Daily Papers

In this paper, we propose an end-to-end deep learning model, called E2Efold, for RNA secondary structure prediction which can effectively take into account the inherent constraints in the problem. The key idea of E2Efold is to directly predict the RNA base-pairing matrix, and use an unrolled algorithm for constrained programming as the template for deep architectures to enforce constraints. With comprehensive experiments on benchmark datasets, we demonstrate the superior performance of E2Efold: it predicts significantly better structures compared to previous SOTA (especially for pseudoknotted structures), while being as efficient as the fastest algorithms in terms of inference time.

Magnetic Resonance Imaging can produce detailed images of the anatomy and physiology of the human body that can assist doctors in diagnosing and treating pathologies such as tumours. However, MRI suffers from very long acquisition times that make it susceptible to patient motion artifacts and limit its potential to deliver dynamic treatments. Conventional approaches such as Parallel Imaging and Compressed Sensing allow for an increase in MRI acquisition speed by reconstructing MR images from sub-sampled MRI data acquired using multiple receiver coils. Recent advancements in Deep Learning combined with Parallel Imaging and Compressed Sensing techniques have the potential to produce high-fidelity reconstructions from highly accelerated MRI data. In this work we present a novel Deep Learning-based Inverse Problem solver applied to the task of Accelerated MRI Reconstruction, called the Recurrent Variational Network (RecurrentVarNet), by exploiting the properties of Convolutional Recurrent Neural Networks and unrolled algorithms for solving Inverse Problems. The RecurrentVarNet consists of multiple recurrent blocks, each responsible for one iteration of the unrolled variational optimization scheme for solving the inverse problem of multi-coil Accelerated MRI Reconstruction. Contrary to traditional approaches, the optimization steps are performed in the observation domain (k-space) instead of the image domain. Each block of the RecurrentVarNet refines the observed k-space and comprises a data consistency term and a recurrent unit which takes as input a learned hidden state and the prediction of the previous block. Our proposed method achieves new state of the art qualitative and quantitative reconstruction results on 5-fold and 10-fold accelerated data from a public multi-coil brain dataset, outperforming previous conventional and deep learning-based approaches.

Removing optical and atmospheric blur from galaxy images significantly improves galaxy shape measurements for weak gravitational lensing and galaxy evolution studies. This ill-posed linear inverse problem is usually solved with deconvolution algorithms enhanced by regularisation priors or deep learning. We introduce a so-called "physics-informed deep learning" approach to the Point Spread Function (PSF) deconvolution problem in galaxy surveys. We apply algorithm unrolling and the Plug-and-Play technique to the Alternating Direction Method of Multipliers (ADMM), in which a neural network learns appropriate hyperparameters and denoising priors from simulated galaxy images. We characterise the time-performance trade-off of several methods for galaxies of differing brightness levels as well as our method's robustness to systematic PSF errors and network ablations. We show an improvement in reduced shear ellipticity error of 38.6% (SNR=20)/45.0% (SNR=200) compared to classic methods and 7.4% (SNR=20)/33.2% (SNR=200) compared to modern methods.

Machine unlearning aims to unlearn data points from a learned model, offering a principled way to process data-deletion requests and mitigate privacy risks without full retraining. Prior work has mainly studied unsupervised / supervised machine unlearning, leaving unlearning for sequential decision-making systems far less understood. We initiate the first study of a foundational sequential decision-making problem: offline stochastic multi-armed bandits (MAB). We formalize the privacy constraint for offline MAB and measure utility by the post-unlearning decision quality. We conduct a systematic study of both single- and multi-source unlearning scenarios under two data-generation models, the fixed-sample model and the distribution model. For these settings, our algorithmic design is built on two canonical base algorithms: Gaussian mechanism and rollback, and we propose adaptive algorithms that switch between them according to the data regime and privacy constraint. We further introduce a mixing procedure that elucidates the rationale behind these baselines. We provide performance guarantees across the above settings and establish lower bounds under both dataset models. Experiments validate the predicted tradeoffs and demonstrate the effectiveness of the proposed methods.

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods, that leverage pretrained denoisers, and unrolled architectures that are trained end-to-end for specific imaging problems. Iterative methods in the first class are computationally costly and often provide suboptimal reconstruction performance, whereas unrolled architectures are generally specific to a single inverse problem and require expensive training. In this work, we propose a novel non-iterative, lightweight architecture that incorporates knowledge about the forward operator (acquisition physics and noise parameters) without relying on unrolling. Our model is trained to solve a wide range of inverse problems beyond denoising, including deblurring, magnetic resonance imaging, computed tomography, inpainting, and super-resolution. The proposed model can be easily adapted to unseen inverse problems or datasets with a few fine-tuning steps (up to a few images) in a self-supervised way, without ground-truth references. Throughout a series of experiments, we demonstrate state-of-the-art performance from medical imaging to low-photon imaging and microscopy.

Transductive few-shot learning has recently triggered wide attention in computer vision. Yet, current methods introduce key hyper-parameters, which control the prediction statistics of the test batches, such as the level of class balance, affecting performances significantly. Such hyper-parameters are empirically grid-searched over validation data, and their configurations may vary substantially with the target dataset and pre-training model, making such empirical searches both sub-optimal and computationally intractable. In this work, we advocate and introduce the unrolling paradigm, also referred to as "learning to optimize", in the context of few-shot learning, thereby learning efficiently and effectively a set of optimized hyper-parameters. Specifically, we unroll a generalization of the ubiquitous Expectation-Maximization (EM) optimizer into a neural network architecture, mapping each of its iterates to a layer and learning a set of key hyper-parameters over validation data. Our unrolling approach covers various statistical feature distributions and pre-training paradigms, including recent foundational vision-language models and standard vision-only classifiers. We report comprehensive experiments, which cover a breadth of fine-grained downstream image classification tasks, showing significant gains brought by the proposed unrolled EM algorithm over iterative variants. The achieved improvements reach up to 10% and 7.5% on vision-only and vision-language benchmarks, respectively.

We propose an evolution strategies-based algorithm for estimating gradients in unrolled computation graphs, called ES-Single. Similarly to the recently-proposed Persistent Evolution Strategies (PES), ES-Single is unbiased, and overcomes chaos arising from recursive function applications by smoothing the meta-loss landscape. ES-Single samples a single perturbation per particle, that is kept fixed over the course of an inner problem (e.g., perturbations are not re-sampled for each partial unroll). Compared to PES, ES-Single is simpler to implement and has lower variance: the variance of ES-Single is constant with respect to the number of truncated unrolls, removing a key barrier in applying ES to long inner problems using short truncations. We show that ES-Single is unbiased for quadratic inner problems, and demonstrate empirically that its variance can be substantially lower than that of PES. ES-Single consistently outperforms PES on a variety of tasks, including a synthetic benchmark task, hyperparameter optimization, training recurrent neural networks, and training learned optimizers.

We introduce Evolution Guided General Optimization via Low-rank Learning (EGGROLL), an evolution strategies (ES) algorithm designed to scale backprop-free optimization to large population sizes for modern large neural network architectures with billions of parameters. ES is a set of powerful blackbox optimisation methods that can handle non-differentiable or noisy objectives with excellent scaling potential through parallelisation. Na{ï}ve ES becomes prohibitively expensive at scale due to the computational and memory costs associated with generating matrix perturbations EinR^{mtimes n} and the batched matrix multiplications needed to compute per-member forward passes. EGGROLL overcomes these bottlenecks by generating random matrices Ain R^{mtimes r}, Bin R^{ntimes r} with rll min(m,n) to form a low-rank matrix perturbation A B^top that are used in place of the full-rank perturbation E. As the overall update is an average across a population of N workers, this still results in a high-rank update but with significant memory and computation savings, reducing the auxiliary storage from mn to r(m+n) per layer and the cost of a forward pass from O(mn) to O(r(m+n)) when compared to full-rank ES. A theoretical analysis reveals our low-rank update converges to the full-rank update at a fast Oleft(1{r}right) rate. Our experiments show that (1) EGGROLL does not compromise the performance of ES in tabula-rasa RL settings, despite being faster, (2) it is competitive with GRPO as a technique for improving LLM reasoning, and (3) EGGROLL enables stable pre-training of nonlinear recurrent language models that operate purely in integer datatypes.

