to stringent regulations. However, existing machine unlearning methods have been primarily focused on classification models, leaving the landscape of unlearning for generative models relatively unexplored. This paper serves as a bridge, addressing the gap by providing a unifying framework of machine unlearning for image-to-image generative models. Within this framework, we propose a computationally-efficient algorithm, underpinned by rigorous theoretical analysis, that demonstrates negligible performance degradation on the retain samples, while effectively removing the information from the forget samples. Empirical studies on two large-scale datasets, ImageNet-1K and Places-365, further show that our algorithm does not rely on the availability of the retain samples, which further complies with data retention policy. To our best knowledge, this work is the first that represents systemic, theoretical, empirical explorations of machine unlearning specifically tailored for image-to-image generative models. Our code is available at https://github.com/jpmorganchase/l2l-generator-unlearning.

A conventional LLM Unlearning setting consists of two subsets -"forget" and "retain", with the objectives of removing the undesired knowledge from the forget set while preserving the remaining knowledge from the retain. In privacy-focused unlearning research, a retain set is often further divided into neighbor sets, containing either directly or indirectly connected to the forget targets; and augmented by a general-knowledge set. A common practice in existing benchmarks is to employ only a single neighbor set, with general knowledge which fails to reflect the real-world data complexities and relationships. LLM Unlearning typically involves 1:1 sampling or cyclic iteration sampling. However, the efficacy and stability of these de facto standards have not been critically examined. In this study, we systematically evaluate these common practices. Our findings reveal that relying on a single neighbor set is suboptimal and that a standard sampling approach can obscure performance trade-offs. Based on this analysis, we propose and validate an initial set of best practices: (1) Incorporation of diverse neighbor sets to balance forget efficacy and model utility, (2) Standard 1:1 sampling methods are inefficient and yield poor results, (3) Our proposed Modular Entity-Level Unlearning (MELU) strategy as an alternative to cyclic sampling. We demonstrate that this modular approach, combined with robust algorithms, provides a clear and stable path towards effective unlearning.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data during its entire lifetime. Although major advances have been made in the field, one recurring problem which remains unsolved is that of Catastrophic Forgetting (CF). While the issue has been extensively studied empirically, little attention has been paid from a theoretical angle. In this paper, we show that the impact of CF increases as two tasks increasingly align. We introduce a measure of task similarity called the NTK overlap matrix which is at the core of CF. We analyze common projected gradient algorithms and demonstrate how they mitigate forgetting. Then, we propose a variant of Orthogonal Gradient Descent (OGD) which leverages structure of the data through Principal Component Analysis (PCA). Experiments support our theoretical findings and show how our method can help reduce CF on classical CL datasets.

Large Language Model (LLM) unlearning is often evaluated primarily by target suppression and clean retain utility. These metrics can miss a local failure mode: a model may perform well on standard retain prompts, yet degrade on benign reasoning when prompts lie near the forgotten domain. This phenomenon is termed forget-adjacent utility loss. A fundamental question is: where should forget representations go after they leave the removed behavior? Successful unlearning depends not only on whether forget-conditioned representations depart from the harmful computation, but also on the direction in which they are redirected afterward. We propose RA^2 (Retain-Anchored Attraction), a latent-space unlearning method that redirects forget-token states toward nearby retain-supported representations while preserving higher-layer behavior on retain data. On WMDP and MUSE, RA^2 yields higher forget-adjacent utility than strong unlearning baselines at similar broad-utility levels. These results show that the migration direction of forget representations materially affects benign behavior near the forget boundary. Our code is available at https://github.com/ZacLing/retain_anchored_attraction.

Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of continual learning in a tractable yet representative setting. Specifically, we analyze one-hidden-layer quadratic neural networks trained by gradient descent on a sequence of XOR-cluster datasets with Gaussian noise, where different tasks correspond to clusters with orthogonal means. Our analysis is based on a tight characterization of gradient descent dynamics for the training loss, which yields explicit bounds on the rate of train-time forgetting as functions of the number of iterations, sample size, number of tasks, and hidden-layer width. We then leverage an algorithmic stability framework to bound the generalization gap, leading to corresponding guarantees on test-time forgetting. Together, our results provide the first closed-form guarantees for forgetting in continual learning with neural networks and show how key problem parameters jointly govern forgetting dynamics. Numerical experiments corroborate our theoretical results.

Recently, we have witnessed the bloom of neural ranking models in the information retrieval (IR) field. So far, much effort has been devoted to developing effective neural ranking models that can generalize well on new data. There has been less attention paid to the robustness perspective. Unlike the effectiveness which is about the average performance of a system under normal purpose, robustness cares more about the system performance in the worst case or under malicious operations instead. When a new technique enters into the real-world application, it is critical to know not only how it works in average, but also how would it behave in abnormal situations. So we raise the question in this work: Are neural ranking models robust? To answer this question, firstly, we need to clarify what we refer to when we talk about the robustness of ranking models in IR. We show that robustness is actually a multi-dimensional concept and there are three ways to define it in IR: 1) The performance variance under the independent and identically distributed (I.I.D.) setting; 2) The out-of-distribution (OOD) generalizability; and 3) The defensive ability against adversarial operations. The latter two definitions can be further specified into two different perspectives respectively, leading to 5 robustness tasks in total. Based on this taxonomy, we build corresponding benchmark datasets, design empirical experiments, and systematically analyze the robustness of several representative neural ranking models against traditional probabilistic ranking models and learning-to-rank (LTR) models. The empirical results show that there is no simple answer to our question. While neural ranking models are less robust against other IR models in most cases, some of them can still win 1 out of 5 tasks. This is the first comprehensive study on the robustness of neural ranking models.

We study and quantify the problem of forgetting when fine-tuning pre-trained large language models (LLMs) on a downstream task. We find that parameter-efficient fine-tuning (PEFT) strategies, such as Low-Rank Adapters (LoRA), still suffer from catastrophic forgetting. In particular, we identify a strong inverse linear relationship between the fine-tuning performance and the amount of forgetting when fine-tuning LLMs with LoRA. We further obtain precise scaling laws that show forgetting increases as a shifted power law in the number of parameters fine-tuned and the number of update steps. We also examine the impact of forgetting on knowledge, reasoning, and the safety guardrails trained into Llama 2 7B chat. Our study suggests that forgetting cannot be avoided through early stopping or by varying the number of parameters fine-tuned. We believe this opens up an important safety-critical direction for future research to evaluate and develop fine-tuning schemes which mitigate forgetting

Machine Unlearning (MU) aims to remove target training data from a trained model so that the removed data no longer influences the model's behavior, fulfilling "right to be forgotten" obligations under data privacy laws. Yet, we observe that researchers in this rapidly emerging field face challenges in analyzing and understanding the behavior of different MU methods, especially in terms of three fundamental principles in MU: accuracy, efficiency, and privacy. Consequently, they often rely on aggregate metrics and ad-hoc evaluations, making it difficult to accurately assess the trade-offs between methods. To fill this gap, we introduce a visual analytics system, Unlearning Comparator, designed to facilitate the systematic evaluation of MU methods. Our system supports two important tasks in the evaluation process: model comparison and attack simulation. First, it allows the user to compare the behaviors of two models, such as a model generated by a certain method and a retrained baseline, at class-, instance-, and layer-levels to better understand the changes made after unlearning. Second, our system simulates membership inference attacks (MIAs) to evaluate the privacy of a method, where an attacker attempts to determine whether specific data samples were part of the original training set. We evaluate our system through a case study visually analyzing prominent MU methods and demonstrate that it helps the user not only understand model behaviors but also gain insights that can inform the improvement of MU methods.