Machine unlearning -- efficiently removing the effect of a small "forget set" of training data on a pre-trained machine learning model -- has recently attracted significant research interest. Despite this interest, however, recent work shows that existing machine unlearning techniques do not hold up to thorough evaluation in non-convex settings. In this work, we introduce a new machine unlearning technique that exhibits strong empirical performance even in such challenging settings. Our starting point is the perspective that the goal of unlearning is to produce a model whose outputs are statistically indistinguishable from those of a model re-trained on all but the forget set. This perspective naturally suggests a reduction from the unlearning problem to that of data attribution, where the goal is to predict the effect of changing the training set on a model's outputs. Thus motivated, we propose the following meta-algorithm, which we call Datamodel Matching (DMM): given a trained model, we (a) use data attribution to predict the output of the model if it were re-trained on all but the forget set points; then (b) fine-tune the pre-trained model to match these predicted outputs. In a simple convex setting, we show how this approach provably outperforms a variety of iterative unlearning algorithms. Empirically, we use a combination of existing evaluations and a new metric based on the KL-divergence to show that even in non-convex settings, DMM achieves strong unlearning performance relative to existing algorithms. An added benefit of DMM is that it is a meta-algorithm, in the sense that future advances in data attribution translate directly into better unlearning algorithms, pointing to a clear direction for future progress in unlearning.

Machine unlearning for large language models often faces a privacy dilemma in which strict constraints prohibit sharing either the server's parameters or the client's forget set. To address this dual non-disclosure constraint, we propose MPU, an algorithm-agnostic privacy-preserving Multiple Perturbed Copies Unlearning framework that primarily introduces two server-side modules: Pre-Process for randomized copy generation and Post-Process for update aggregation. In Pre-Process, the server distributes multiple perturbed and reparameterized model instances, allowing the client to execute unlearning locally on its private forget set without accessing the server's exact original parameters. After local unlearning, the server performs Post-Process by inverting the reparameterization and aggregating updates with a harmonic denoising procedure to alleviate the impact of perturbation. Experiments with seven unlearning algorithms show that MPU achieves comparable unlearning performance to noise-free baselines, with most algorithms' average degradation well below 1% under 10% noise, and can even outperform the noise-free baseline for some algorithms under 1% noise. Code is available at https://github.com/Tristan-SHU/MPU.

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.

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.

With the rapid development of Large Language Models (LLMs), we have witnessed intense competition among the major LLM products like ChatGPT, LLaMa, and Gemini. However, various issues (e.g. privacy leakage and copyright violation) of the training corpus still remain underexplored. For example, the Times sued OpenAI and Microsoft for infringing on its copyrights by using millions of its articles for training. From the perspective of LLM practitioners, handling such unintended privacy violations can be challenging. Previous work addressed the ``unlearning" problem of LLMs using gradient information, while they mostly introduced significant overheads like data preprocessing or lacked robustness. In this paper, contrasting with the methods based on first-order information, we revisit the unlearning problem via the perspective of second-order information (Hessian). Our unlearning algorithms, which are inspired by classic Newton update, are not only data-agnostic/model-agnostic but also proven to be robust in terms of utility preservation or privacy guarantee. Through a comprehensive evaluation with four NLP datasets as well as a case study on real-world datasets, our methods consistently show superiority over the first-order methods.

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.

The use of deep unfolding networks in compressive sensing (CS) has seen wide success as they provide both simplicity and interpretability. However, since most deep unfolding networks are iterative, this incurs significant redundancies in the network. In this work, we propose a novel recursion-based framework to enhance the efficiency of deep unfolding models. First, recursions are used to effectively eliminate the redundancies in deep unfolding networks. Secondly, we randomize the number of recursions during training to decrease the overall training time. Finally, to effectively utilize the power of recursions, we introduce a learnable unit to modulate the features of the model based on both the total number of iterations and the current iteration index. To evaluate the proposed framework, we apply it to both ISTA-Net+ and COAST. Extensive testing shows that our proposed framework allows the network to cut down as much as 75% of its learnable parameters while mostly maintaining its performance, and at the same time, it cuts around 21% and 42% from the training time for ISTA-Net+ and COAST respectively. Moreover, when presented with a limited training dataset, the recursive models match or even outperform their respective non-recursive baseline. Codes and pretrained models are available at https://github.com/Rawwad-Alhejaili/Recursions-Are-All-You-Need .

As generative models become increasingly powerful and pervasive, the ability to unlearn specific data, whether due to privacy concerns, legal requirements, or the correction of harmful content, has become increasingly important. Unlike in conventional training, where data are accumulated and knowledge is reinforced, unlearning aims to selectively remove the influence of particular data points without costly retraining from scratch. To be effective and reliable, such algorithms need to achieve (i) forgetting of the undesired data, (ii) preservation of the quality of the generation, (iii) preservation of the influence of the desired training data on the model parameters, and (iv) small number of training steps. We propose fast unlearning algorithms based on loss gradient orthogonalization. We show that our algorithms are able to forget data while maintaining the fidelity of the original model. Using MNIST and CelebA data, we demonstrate that our algorithms achieve orders of magnitude faster unlearning times than their predecessors, such as gradient surgery.

Machine unlearning has emerged as a prevalent technical solution for selectively removing unwanted knowledge absorbed during pre-training, without requiring full retraining. While recent unlearning techniques can effectively remove undesirable content without severely compromising performance on standard benchmarks, we find that they may inadvertently create ``knowledge holes'' -- unintended losses of benign knowledge that standard benchmarks fail to capture. To probe where unlearned models reveal knowledge holes, we propose a test case generation framework that explores both immediate neighbors of unlearned content and broader areas of potential failures. Our evaluation demonstrates significant hidden costs of unlearning: up to 98.7\% of the test cases yield irrelevant or nonsensical responses from unlearned models, despite being answerable by the pretrained model. These findings necessitate rethinking the conventional approach to evaluating knowledge preservation in unlearning, moving beyond standard, static benchmarks.

Personal digital data is a critical asset, and governments worldwide have enforced laws and regulations to protect data privacy. Data users have been endowed with the right to be forgotten of their data. In the course of machine learning (ML), the forgotten right requires a model provider to delete user data and its subsequent impact on ML models upon user requests. Machine unlearning emerges to address this, which has garnered ever-increasing attention from both industry and academia. While the area has developed rapidly, there is a lack of comprehensive surveys to capture the latest advancements. Recognizing this shortage, we conduct an extensive exploration to map the landscape of machine unlearning including the (fine-grained) taxonomy of unlearning algorithms under centralized and distributed settings, debate on approximate unlearning, verification and evaluation metrics, challenges and solutions for unlearning under different applications, as well as attacks targeting machine unlearning. The survey concludes by outlining potential directions for future research, hoping to serve as a guide for interested scholars.

Algorithm learning is a core problem in artificial intelligence with significant implications on automation level that can be achieved by machines. Recently deep learning methods are emerging for synthesizing an algorithm from its input-output examples, the most successful being the Neural GPU, capable of learning multiplication. We present several improvements to the Neural GPU that substantially reduces training time and improves generalization. We introduce a new technique - hard nonlinearities with saturation costs- that has general applicability. We also introduce a technique of diagonal gates that can be applied to active-memory models. The proposed architecture is the first capable of learning decimal multiplication end-to-end.

Large Language Models for Code (LLMs4Code) have achieved strong performance in code generation, but recent studies reveal that they may memorize and leak sensitive information contained in training data, posing serious privacy risks. To address this gap, this work presents the first comprehensive empirical study on applying machine unlearning to mitigate sensitive information leakage in LLMs4Code. We first construct a dedicated benchmark that includes: (i) a synthetic forget set containing diverse forms of personal information, and (ii) a retain set designed to evaluate whether code-generation capability is preserved after unlearning. Using this benchmark, we systematically assess three representative unlearning algorithms (GA, GA+GD, GA+KL) across three widely used open-source LLMs4Code models (AIXCoder-7B, CodeLlama-7B, CodeQwen-7B). Experimental results demonstrate that machine unlearning can substantially reduce direct memorization-based leakage: on average, the direct leak rate drops by more than 50% while retaining about over 91% of the original code-generation performance. Moreover, by analyzing post-unlearning outputs, we uncover a consistent shift from direct to indirect leakage, revealing an underexplored vulnerability that persists even when the target data has been successfully forgotten. Our findings show that machine unlearning is a feasible and effective solution for enhancing privacy protection in LLMs4Code, while also highlighting the need for future techniques capable of mitigating both direct and indirect leakage simultaneously.