Large language models trained on web-scale corpora can memorize undesirable data containing misinformation, copyrighted material, or private or sensitive information. Recently, several machine unlearning algorithms have been proposed to eliminate the effect of such datapoints from trained models -- that is, to approximate a model that had never been trained on these datapoints in the first place. However, evaluating the effectiveness of unlearning algorithms remains an open challenge. Previous work has relied on heuristics -- such as verifying that the model can no longer reproduce the specific information targeted for removal while maintaining accuracy on unrelated test data. These approaches inadequately capture the complete effect of reversing the influence of datapoints on a trained model. In this work, we propose the RESTOR framework for machine unlearning evaluation, which assesses the ability of unlearning algorithms for targeted data erasure, by evaluating the ability of models to forget the knowledge introduced in these datapoints, while simultaneously recovering the model's knowledge state had it never encountered these datapoints. RESTOR helps uncover several novel insights about popular unlearning algorithms, and the mechanisms through which they operate -- for instance, identifying that some algorithms merely emphasize forgetting but not recovering knowledge, and that localizing unlearning targets can enhance unlearning performance.

Large Reasoning Models (LRMs) generate structured chains of thought (CoTs) before producing final answers, making them especially vulnerable to knowledge leakage through intermediate reasoning steps. Yet, the memorization of sensitive information in the training data such as copyrighted and private content has led to ethical and legal concerns. To address these issues, selective forgetting (also known as machine unlearning) has emerged as a potential remedy for LRMs. However, existing unlearning methods primarily target final answers and may degrade the overall reasoning ability of LRMs after forgetting. Additionally, directly applying unlearning on the entire CoTs could degrade the general reasoning capabilities. The key challenge for LRM unlearning lies in achieving precise unlearning of targeted knowledge while preserving the integrity of general reasoning capabilities. To bridge this gap, we in this paper propose a novel LRM unlearning framework that selectively removes sensitive reasoning components while preserving general reasoning capabilities. Our approach leverages multiple LLMs with retrieval-augmented generation (RAG) to analyze CoT traces, identify forget-relevant segments, and replace them with benign placeholders that maintain logical structure. We also introduce a new feature replacement unlearning loss for LRMs, which can simultaneously suppress the probability of generating forgotten content while reinforcing structurally valid replacements. Extensive experiments on both synthetic and medical datasets verify the desired properties of our proposed method.

We address the challenge of adapting pre-trained Large Language Models (LLMs) for multivariate time-series analysis, where their deployment is often hindered by prohibitive computational and memory demands. Our solution, One-for-All, introduces Gaussian Rank-Stabilized Low-Rank Adapters (rsLoRA) to enable parameter-efficient fine-tuning of frozen LLMs. While inspired by LoRA, rsLoRA introduces a mathematically grounded rank-stabilization mechanism that enables provable gradient stability at low ranks a novel contribution absent in prior PEFT methods. Our framework injects trainable rank decomposition matrices (rank 16) into positional embeddings and output layers, while keeping self-attention weights fixed. This design reduces trainable parameters by 6.8times (vs. TimesNet), 21times (vs. GPT4TS), and 11.8times (vs. TIME-LLM), while achieving a 168-1,776times smaller memory footprint (2.2MiB vs. 340MiB-4.18GiB in SOTA models). Rigorous evaluation across six time-series tasks demonstrates that One-for-All achieves state-of-the-art efficiency-accuracy trade-offs: 5.5times higher parameter efficiency (MSE=5.50) than TimesNet and 21times better than GPT4TS, while matching their forecasting accuracy (MSE=0.33). The framework's stability is validated through consistent performance across diverse horizons (96-720 steps) and datasets (ETT, Weather, M3, M4), with 98.3% fewer parameters than conventional transformers. These advances enable deployment on edge devices for healthcare, finance, and environmental monitoring without compromising performance.

We consider representation misdirection (RM), a class of LLM unlearning methods that achieves forgetting by manipulating the forget-representations, that is, latent representations of forget samples. Despite being important, the roles of target vectors used in RM, however, remain underexplored. Here, we approach and revisit RM through the lens of the linear representation hypothesis. Specifically, if one can somehow identify a one-dimensional representation corresponding to a high-level concept, the linear representation hypothesis enables linear operations on this concept vector within the forget-representation space. Under this view, we hypothesize that, beyond forgetting, machine unlearning elicits controllable side behaviors and stronger side capabilities corresponding to the high-level concept. Our hypothesis is empirically validated across a wide range of tasks, including behavioral control (e.g., controlling unlearned models' truth, sentiment, and refusal) and capability enhancement (e.g., improving unlearned models' in-context learning capability). Our findings reveal that this fairly attractive phenomenon could be either a hidden risk if misused or a mechanism that can be harnessed for developing models that require stronger capabilities and controllable behaviors.

Model-based reinforcement-learning agents of the DreamerV3 family forget catastrophically when trained on task sequences, even when an unbounded replay buffer preserves every earlier experience. We ask a question the continual-RL literature has assumed an answer to but never measured: which component forgets? Under never-clear replay, pre-registered component-level probes (n=3 seeds throughout) show that the world model retains essentially everything measurable about old tasks -- reward discrimination (retention ratio ~1.0), value estimates, and termination structure -- while the actor's behavior collapses. Forgetting in this regime is a channel problem, not a memory problem. We demonstrate this by intervention: with the world model frozen and identical imagined rollouts, reinforcement learning in imagination fails to recover a lost skill (0/3 seeds), while supervised self-imitation on the world model's own graded dreams recovers it on 3/3 seeds with zero environment interaction. Interleaved during training, this graded dream rehearsal yields a task-label-free, parameter-constant continual learner: 3/3 four-task chains retained where plain replay passes 0/3, 3/3 eight-task chains, and consistent gains over matched real-episode cloning (paired difference +0.13, bootstrap 95% CI [0.07, 0.24], complete seed separation). The dream-grading step is load-bearing: we characterize two scoring failure modes, provide an offline selection gauge that caught both before they contaminated results, and give a realized-first grading rule that closes them. All experiments were pre-registered with committed protocols; every refuted hypothesis is reported.

As the Large Language Model (LLM) gains widespread adoption, increasing attention has been given to the challenge of making LLM forget non-compliant data memorized during its pre-training. Machine Unlearning focuses on efficiently erasing sensitive information from LLM under limited computational resources. To advance research in this area, SemEval 2025 Task 4: "Unlearning Sensitive Content from Large Language Models" introduces three unlearning datasets and establishes a benchmark by evaluating both forgetting effectiveness and the preservation of standard capabilities. In this work, we propose a more controllable forgetting loss, Effective Unlearning Loss, and explore its integration with various techniques to achieve more efficient and controlled unlearning. Our system ultimately ranked 5th on the competition leaderboard.

Large language models (LLMs) inevitably memorize sensitive, copyrighted, and harmful knowledge from the training corpus; therefore, it is crucial to erase this knowledge from the models. Machine unlearning is a promising solution for efficiently removing specific knowledge by post hoc modifying models. In this paper, we propose a Real-World Knowledge Unlearning benchmark (RWKU) for LLM unlearning. RWKU is designed based on the following three key factors: (1) For the task setting, we consider a more practical and challenging unlearning setting, where neither the forget corpus nor the retain corpus is accessible. (2) For the knowledge source, we choose 200 real-world famous people as the unlearning targets and show that such popular knowledge is widely present in various LLMs. (3) For the evaluation framework, we design the forget set and the retain set to evaluate the model's capabilities across various real-world applications. Regarding the forget set, we provide four four membership inference attack (MIA) methods and nine kinds of adversarial attack probes to rigorously test unlearning efficacy. Regarding the retain set, we assess locality and utility in terms of neighbor perturbation, general ability, reasoning ability, truthfulness, factuality, and fluency. We conduct extensive experiments across two unlearning scenarios, two models and six baseline methods and obtain some meaningful findings. We release our benchmark and code publicly at http://rwku-bench.github.io for future work.