Large language models have been widely applied, but can inadvertently encode sensitive or harmful information, raising significant safety concerns. Machine unlearning has emerged to alleviate this concern; however, existing training-time unlearning approaches, relying on coarse-grained loss combinations, have limitations in precisely separating knowledge and balancing removal effectiveness with model utility. In contrast, we propose Fine-grained Activation manipuLation by Contrastive Orthogonal uNalignment (FALCON), a novel representation-guided unlearning approach that leverages information-theoretic guidance for efficient parameter selection, employs contrastive mechanisms to enhance representation separation, and projects conflict gradients onto orthogonal subspaces to resolve conflicts between forgetting and retention objectives. Extensive experiments demonstrate that FALCON achieves superior unlearning effectiveness while maintaining model utility, exhibiting robust resistance against knowledge recovery attempts.

The key components of machine learning are data samples for training, model for learning patterns, and loss function for optimizing accuracy. Analogously, unlearning can potentially be achieved through anti-data samples (or anti-samples), unlearning method, and reversed loss function. While prior research has explored unlearning methods and reversed loss functions, the potential of anti-samples remains largely untapped. In this paper, we introduce UnSTAR: Unlearning with Self-Taught Anti-Sample Reasoning for large language models (LLMs). Our contributions are threefold; first, we propose a novel concept of anti-sample-induced unlearning; second, we generate anti-samples by leveraging misleading rationales, which help reverse learned associations and accelerate the unlearning process; and third, we enable fine-grained targeted unlearning, allowing for the selective removal of specific associations without impacting related knowledge - something not achievable by previous works. Results demonstrate that anti-samples offer an efficient, targeted unlearning strategy for LLMs, opening new avenues for privacy-preserving machine learning and model modification.

The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the protection of user data, as individuals may not have given consent for their data to be used in training. To address this concern, recent studies introduce the concept of unlearnable examples, i.e., data instances that appear natural but are intentionally altered to prevent models from effectively learning from them. While existing methods demonstrate empirical effectiveness, they typically rely on heuristic trials and lack formal guarantees. Besides, when unlearnable examples are mixed with clean data, as is often the case in practice, their unlearnability disappears. In this work, we propose a novel approach to constructing unlearnable examples by systematically maximising the Bayes error, a measurement of irreducible classification error. We develop an optimisation-based approach and provide an efficient solution using projected gradient ascent. Our method provably increases the Bayes error and remains effective when the unlearning examples are mixed with clean samples. Experimental results across multiple datasets and model architectures are consistent with our theoretical analysis and show that our approach can restrict data learnability, effectively in practice.

Modern machine learning models are expensive to train, and there is a growing concern about the challenge of retroactively removing specific training data. Achieving exact unlearning in deep learning pipelines--producing models as if certain data had never been included in training--remains an open problem. In this paper, we revisit exact unlearning in deep learning and show that for large language models (LLMs) we can efficiently exactly unlearn "fine-tuning data" (the data used to adapt a pre-trained model). This follows from two observations. First, we can use in-context learning to adapt the LLM to the fine-tuning dataset instead of SGD based algorithms. Second, we show that accurate in-context learning can be done with quantized k-means, which allows for effectively constant time unlearning operations. Our evaluation shows that this unlearning recipe has similar performance to fine-tuning alternatives, but vastly reduces the unlearning costs. Our study also highlights the need for new measures of unlearning cost when adapting the learning algorithm to have faster unlearn operations.

Recent legislation has led to interest in machine unlearning, i.e., removing specific training samples from a predictive model as if they never existed in the training dataset. Unlearning may also be required due to corrupted/adversarial data or simply a user's updated privacy requirement. For models which require no training (k-NN), simply deleting the closest original sample can be effective. But this idea is inapplicable to models which learn richer representations. Recent ideas leveraging optimization-based updates scale poorly with the model dimension d, due to inverting the Hessian of the loss function. We use a variant of a new conditional independence coefficient, L-CODEC, to identify a subset of the model parameters with the most semantic overlap on an individual sample level. Our approach completely avoids the need to invert a (possibly) huge matrix. By utilizing a Markov blanket selection, we premise that L-CODEC is also suitable for deep unlearning, as well as other applications in vision. Compared to alternatives, L-CODEC makes approximate unlearning possible in settings that would otherwise be infeasible, including vision models used for face recognition, person re-identification and NLP models that may require unlearning samples identified for exclusion. Code can be found at https://github.com/vsingh-group/LCODEC-deep-unlearning/

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.

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.

Large language model unlearning has become a critical challenge in ensuring safety and controlled model behavior by removing undesired data-model influences from the pretrained model while preserving general utility. Significant recent efforts have been dedicated to developing LLM unlearning benchmarks such as WMDP (Weapons of Mass Destruction Proxy) and MUSE (Machine Unlearning Six-way Evaluation), facilitating standardized unlearning performance assessment and method comparison. Despite their usefulness, we uncover for the first time a novel coreset effect within these benchmarks. Specifically, we find that LLM unlearning achieved with the original (full) forget set can be effectively maintained using a significantly smaller subset (functioning as a "coreset"), e.g., as little as 5% of the forget set, even when selected at random. This suggests that LLM unlearning in these benchmarks can be performed surprisingly easily, even in an extremely low-data regime. We demonstrate that this coreset effect remains strong, regardless of the LLM unlearning method used, such as NPO (Negative Preference Optimization) and RMU (Representation Misdirection Unlearning), the popular ones in these benchmarks. The surprisingly strong coreset effect is also robust across various data selection methods, ranging from random selection to more sophisticated heuristic approaches. We explain the coreset effect in LLM unlearning through a keyword-based perspective, showing that keywords extracted from the forget set alone contribute significantly to unlearning effectiveness and indicating that current unlearning is driven by a compact set of high-impact tokens rather than the entire dataset. We further justify the faithfulness of coreset-unlearned models along additional dimensions, such as mode connectivity and robustness to jailbreaking attacks. Codes are available at https://github.com/OPTML-Group/MU-Coreset.

In response to recent data regulation requirements, machine unlearning (MU) has emerged as a critical process to remove the influence of specific examples from a given model. Although exact unlearning can be achieved through complete model retraining using the remaining dataset, the associated computational costs have driven the development of efficient, approximate unlearning techniques. Moving beyond data-centric MU approaches, our study introduces a novel model-based perspective: model sparsification via weight pruning, which is capable of reducing the gap between exact unlearning and approximate unlearning. We show in both theory and practice that model sparsity can boost the multi-criteria unlearning performance of an approximate unlearner, closing the approximation gap, while continuing to be efficient. This leads to a new MU paradigm, termed prune first, then unlearn, which infuses a sparse model prior into the unlearning process. Building on this insight, we also develop a sparsity-aware unlearning method that utilizes sparsity regularization to enhance the training process of approximate unlearning. Extensive experiments show that our proposals consistently benefit MU in various unlearning scenarios. A notable highlight is the 77% unlearning efficacy gain of fine-tuning (one of the simplest unlearning methods) when using sparsity-aware unlearning. Furthermore, we demonstrate the practical impact of our proposed MU methods in addressing other machine learning challenges, such as defending against backdoor attacks and enhancing transfer learning. Codes are available at https://github.com/OPTML-Group/Unlearn-Sparse.

Evaluating machine unlearning methods remains technically challenging, with recent benchmarks requiring complex setups and significant engineering overhead. We introduce a unified and extensible benchmarking suite that simplifies the evaluation of unlearning algorithms using the KLoM (KL divergence of Margins) metric. Our framework provides precomputed model ensembles, oracle outputs, and streamlined infrastructure for running evaluations out of the box. By standardizing setup and metrics, it enables reproducible, scalable, and fair comparison across unlearning methods. We aim for this benchmark to serve as a practical foundation for accelerating research and promoting best practices in machine unlearning. Our code and data are publicly available.

Recent advances in large-scale text-to-image diffusion models have heightened concerns about their potential misuse, especially in generating harmful or misleading content. This underscores the urgent need for effective machine unlearning, i.e., removing specific knowledge or concepts from pretrained models without compromising overall performance. One possible approach is Low-Rank Adaptation (LoRA), which offers an efficient means to fine-tune models for targeted unlearning. However, LoRA often inadvertently alters unrelated content, leading to diminished image fidelity and realism. To address this limitation, we introduce UnGuide -- a novel approach which incorporates UnGuidance, a dynamic inference mechanism that leverages Classifier-Free Guidance (CFG) to exert precise control over the unlearning process. UnGuide modulates the guidance scale based on the stability of a few first steps of denoising processes, enabling selective unlearning by LoRA adapter. For prompts containing the erased concept, the LoRA module predominates and is counterbalanced by the base model; for unrelated prompts, the base model governs generation, preserving content fidelity. Empirical results demonstrate that UnGuide achieves controlled concept removal and retains the expressive power of diffusion models, outperforming existing LoRA-based methods in both object erasure and explicit content removal tasks.

In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. As the latter is known to exhibit a heavy-tail distribution, an algorithm is normally stopped when exceeding a predefined upper time limit. As a consequence, machine learning methods used to optimize an algorithm selection strategy in a data-driven manner need to deal with right-censored samples, a problem that has received little attention in the literature so far. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. Moreover, we adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon. In an extensive experimental evaluation on an adapted version of the ASlib benchmark, we demonstrate that theoretically well-founded methods based on Thompson sampling perform specifically strong and improve in comparison to existing methods.

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.

Unlearning algorithms aim to remove deleted data's influence from trained models at a cost lower than full retraining. However, prior guarantees of unlearning in literature are flawed and don't protect the privacy of deleted records. We show that when users delete their data as a function of published models, records in a database become interdependent. So, even retraining a fresh model after deletion of a record doesn't ensure its privacy. Secondly, unlearning algorithms that cache partial computations to speed up the processing can leak deleted information over a series of releases, violating the privacy of deleted records in the long run. To address these, we propose a sound deletion guarantee and show that the privacy of existing records is necessary for the privacy of deleted records. Under this notion, we propose an accurate, computationally efficient, and secure machine unlearning algorithm based on noisy gradient descent.

Machine unlearning aims to remove information derived from forgotten data while preserving that of the remaining dataset in a well-trained model. With the increasing emphasis on data privacy, several approaches to machine unlearning have emerged. However, these methods typically rely on complete supervision throughout the unlearning process. Unfortunately, obtaining such supervision, whether for the forgetting or remaining data, can be impractical due to the substantial cost associated with annotating real-world datasets. This challenge prompts us to propose a supervision-free unlearning approach that operates without the need for labels during the unlearning process. Specifically, we introduce a variational approach to approximate the distribution of representations for the remaining data. Leveraging this approximation, we adapt the original model to eliminate information from the forgotten data at the representation level. To further address the issue of lacking supervision information, which hinders alignment with ground truth, we introduce a contrastive loss to facilitate the matching of representations between the remaining data and those of the original model, thus preserving predictive performance. Experimental results across various unlearning tasks demonstrate the effectiveness of our proposed method, Label-Agnostic Forgetting (LAF) without using any labels, which achieves comparable performance to state-of-the-art methods that rely on full supervision information. Furthermore, our approach excels in semi-supervised scenarios, leveraging limited supervision information to outperform fully supervised baselines. This work not only showcases the viability of supervision-free unlearning in deep models but also opens up a new possibility for future research in unlearning at the representation level.

Exact unlearning was first introduced as a privacy mechanism that allowed a user to retract their data from machine learning models on request. Shortly after, inexact schemes were proposed to mitigate the impractical costs associated with exact unlearning. More recently unlearning is often discussed as an approach for removal of impermissible knowledge i.e. knowledge that the model should not possess such as unlicensed copyrighted, inaccurate, or malicious information. The promise is that if the model does not have a certain malicious capability, then it cannot be used for the associated malicious purpose. In this paper we revisit the paradigm in which unlearning is used for in Large Language Models (LLMs) and highlight an underlying inconsistency arising from in-context learning. Unlearning can be an effective control mechanism for the training phase, yet it does not prevent the model from performing an impermissible act during inference. We introduce a concept of ununlearning, where unlearned knowledge gets reintroduced in-context, effectively rendering the model capable of behaving as if it knows the forgotten knowledge. As a result, we argue that content filtering for impermissible knowledge will be required and even exact unlearning schemes are not enough for effective content regulation. We discuss feasibility of ununlearning for modern LLMs and examine broader implications.

Recent progress in Machine Unlearning (MU) has introduced solutions for the selective removal of private or sensitive information encoded within deep neural networks. Nonetheless, MU for Multimodal Large Language Models (MLLMs) remains in its nascent phase. Therefore, we propose to reformulate the task of multimodal MU in the era of MLLMs, which aims to erase only the visual patterns associated with a given entity while preserving the corresponding textual knowledge encoded within the original parameters of the language model backbone. Furthermore, we develop a novel geometry-constrained gradient ascent method MMUnlearner. It updates the weights of MLLMs with a weight saliency map jointly restricted by the remaining concepts and textual knowledge during unlearning, thereby preserving parameters essential for non-target knowledge. Extensive experiments demonstrate that MMUnlearner surpasses baselines that finetuning MLLMs with VQA data directly through Gradient Ascent (GA) or Negative Preference Optimization (NPO), across all evaluation dimensions. Our code can be found in [this URL](https://github.com/Z1zs/MMUnlearner).

We resolve an open problem of Hanneke on the subject of universally consistent online learning with non-i.i.d. processes and unbounded losses. The notion of an optimistically universal learning rule was defined by Hanneke in an effort to study learning theory under minimal assumptions. A given learning rule is said to be optimistically universal if it achieves a low long-run average loss whenever the data generating process makes this goal achievable by some learning rule. Hanneke posed as an open problem whether, for every unbounded loss, the family of processes admitting universal learning are precisely those having a finite number of distinct values almost surely. In this paper, we completely resolve this problem, showing that this is indeed the case. As a consequence, this also offers a dramatically simpler formulation of an optimistically universal learning rule for any unbounded loss: namely, the simple memorization rule already suffices. Our proof relies on constructing random measurable partitions of the instance space and could be of independent interest for solving other open questions. We extend the results to the non-realizable setting thereby providing an optimistically universal Bayes consistent learning rule.

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.

Machine unlearning, the study of efficiently removing the impact of specific training instances on a model, has garnered increased attention in recent years due to regulatory guidelines such as the Right to be Forgotten. Achieving precise unlearning typically involves fully retraining the model and is computationally infeasible in case of very large models such as Large Language Models (LLMs). To this end, recent work has proposed several algorithms which approximate the removal of training data without retraining the model. These algorithms crucially rely on access to the model parameters in order to update them, an assumption that may not hold in practice due to computational constraints or having only query access to the LLMs. In this work, we propose a new class of unlearning methods for LLMs called ``In-Context Unlearning.'' This method unlearns instances from the model by simply providing specific kinds of inputs in context, without the need to update model parameters. To unlearn specific training instances, we present these instances to the LLMs at inference time along with labels that differ from their ground truth. Our experimental results demonstrate that in-context unlearning performs on par with, or in some cases outperforms other state-of-the-art methods that require access to model parameters, effectively removing the influence of specific instances on the model while preserving test accuracy.

Online conformal prediction (OCP) seeks prediction intervals that achieve long-run 1-α coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual learning-rate tuning to work well, and may also require algorithm-specific analyses. Here, we develop a general regret-to-coverage theory for interval-valued OCP based on the (1-α)-pinball loss. Our first contribution is to identify linearized regret as a key notion, showing that controlling it implies coverage bounds for any online algorithm. This relies on a black-box reduction that depends only on the Fenchel conjugate of an upper bound on the linearized regret. Building on this theory, we propose UP-OCP, a parameter-free method for OCP, via a reduction to a two-asset portfolio selection problem, leveraging universal portfolio algorithms. We show strong finite-time bounds on the miscoverage of UP-OCP, even for polynomially growing predictions. Extensive experiments support that UP-OCP delivers consistently better size/coverage trade-offs than prior online conformal baselines.