Large language models (LLMs) sometimes memorize undesirable knowledge, which must be removed after deployment. Prior work on machine unlearning has focused largely on optimization methods that adjust parameters to enforce forgetting while preserving retention. However, these approaches assume that the forget and retain sets are readily available, which rarely holds in practice. Unlearning is typically triggered by an undesired generation at inference time, making the retrieval of relevant data the central challenge. We introduce the notion of data Pareto improvement for LLM unlearning, which formalizes how retrieval can expand the achievable trade-off frontier between forgetting and retention. To realize this principle, we propose Randomized Antipodal Search on Linearized Influence Kernel (RASLIK), a retrieval algorithm that combines permutation-projection hashing with randomized antipodal search. RASLIK reduces selection variance, achieves sublinear complexity, and yields a double gain in both quality and efficiency. Across multiple models, datasets, and unlearning algorithms, RASLIK consistently outperforms deterministic baselines and even oracle sampling, establishing randomized search as a principled and scalable solution for data-centric unlearning.

A collection of robust Mahalanobis distances for multivariate outlier detection is proposed, based on the notion of shrinkage. Robust intensity and scaling factors are optimally estimated to define the shrinkage. Some properties are investigated, such as affine equivariance and breakdown value. The performance of the proposal is illustrated through the comparison to other techniques from the literature, in a simulation study and with a real dataset. The behavior when the underlying distribution is heavy-tailed or skewed, shows the appropriateness of the method when we deviate from the common assumption of normality. The resulting high correct detection rates and low false detection rates in the vast majority of cases, as well as the significantly smaller computation time shows the advantages of our proposal.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

Machine unlearning for LLMs aims to remove sensitive or copyrighted data from trained models. However, the true efficacy of current unlearning methods remains uncertain. Standard evaluation metrics rely on benign queries that often mistake superficial information suppression for genuine knowledge removal. Such metrics fail to detect residual knowledge that more sophisticated prompting strategies could still extract. We introduce REBEL, an evolutionary approach for adversarial prompt generation designed to probe whether unlearned data can still be recovered. Our experiments demonstrate that REBEL successfully elicits ``forgotten'' knowledge from models that seemed to be forgotten in standard unlearning benchmarks, revealing that current unlearning methods may provide only a superficial layer of protection. We validate our framework on subsets of the TOFU and WMDP benchmarks, evaluating performance across a diverse suite of unlearning algorithms. Our experiments show that REBEL consistently outperforms static baselines, recovering ``forgotten'' knowledge with Attack Success Rates (ASRs) reaching up to 60% on TOFU and 93% on WMDP. We will make all code publicly available upon acceptance. Code is available at https://github.com/patryk-rybak/REBEL/

We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random weights. We consider the asymptotic limit where the input dimension and the network width are proportionally large. Recent work [Cui & al '23] established that linear regression provides Bayes-optimal test error to learn such a function when the number of available samples is only linear in the dimension. That work stressed the open challenge of theoretically analyzing the optimal test error in the more interesting regime where the number of samples is quadratic in the dimension. In this paper, we solve this challenge for quadratic activations and derive a closed-form expression for the Bayes-optimal test error. We also provide an algorithm, that we call GAMP-RIE, which combines approximate message passing with rotationally invariant matrix denoising, and that asymptotically achieves the optimal performance. Technically, our result is enabled by establishing a link with recent works on optimal denoising of extensive-rank matrices and on the ellipsoid fitting problem. We further show empirically that, in the absence of noise, randomly-initialized gradient descent seems to sample the space of weights, leading to zero training loss, and averaging over initialization leads to a test error equal to the Bayes-optimal one.