While the history of machine learning so far largely encompasses a series of problems posed by researchers and algorithms that learn their solutions, an important question is whether the problems themselves can be generated by the algorithm at the same time as they are being solved. Such a process would in effect build its own diverse and expanding curricula, and the solutions to problems at various stages would become stepping stones towards solving even more challenging problems later in the process. The Paired Open-Ended Trailblazer (POET) algorithm introduced in this paper does just that: it pairs the generation of environmental challenges and the optimization of agents to solve those challenges. It simultaneously explores many different paths through the space of possible problems and solutions and, critically, allows these stepping-stone solutions to transfer between problems if better, catalyzing innovation. The term open-ended signifies the intriguing potential for algorithms like POET to continue to create novel and increasingly complex capabilities without bound. Our results show that POET produces a diverse range of sophisticated behaviors that solve a wide range of environmental challenges, many of which cannot be solved by direct optimization alone, or even through a direct-path curriculum-building control algorithm introduced to highlight the critical role of open-endedness in solving ambitious challenges. The ability to transfer solutions from one environment to another proves essential to unlocking the full potential of the system as a whole, demonstrating the unpredictable nature of fortuitous stepping stones. We hope that POET will inspire a new push towards open-ended discovery across many domains, where algorithms like POET can blaze a trail through their interesting possible manifestations and solutions.

We revisit the efficacy of several practical methods for approximate machine unlearning developed for large-scale deep learning. In addition to complying with data deletion requests, one often-cited potential application for unlearning methods is to remove the effects of poisoned data. We experimentally demonstrate that, while existing unlearning methods have been demonstrated to be effective in a number of settings, they fail to remove the effects of data poisoning across a variety of types of poisoning attacks (indiscriminate, targeted, and a newly-introduced Gaussian poisoning attack) and models (image classifiers and LLMs); even when granted a relatively large compute budget. In order to precisely characterize unlearning efficacy, we introduce new evaluation metrics for unlearning based on data poisoning. Our results suggest that a broader perspective, including a wider variety of evaluations, are required to avoid a false sense of confidence in machine unlearning procedures for deep learning without provable guarantees. Moreover, while unlearning methods show some signs of being useful to efficiently remove poisoned data without having to retrain, our work suggests that these methods are not yet ``ready for prime time,'' and currently provide limited benefit over retraining.

There is a growing interest in developing unlearnable examples (UEs) against visual privacy leaks on the Internet. UEs are training samples added with invisible but unlearnable noise, which have been found can prevent unauthorized training of machine learning models. UEs typically are generated via a bilevel optimization framework with a surrogate model to remove (minimize) errors from the original samples, and then applied to protect the data against unknown target models. However, existing UE generation methods all rely on an ideal assumption called label-consistency, where the hackers and protectors are assumed to hold the same label for a given sample. In this work, we propose and promote a more practical label-agnostic setting, where the hackers may exploit the protected data quite differently from the protectors. E.g., a m-class unlearnable dataset held by the protector may be exploited by the hacker as a n-class dataset. Existing UE generation methods are rendered ineffective in this challenging setting. To tackle this challenge, we present a novel technique called Unlearnable Clusters (UCs) to generate label-agnostic unlearnable examples with cluster-wise perturbations. Furthermore, we propose to leverage VisionandLanguage Pre-trained Models (VLPMs) like CLIP as the surrogate model to improve the transferability of the crafted UCs to diverse domains. We empirically verify the effectiveness of our proposed approach under a variety of settings with different datasets, target models, and even commercial platforms Microsoft Azure and Baidu PaddlePaddle. Code is available at https://github.com/jiamingzhang94/Unlearnable-Clusters.

Although deep learning has made great progress in recent years, the exploding economic and environmental costs of training neural networks are becoming unsustainable. To address this problem, there has been a great deal of research on *algorithmically-efficient deep learning*, which seeks to reduce training costs not at the hardware or implementation level, but through changes in the semantics of the training program. In this paper, we present a structured and comprehensive overview of the research in this field. First, we formalize the *algorithmic speedup* problem, then we use fundamental building blocks of algorithmically efficient training to develop a taxonomy. Our taxonomy highlights commonalities of seemingly disparate methods and reveals current research gaps. Next, we present evaluation best practices to enable comprehensive, fair, and reliable comparisons of speedup techniques. To further aid research and applications, we discuss common bottlenecks in the training pipeline (illustrated via experiments) and offer taxonomic mitigation strategies for them. Finally, we highlight some unsolved research challenges and present promising future directions.

As models become increasingly sophisticated, conventional algorithm benchmarks are increasingly saturated, underscoring the need for more challenging benchmarks to guide future improvements in algorithmic reasoning. This paper introduces OIBench, a high-quality, private, and challenging olympiad-level informatics dataset comprising 250 carefully curated original problems. We detail the construction methodology of the benchmark, ensuring a comprehensive assessment across various programming paradigms and complexities, and we demonstrate its contamination-resistant properties via experiments. We propose Time/Space Completion Curves for finer-grained efficiency analysis and enable direct human-model comparisons through high-level participant evaluations. Our experiments reveal that while open-source models lag behind closed-source counterparts, current SOTA models already outperform most human participants in both correctness and efficiency, while still being suboptimal compared to the canonical solutions. By releasing OIBench as a fully open-source resource (https://huggingface.co/datasets/AGI-Eval/OIBench), we hope this benchmark will contribute to advancing code reasoning capabilities for future LLMs.

Standard large language model training can create models that produce outputs their trainer deems unacceptable in deployment. The probability of these outputs can be reduced using methods such as LLM unlearning. However, unlearning a set of data (called the forget set) can degrade model performance on other distributions where the trainer wants to retain the model's behavior. To improve this trade-off, we demonstrate that using the forget set to compute only a few uphill Gauss-Newton steps provides a conceptually simple, state-of-the-art unlearning approach for LLMs. While Gauss-Newton steps adapt Newton's method to non-linear models, it is non-trivial to efficiently and accurately compute such steps for LLMs. Hence, our approach crucially relies on parametric Hessian approximations such as Kronecker-Factored Approximate Curvature (K-FAC). We call this combined approach K-FADE (K-FAC for Distribution Erasure). Our evaluation on the WMDP and ToFU benchmarks demonstrates that K-FADE suppresses outputs from the forget set and approximates, in output space, the results of retraining without the forget set. Critically, our method does this while altering the outputs on the retain set less than previous methods. This is because K-FADE transforms a constraint on the model's outputs across the entire retain set into a constraint on the model's weights, allowing the algorithm to minimally change the model's behavior on the retain set at each step. Moreover, the unlearning updates computed by K-FADE can be reapplied later if the model undergoes further training, allowing unlearning to be cheaply maintained.

Machine unlearning methods seek to revise pretrained models such that effects of certain training samples can be removed. In addition to effective erasure, low computational cost and general utility retention are also highly desirable. Existing unlearning methods usually involve iterative updates over the model parameters, which incurs a high computational cost. In this work, we propose an efficient method that only requires a one-time gradient computation, with which we modify only a single layer of model parameters. Specifically, we first identify a small number of model layers that lie on the Pareto front of high forget importance and low retain influence as critical layers. Then we search for a suitable step size and take a step along the gradient direction of a single critical layer while keeping other layers frozen. This method is highly modular and can be used to unlearn multiple concepts simultaneously in a controllable manner. We demonstrate the effectiveness and efficiency of this method on various models including CLIP, stable diffusion, and VLMs, surpassing other state-of-the-art methods.

This paper concludes a series of studies on the polyharmonic cascade, a deep machine learning architecture theoretically derived from indifference principles and the theory of random functions. A universal initialization procedure is proposed, based on symmetric constellations in the form of hyperoctahedra with a central point. This initialization not only ensures stable training of cascades with tens and hundreds of layers (up to 500 layers without skip connections), but also radically simplifies the computations. Scalability and robustness are demonstrated on MNIST (98.3% without convolutions or augmentations), HIGGS (AUC approximately 0.885 on 11M examples), and Epsilon (AUC approximately 0.963 with 2000 features). All linear algebra is reduced to 2D operations and is efficiently executed on GPUs. A public repository and an archived snapshot are provided for full reproducibility.

Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose algorithmic enhancements and a topological hardness measure with implications for a broad class of search problems. As part of our study, we also address several open mathematical questions. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981), and resolve various potential counterexamples in the Miller-Schupp series (1991), including three infinite subfamilies.

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.

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.

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 language models (LLMs) may memorize sensitive or copyrighted content, raising privacy and legal concerns. Due to the high cost of retraining from scratch, researchers attempt to employ machine unlearning to remove specific content from LLMs while preserving the overall performance. In this paper, we discuss several issues in machine unlearning for LLMs and provide our insights on possible approaches. To address the issue of inadequate evaluation of model outputs after unlearning, we introduce three additional metrics to evaluate token diversity, sentence semantics, and factual correctness. We then categorize unlearning methods into untargeted and targeted, and discuss their issues respectively. Specifically, the behavior that untargeted unlearning attempts to approximate is unpredictable and may involve hallucinations, and existing regularization is insufficient for targeted unlearning. To alleviate these issues, we propose using the objective of maximizing entropy (ME) for untargeted unlearning and incorporate answer preservation (AP) loss as regularization for targeted unlearning. Experimental results across three scenarios, i.e., fictitious unlearning, continual unlearning, and real-world unlearning, demonstrate the effectiveness of our approaches. The code is available at https://github.com/sail-sg/closer-look-LLM-unlearning.

Large language models (LLMs) have shown remarkable proficiency in generating text, benefiting from extensive training on vast textual corpora. However, LLMs may also acquire unwanted behaviors from the diverse and sensitive nature of their training data, which can include copyrighted and private content. Machine unlearning has been introduced as a viable solution to remove the influence of such problematic content without the need for costly and time-consuming retraining. This process aims to erase specific knowledge from LLMs while preserving as much model utility as possible. Despite the effectiveness of current unlearning methods, little attention has been given to whether existing unlearning methods for LLMs truly achieve forgetting or merely hide the knowledge, which current unlearning benchmarks fail to detect. This paper reveals that applying quantization to models that have undergone unlearning can restore the "forgotten" information. To thoroughly evaluate this phenomenon, we conduct comprehensive experiments using various quantization techniques across multiple precision levels. We find that for unlearning methods with utility constraints, the unlearned model retains an average of 21\% of the intended forgotten knowledge in full precision, which significantly increases to 83\% after 4-bit quantization. ... Our code is available at: https://github.com/zzwjames/FailureLLMUnlearning{https://github.com/zzwjames/FailureLLMUnlearning}.

Large language model (LLM) unlearning aims to surgically remove the influence of undesired data or knowledge from an existing model while preserving its utility on unrelated tasks. This paradigm has shown promise in addressing privacy and safety concerns. However, recent findings reveal that unlearning effects are often fragile: post-unlearning manipulations such as weight quantization or fine-tuning can quickly neutralize the intended forgetting. Prior efforts to improve robustness primarily reformulate unlearning objectives by explicitly assuming the role of vulnerability sources. In this work, we take a different perspective by investigating the role of the optimizer, independent of unlearning objectives and formulations, in shaping unlearning robustness. We show that the 'grade' of the optimizer, defined by the level of information it exploits, ranging from zeroth-order (gradient-free) to first-order (gradient-based) to second-order (Hessian-based), is tightly linked to the resilience of unlearning. Surprisingly, we find that downgrading the optimizer, such as using zeroth-order methods or compressed-gradient variants (e.g., gradient sign-based optimizers), often leads to stronger robustness. While these optimizers produce noisier and less precise updates, they encourage convergence to harder-to-disturb basins in the loss landscape, thereby resisting post-training perturbations. By connecting zeroth-order methods with randomized smoothing, we further highlight their natural advantage for robust unlearning. Motivated by these insights, we propose a hybrid optimizer that combines first-order and zeroth-order updates, preserving unlearning efficacy while enhancing robustness. Extensive experiments on the MUSE and WMDP benchmarks, across multiple LLM unlearning algorithms, validate that our approach achieves more resilient forgetting without sacrificing unlearning quality.

Neural algorithmic reasoning is an emerging area of machine learning focusing on building models that can imitate the execution of classic algorithms, such as sorting, shortest paths, etc. One of the main challenges is to learn algorithms that are able to generalize to out-of-distribution data, in particular with significantly larger input sizes. Recent work on this problem has demonstrated the advantages of learning algorithms step-by-step, giving models access to all intermediate steps of the original algorithm. In this work, we instead focus on learning neural algorithmic reasoning only from the input-output pairs without appealing to the intermediate supervision. We propose simple but effective architectural improvements and also build a self-supervised objective that can regularise intermediate computations of the model without access to the algorithm trajectory. We demonstrate that our approach is competitive to its trajectory-supervised counterpart on tasks from the CLRS Algorithmic Reasoning Benchmark and achieves new state-of-the-art results for several problems, including sorting, where we obtain significant improvements. Thus, learning without intermediate supervision is a promising direction for further research on neural reasoners.

We study the problem of online clustering where a clustering algorithm has to assign a new point that arrives to one of k clusters. The specific formulation we use is the k-means objective: At each time step the algorithm has to maintain a set of k candidate centers and the loss incurred is the squared distance between the new point and the closest center. The goal is to minimize regret with respect to the best solution to the k-means objective (C) in hindsight. We show that provided the data lies in a bounded region, an implementation of the Multiplicative Weights Update Algorithm (MWUA) using a discretized grid achieves a regret bound of O(T) in expectation. We also present an online-to-offline reduction that shows that an efficient no-regret online algorithm (despite being allowed to choose a different set of candidate centres at each round) implies an offline efficient algorithm for the k-means problem. In light of this hardness, we consider the slightly weaker requirement of comparing regret with respect to (1 + ε) C and present a no-regret algorithm with runtime Oleft(T(poly(log(T),k,d,1/ε)^{k(d+O(1))}right). Our algorithm is based on maintaining an incremental coreset and an adaptive variant of the MWUA. We show that naïve online algorithms, such as Follow The Leader, fail to produce sublinear regret in the worst case. We also report preliminary experiments with synthetic and real-world data.

Unlearning in large language models (LLMs) is critical for regulatory compliance and for building ethical generative AI systems that avoid producing private, toxic, illegal, or copyrighted content. Despite rapid progress, in this work we show that almost all existing unlearning methods fail to achieve true forgetting in practice. Specifically, while evaluations of these `unlearned' models under deterministic (greedy) decoding often suggest successful knowledge removal using standard benchmarks (as has been done in the literature), we show that sensitive information reliably resurfaces when models are sampled with standard probabilistic decoding. To rigorously capture this vulnerability, we introduce leak@k, a new meta-evaluation metric that quantifies the likelihood of forgotten knowledge reappearing when generating k samples from the model under realistic decoding strategies. Using three widely adopted benchmarks, TOFU, MUSE, and WMDP, we conduct the first large-scale, systematic study of unlearning reliability using our newly defined leak@k metric. Our findings demonstrate that knowledge leakage persists across methods and tasks, underscoring that current state-of-the-art unlearning techniques provide only limited forgetting and highlighting the urgent need for more robust approaches to LLM unlearning.

Machine unlearning is a promising approach to mitigate undesirable memorization of training data in ML models. However, in this work we show that existing approaches for unlearning in LLMs are surprisingly susceptible to a simple set of benign relearning attacks. With access to only a small and potentially loosely related set of data, we find that we can ''jog'' the memory of unlearned models to reverse the effects of unlearning. For example, we show that relearning on public medical articles can lead an unlearned LLM to output harmful knowledge about bioweapons, and relearning general wiki information about the book series Harry Potter can force the model to output verbatim memorized text. We formalize this unlearning-relearning pipeline, explore the attack across three popular unlearning benchmarks, and discuss future directions and guidelines that result from our study. Our work indicates that current approximate unlearning methods simply suppress the model outputs and fail to robustly forget target knowledge in the LLMs.