For privacy and security concerns, the need to erase unwanted information from pre-trained vision models is becoming evident nowadays. In real-world scenarios, erasure requests originate at any time from both users and model owners, and these requests usually form a sequence. Therefore, under such a setting, selective information is expected to be continuously removed from a pre-trained model while maintaining the rest. We define this problem as continual forgetting and identify three key challenges. (i) For unwanted knowledge, efficient and effective deleting is crucial. (ii) For remaining knowledge, the impact brought by the forgetting procedure should be minimal. (iii) In real-world scenarios, the training samples may be scarce or partially missing during the process of forgetting. To address them, we first propose Group Sparse LoRA (GS-LoRA). Specifically, towards (i), we introduce LoRA modules to fine-tune the FFN layers in Transformer blocks for each forgetting task independently, and towards (ii), a simple group sparse regularization is adopted, enabling automatic selection of specific LoRA groups and zeroing out the others. To further extend GS-LoRA to more practical scenarios, we incorporate prototype information as additional supervision and introduce a more practical approach, GS-LoRA++. For each forgotten class, we move the logits away from its original prototype. For the remaining classes, we pull the logits closer to their respective prototypes. We conduct extensive experiments on face recognition, object detection and image classification and demonstrate that our method manages to forget specific classes with minimal impact on other classes. Codes have been released on https://github.com/bjzhb666/GS-LoRA.

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest situations, are no exception and the demand for appropriate concepts and tools is all the more pressing given that technologies fed by or producing this type of data (e.g. search engines, recommending systems) are now massively deployed. However, the lack of vector space structure for the set of rankings (i.e. the symmetric group S_n) and the complex nature of statistics considered in ranking data analysis make the formulation of robustness objectives in this domain challenging. In this paper, we introduce notions of robustness, together with dedicated statistical methods, for Consensus Ranking the flagship problem in ranking data analysis, aiming at summarizing a probability distribution on S_n by a median ranking. Precisely, we propose specific extensions of the popular concept of breakdown point, tailored to consensus ranking, and address the related computational issues. Beyond the theoretical contributions, the relevance of the approach proposed is supported by an experimental study.

Deep neural networks are susceptible to adversarial attacks, which can compromise their performance and accuracy. Adversarial Training (AT) has emerged as a popular approach for protecting neural networks against such attacks. However, a key challenge of AT is robust overfitting, where the network's robust performance on test data deteriorates with further training, thus hindering generalization. Motivated by the concept of active forgetting in the brain, we introduce a novel learning paradigm called "Forget to Mitigate Overfitting (FOMO)". FOMO alternates between the forgetting phase, which randomly forgets a subset of weights and regulates the model's information through weight reinitialization, and the relearning phase, which emphasizes learning generalizable features. Our experiments on benchmark datasets and adversarial attacks show that FOMO alleviates robust overfitting by significantly reducing the gap between the best and last robust test accuracy while improving the state-of-the-art robustness. Furthermore, FOMO provides a better trade-off between standard and robust accuracy, outperforming baseline adversarial methods. Finally, our framework is robust to AutoAttacks and increases generalization in many real-world scenarios.

Machine unlearning is increasingly important for large language models, yet unlearning in Mixture-of-Experts (MoE) architectures remains underexplored. Unlike dense models, MoE architectures employ a router at each layer to assign each token to a sparse subset of experts. In this work, we observe that forget data often activates a small subset of experts disproportionately, while these experts may receive much weaker activation from retain data. This forget--retain routing mismatch can leave forget-critical experts under-regularized during unlearning. To address this, we propose TRACE, Targeted Routing-Aware Calibration of Experts, for MoE unlearning. TRACE first detects forget-critical experts from offline activation statistics, and then calibrates retain regularization by reweighting token-level retain losses so that each selected expert's retain-side activation frequency better matches its forget-side counterpart. Experiments on WMDP and MUSE-BOOKS across multiple MoE LLMs show that TRACE consistently improves the forget-utility trade-off, yielding a 9\% relative utility improvement over the strongest baseline under comparable forgetting quality and the best performance on three out of four MUSE-BOOKS metrics.