This work presents LURK (Latent UnleaRned Knowledge), a novel framework that probes for hidden retained knowledge in unlearned LLMs through adversarial suffix prompting. LURK automatically generates adversarial prompt suffixes designed to elicit residual knowledge about the Harry Potter domain, a commonly used benchmark for unlearning. Our experiments reveal that even models deemed successfully unlearned can leak idiosyncratic information under targeted adversarial conditions, highlighting critical limitations of current unlearning evaluation standards. By uncovering latent knowledge through indirect probing, LURK offers a more rigorous and diagnostic tool for assessing the robustness of unlearning algorithms. All code will be publicly available.

Large-scale generative models have shown impressive image-generation capabilities, propelled by massive data. However, this often inadvertently leads to the generation of harmful or inappropriate content and raises copyright concerns. Driven by these concerns, machine unlearning has become crucial to effectively purge undesirable knowledge from models. While existing literature has studied various unlearning techniques, these often suffer from either poor unlearning quality or degradation in text-image alignment after unlearning, due to the competitive nature of these objectives. To address these challenges, we propose a framework that seeks an optimal model update at each unlearning iteration, ensuring monotonic improvement on both objectives. We further derive the characterization of such an update. In addition, we design procedures to strategically diversify the unlearning and remaining datasets to boost performance improvement. Our evaluation demonstrates that our method effectively removes target classes from recent diffusion-based generative models and concepts from stable diffusion models while maintaining close alignment with the models' original trained states, thus outperforming state-of-the-art baselines. Our code will be made available at https://github.com/reds-lab/Restricted_gradient_diversity_unlearning.git.

Language models (LMs) are trained on vast amounts of text data, which may include private and copyrighted content. Data owners may request the removal of their data from a trained model due to privacy or copyright concerns. However, exactly unlearning only these datapoints (i.e., retraining with the data removed) is intractable in modern-day models. This has led to the development of many approximate unlearning algorithms. The evaluation of the efficacy of these algorithms has traditionally been narrow in scope, failing to precisely quantify the success and practicality of the algorithm from the perspectives of both the model deployers and the data owners. We address this issue by proposing MUSE, a comprehensive machine unlearning evaluation benchmark that enumerates six diverse desirable properties for unlearned models: (1) no verbatim memorization, (2) no knowledge memorization, (3) no privacy leakage, (4) utility preservation on data not intended for removal, (5) scalability with respect to the size of removal requests, and (6) sustainability over sequential unlearning requests. Using these criteria, we benchmark how effectively eight popular unlearning algorithms on 7B-parameter LMs can unlearn Harry Potter books and news articles. Our results demonstrate that most algorithms can prevent verbatim memorization and knowledge memorization to varying degrees, but only one algorithm does not lead to severe privacy leakage. Furthermore, existing algorithms fail to meet deployer's expectations because they often degrade general model utility and also cannot sustainably accommodate successive unlearning requests or large-scale content removal. Our findings identify key issues with the practicality of existing unlearning algorithms on language models, and we release our benchmark to facilitate further evaluations: muse-bench.github.io

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

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.

Training machine learning models requires the storage of large datasets, which often contain sensitive or private data. Storing data is associated with a number of potential risks which increase over time, such as database breaches and malicious adversaries. Machine unlearning is the study of methods to efficiently remove the influence of training data subsets from previously-trained models. Existing unlearning methods typically require direct access to the "forget set" -- the data to be forgotten-and organisations must retain this data for unlearning rather than deleting it immediately upon request, increasing risks associated with the forget set. We introduce partially-blind unlearning -- utilizing auxiliary information to unlearn without explicit access to the forget set. We also propose a practical framework Reload, a partially-blind method based on gradient optimization and structured weight sparsification to operationalize partially-blind unlearning. We show that Reload efficiently unlearns, approximating models retrained from scratch, and outperforms several forget set-dependent approaches. On language models, Reload unlearns entities using <0.025% of the retain set and <7% of model weights in <8 minutes on Llama2-7B. In the corrective case, Reload achieves unlearning even when only 10% of corrupted data is identified.

We expose a critical limitation in current approaches to machine unlearning in language models: despite the apparent success of unlearning algorithms, information about the forgotten data remains linearly decodable from internal representations. To systematically assess this discrepancy, we introduce an interpretable, information-theoretic framework for auditing unlearning using Partial Information Decomposition (PID). By comparing model representations before and after unlearning, we decompose the mutual information with the forgotten data into distinct components, formalizing the notions of unlearned and residual knowledge. Our analysis reveals that redundant information, shared across both models, constitutes residual knowledge that persists post-unlearning and correlates with susceptibility to known adversarial reconstruction attacks. Leveraging these insights, we propose a representation-based risk score that can guide abstention on sensitive inputs at inference time, providing a practical mechanism to mitigate privacy leakage. Our work introduces a principled, representation-level audit for unlearning, offering theoretical insight and actionable tools for safer deployment of language models.

As Large Language Models (LLMs) demonstrate extensive capability in learning from documents, LLM unlearning becomes an increasingly important research area to address concerns of LLMs in terms of privacy, copyright, etc. A conventional LLM unlearning task typically involves two goals: (1) The target LLM should forget the knowledge in the specified forget documents, and (2) it should retain the other knowledge that the LLM possesses, for which we assume access to a small number of retain documents. To achieve both goals, a mainstream class of LLM unlearning methods introduces an optimization framework with a combination of two objectives - maximizing the prediction loss on the forget documents while minimizing that on the retain documents, which suffers from two challenges, degenerated output and catastrophic forgetting. In this paper, we propose a novel unlearning framework called Unlearning from Logit Difference (ULD), which introduces an assistant LLM that aims to achieve the opposite of the unlearning goals: remembering the forget documents and forgetting the retain knowledge. ULD then derives the unlearned LLM by computing the logit difference between the target and the assistant LLMs. We show that such reversed objectives would naturally resolve both aforementioned challenges while significantly improving the training efficiency. Extensive experiments demonstrate that our method efficiently achieves the intended forgetting while preserving the LLM's overall capabilities, reducing training time by more than threefold. Notably, our method loses 0% of model utility on the ToFU benchmark, whereas baseline methods may sacrifice 17% of utility on average to achieve comparable forget quality. Our code will be publicly available at https://github.com/UCSB-NLP-Chang/ULD.

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

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.

While LLMs have demonstrated impressive performance across various domains and tasks, their security issues have become increasingly severe. Machine unlearning (MU) has emerged as a promising solution to address these issues by removing the influence of undesired data on the target model without compromising its utility in other aspects. MU typically assumes full access to the original training data to preserve utility, which is difficult to achieve in LLM unlearning. Existing LLM unlearning methods often assume access to data most affected by undesired data unlearning. However, this assumption underestimates the entanglement among various LLM capabilities and ignores data access limitations due to various issues. Moreover, these LLM unlearning methods do not sufficiently consider that unlearning requests in real-world scenarios are continuously emerging. To overcome these challenges and achieve practical LLM unlearning, we propose the O3 framework. The O3 framework includes an Out-Of-Distribution (OOD) detector to measure the similarity between input and unlearning data, and an Orthogonal low-rank adapter (LoRA) for continuously unlearning requested data. The OOD detector is trained with a novel contrastive entropy loss and utilizes a local-global layer-aggregated scoring mechanism. The orthogonal LoRA achieves parameter disentanglement among continual unlearning requests. During inference, our O3 framework can smartly decide whether and to what extent to load the unlearning LoRA based on the OOD detector's predictions. Notably, O3's effectiveness does not rely on any retained data. We conducted extensive experiments on O3 and state-of-the-art LLM unlearning methods across three tasks and seven datasets. The results indicate that O3 consistently achieves the best trade-off between unlearning effectiveness and utility preservation, especially when facing continuous unlearning requests.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

Large Language Models (LLMs) have shown strong potential in accelerating digital hardware design through automated code generation. Yet, ensuring their reliability remains a critical challenge, as existing LLMs trained on massive heterogeneous datasets often exhibit problematic memorization of proprietary intellectual property (IP), contaminated benchmarks, and unsafe coding patterns. To mitigate these risks, we propose a novel unlearning framework tailored for LLM-based hardware code generation. Our method combines (i) a syntax-preserving unlearning strategy that safeguards the structural integrity of hardware code during forgetting, and (ii) a fine-grained floor-aware selective loss that enables precise and efficient removal of problematic knowledge. This integration achieves effective unlearning without degrading LLM code generation capabilities. Extensive experiments show that our framework supports forget sets up to 3x larger, typically requiring only a single training epoch, while preserving both syntactic correctness and functional integrity of register-transfer level (RTL) codes. Our work paves an avenue towards reliable LLM-assisted hardware design.