Machine unlearning, the removal of a training subset's influence from a deployed model, is critical for privacy preservation and model reliability, yet gradient ascent on forget samples often harms retained knowledge. Existing approaches face a persistent tradeoff between effective forgetting and preservation on the retain set. While previous methods provide useful heuristics, they often lack a formal analysis on how exactly forgetting updates harm retained knowledge, and whether the side effects can be removed with theoretical guarantees. To explore a theoretically sound and simple solution, we start from the first principle on how performance on the retain set is actually affected: a first-order analysis of the local change of the retain loss under small parameter updates during model training. We start from a crisp equivalence: the retain loss is unchanged to first order iff the update direction is orthogonal to the subspace spanned by retain gradients ("retain-invariant"). This identifies the entangled component as the tangential part of forget update within the retain-gradient subspace, and characterizes disentanglement as orthogonality. Guided by this, we propose the Geometric-disentanglement Unlearning (GU) that decomposes any candidate forget gradient update into tangential and normal components to retain space and executes only the normal component. Under a standard trust-region budget, the projected direction aligned with the raw forget gradient is optimal among all first-order retain-invariant moves, and we also derive the optimal projected direction for joint forget-retain updating objectives. Our method is plug-and-play and can be attached to existing gradient-based unlearning procedures to mitigate side effects. GU achieves consistent improvement on various methods across three benchmarks TOFU, MUSE, and WMDP.

This paper explores Machine Unlearning (MU), an emerging field that is gaining increased attention due to concerns about neural models unintentionally remembering personal or sensitive information. We present SeUL, a novel method that enables selective and fine-grained unlearning for language models. Unlike previous work that employs a fully reversed training objective in unlearning, SeUL minimizes the negative impact on the capability of language models, particularly in terms of generation. Furthermore, we introduce two innovative evaluation metrics, sensitive extraction likelihood (S-EL) and sensitive memorization accuracy (S-MA), specifically designed to assess the effectiveness of forgetting sensitive information. In support of the unlearning framework, we propose efficient automatic online and offline sensitive span annotation methods. The online selection method, based on language probability scores, ensures computational efficiency, while the offline annotation involves a two-stage LLM-based process for robust verification. In summary, this paper contributes a novel selective unlearning method (SeUL), introduces specialized evaluation metrics (S-EL and S-MA) for assessing sensitive information forgetting, and proposes automatic online and offline sensitive span annotation methods to support the overall unlearning framework and evaluation process.

Machine unlearning aims to remove targeted knowledge from a trained model while preserving its general capabilities. For autoregressive language models, not all tokens in a forget sample are equally relevant to forgetting. Existing approaches either ignore this heterogeneity or rely on auxiliary models, heuristics, or external annotations to estimate each token's relevance for forgetting. We instead characterize it through the interaction with the retain objective: a token is forget-specific to the extent that minimizing the forget loss on that token does not conflict with retain optimality. We formalize this perspective as a joint optimization problem over the model parameters and the token weights and show that, under a natural separation condition, the resulting objective recovers the oracle forget-specific token support. Motivated by this formulation, we introduce Alternating Token-Weighted Unlearning (ATWU), a lightweight framework that jointly learns token forget-specificity and model parameters during unlearning using a simple linear scorer over the hidden states, without external token level supervision. Across TOFU and RWKU, ATWU achieves state of the art forget-retain trade-offs, outperforming sample-level methods, probability-based token weighting heuristics, and auxiliary-model-based approaches. Moreover, the learned scores align substantially better with ground truth forget-specific spans, indicating that ATWU identifies semantically meaningful token level forgetting signals. Overall, our results suggest that retain conflict provides an effective criterion for identifying what language models should forget, enabling unsupervised learning of token level forget-specificity directly from model representations with minimal computational overhead.

Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising, representation learning, clustering, and latent variable modeling. In this work, we focus primarily on spectral estimators for high-dimensional factor models, where leading singular vectors of the data matrix are used to estimate latent structure and covariance parameters. In many modern applications, however, data are collected across related but heterogeneous tasks, studies, domains, or populations. Applying such estimators separately to each task can lead to unstable estimates when sample sizes are limited relative to dimension, while completely pooling the data can obscure meaningful task-specific structure. We introduce Hierarchical Spectral Shrinkage (HSS), a scalable empirical-Bayes framework for partially pooling task-specific spectral estimators. The method regularizes the leading spectral directions of each task toward a data-adaptivelylearned common basis, while allowing the amount of shrinkage to vary across tasks and spectral components. The proposed estimator arises as the posterior mean in a surrogate Bayesian regression formulation of the empirical singular vectors. For factor models, HSS yields partially pooled estimators of the group-specific loading spaces and covariance matrices and can be combined with different spectral estimators by replacing their empirical singular vectors with hierarchically regularized counterparts. More broadly, the same construction provides a mechanism for extending spectral estimators to collections of related but heterogeneous datasets. We demonstrate substantial improvements in estimation accuracy and out-of-sample performance over separate, fully pooled, and shared-subspace approaches in synthetic experiments and multi-study gene-expression data.

LLMs have been found to memorize training textual sequences and regurgitate verbatim said sequences during text generation time. This fact is known to be the cause of privacy and related (e.g., copyright) problems. Unlearning in LLMs then takes the form of devising new algorithms that will properly deal with these side-effects of memorized data, while not hurting the model's utility. We offer a fresh perspective towards this goal, namely, that each textual sequence to be forgotten should be treated differently when being unlearned based on its degree of memorization within the LLM. We contribute a new metric for measuring unlearning quality, an adversarial attack showing that SOTA algorithms lacking this perspective fail for privacy, and two new unlearning methods based on Gradient Ascent and Task Arithmetic, respectively. A comprehensive performance evaluation across an extensive suite of NLP tasks then mapped the solution space, identifying the best solutions under different scales in model capacities and forget set sizes and quantified the gains of the new approaches.

The impressive capability of modern text-to-image models to generate realistic visuals has come with a serious drawback: they can be misused to create harmful, deceptive or unlawful content. This has accelerated the push for machine unlearning. This new field seeks to selectively remove specific knowledge from a model's training data without causing a drop in its overall performance. However, it turns out that actually forgetting a given concept is an extremely difficult task. Models exposed to attacks using adversarial prompts show the ability to generate so-called unlearned concepts, which can be not only harmful but also illegal. In this paper, we present considerations regarding the ability of models to forget and recall knowledge, introducing the Memory Self-Regeneration task. Furthermore, we present MemoRa strategy, which we consider to be a regenerative approach supporting the effective recovery of previously lost knowledge. Moreover, we propose that robustness in knowledge retrieval is a crucial yet underexplored evaluation measure for developing more robust and effective unlearning techniques. Finally, we demonstrate that forgetting occurs in two distinct ways: short-term, where concepts can be quickly recalled, and long-term, where recovery is more challenging.

The Unlearning Sensitive Content from Large Language Models task aims to remove targeted datapoints from trained models while minimally affecting their general knowledge. In our work, we leverage parameter-efficient, gradient-based unlearning using low-rank (LoRA) adaptation and layer-focused fine-tuning. To further enhance unlearning effectiveness, we employ data chunking, splitting forget data into disjoint partitions and merging them with cyclically sampled retain samples at a pre-defined ratio. Our task-agnostic method achieves an outstanding forget-retain balance, ranking first on leaderboards and significantly outperforming baselines and competing systems.

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 semantic cues rather than shallow lexical patterns.

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.