Recent advances in large reasoning models (LRMs) have enabled strong chain-of-thought (CoT) generation through test-time computation. While these multi-step reasoning capabilities represent a major milestone in language model performance, they also introduce new safety risks. In this work, we present the first systematic study to revisit the problem of machine unlearning in the context of LRMs. Machine unlearning refers to the process of removing the influence of sensitive, harmful, or undesired data or knowledge from a trained model without full retraining. We show that conventional unlearning algorithms, originally designed for non-reasoning models, are inadequate for LRMs. In particular, even when final answers are successfully erased, sensitive information often persists within the intermediate reasoning steps, i.e., CoT trajectories. To address this challenge, we extend conventional unlearning and propose Reasoning-aware Representation Misdirection for Unlearning (R^2MU), a novel method that effectively suppresses sensitive reasoning traces and prevents the generation of associated final answers, while preserving the model's reasoning ability. Our experiments demonstrate that R^2MU significantly reduces sensitive information leakage within reasoning traces and achieves strong performance across both safety and reasoning benchmarks, evaluated on state-of-the-art models such as DeepSeek-R1-Distill-LLaMA-8B and DeepSeek-R1-Distill-Qwen-14B.

The task of "unlearning" certain concepts in large language models (LLMs) has attracted immense attention recently, due to its importance for mitigating undesirable model behaviours, such as the generation of harmful, private, or incorrect information. Current protocols to evaluate unlearning methods largely rely on behavioral tests, without monitoring the presence of unlearned knowledge within the model's parameters. This residual knowledge can be adversarially exploited to recover the erased information post-unlearning. We argue that unlearning should also be evaluated internally, by considering changes in the parametric knowledge traces of the unlearned concepts. To this end, we propose a general methodology for eliciting directions in the parameter space (termed "concept vectors") that encode concrete concepts, and construct ConceptVectors, a benchmark dataset containing hundreds of common concepts and their parametric knowledge traces within two open-source LLMs. Evaluation on ConceptVectors shows that existing unlearning methods minimally impact concept vectors, while directly ablating these vectors demonstrably removes the associated knowledge from the LLMs and significantly reduces their susceptibility to adversarial manipulation. Our results highlight limitations in behavioral-based unlearning evaluations and call for future work to include parametric-based evaluations. To support this, we release our code and benchmark at https://github.com/yihuaihong/ConceptVectors.

We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental models to the fully dynamic setting when given predictions about the update times of the elements. In the most basic form of our model, we receive a set of predicted update times for all of the updates that occur over the event horizon. We give a novel framework that "lifts" offline divide-and-conquer algorithms into the fully dynamic setting with little overhead. Using this, we are able to interpolate between the offline and fully dynamic settings; when the ell_1 error of the prediction is linear in the number of updates, we achieve the offline runtime of the algorithm (up to poly log n factors). Provided a fully dynamic backstop algorithm, our algorithm will never do worse than the backstop algorithm regardless of the prediction error. Furthermore, our framework achieves a smooth linear trade-off between ell_1 error in the predictions and runtime. These correspond to the desiderata of consistency, robustness, and graceful degradation of the algorithms-with-predictions literature. We further extend our techniques to incremental and decremental settings, transforming algorithms in these settings when given predictions of only the deletion and insertion times, respectively. Our framework is general, and we apply it to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems including triconnectivity, planar digraph all pairs shortest paths, k-edge connectivity, and others, for prediction error of reasonable magnitude.

The releases of powerful open-weight large language models (LLMs) are often not accompanied by access to their full training data. Existing interpretability methods, particularly those based on activations, often require or assume distributionally similar data. This is a significant limitation when detecting and defending against novel potential threats like backdoors, which are by definition out-of-distribution. In this work, we introduce a new method for understanding, monitoring and controlling fine-tuned LLMs that interprets weights, rather than activations, thereby sidestepping the need for data that is distributionally similar to the unknown training data. We demonstrate that the top singular vectors of the weight difference between a fine-tuned model and its base model correspond to newly acquired behaviors. By monitoring the cosine similarity of activations along these directions, we can detect salient behaviors introduced during fine-tuning with high precision. For backdoored models that bypass safety mechanisms when a secret trigger is present, our method stops up to 100% of attacks with a false positive rate below 1%. For models that have undergone unlearning, we detect inference on erased topics with accuracy up to 95.42% and can even steer the model to recover "unlearned" information. Besides monitoring, our method also shows potential for pre-deployment model auditing: by analyzing commercial instruction-tuned models (OLMo, Llama, Qwen), we are able to uncover model-specific fine-tuning focus including mathematical problem solving, emoji usage, and Midjourney prompt generation.

Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the log-likelihood of the model. Central to our approach is an upper bound on the log-partition function parametrized by a function q that we express as a flexible neural network. Our bound makes it possible to track the partition function during learning, to speed-up sampling, and to train a broad class of hybrid directed/undirected models via a unified variational inference framework. We empirically demonstrate the effectiveness of our method on several popular generative modeling datasets.

Recently, Offline Reinforcement Learning (RL) has achieved remarkable progress with the emergence of various algorithms and datasets. However, these methods usually focus on algorithmic advancements, ignoring that many low-level implementation choices considerably influence or even drive the final performance. As a result, it becomes hard to attribute the progress in Offline RL as these choices are not sufficiently discussed and aligned in the literature. In addition, papers focusing on a dataset (e.g., D4RL) often ignore algorithms proposed on another dataset (e.g., RL Unplugged), causing isolation among the algorithms, which might slow down the overall progress. Therefore, this work aims to bridge the gaps caused by low-level choices and datasets. To this end, we empirically investigate 20 implementation choices using three representative algorithms (i.e., CQL, CRR, and IQL) and present a guidebook for choosing implementations. Following the guidebook, we find two variants CRR+ and CQL+ , achieving new state-of-the-art on D4RL. Moreover, we benchmark eight popular offline RL algorithms across datasets under unified training and evaluation framework. The findings are inspiring: the success of a learning paradigm severely depends on the data distribution, and some previous conclusions are biased by the dataset used. Our code is available at https://github.com/sail-sg/offbench.

Instruction-following large language models (LLMs), such as ChatGPT, have become widely popular among everyday users. However, these models inadvertently disclose private, sensitive information to their users, underscoring the need for machine unlearning techniques to remove selective information from the models. While prior work has focused on forgetting small, random subsets of training data at the instance-level, we argue that real-world scenarios often require the removal of an entire user data, which may require a more careful maneuver. In this study, we explore entity-level unlearning, which aims to erase all knowledge related to a target entity while preserving the remaining model capabilities. To address this, we introduce Opt-Out, an optimal transport-based unlearning method that utilizes the Wasserstein distance from the model's initial parameters to achieve more effective and fine-grained unlearning. We also present the first Entity-Level Unlearning Dataset (ELUDe) designed to evaluate entity-level unlearning. Our empirical results demonstrate that Opt-Out surpasses existing methods, establishing a new standard for secure and adaptable LLMs that can accommodate user data removal requests without the need for full retraining.

Machine unlearning aims to remove sensitive or undesired data from large language models. However, recent studies suggest that unlearning is often shallow, claiming that removed knowledge can easily be recovered. In this work, we critically examine standard unlearning evaluation practices and uncover key limitations that shake our trust in those findings. First, we show that some evaluations introduce substantial new information into the model, potentially masking true unlearning performance by re-teaching the model during testing. Second, we demonstrate that evaluation outcomes vary significantly across tasks, undermining the generalizability of current evaluation routines. Finally, we find that many evaluations rely on spurious correlations, making their results difficult to trust and interpret. Taken together, these issues suggest that current evaluation protocols may both overstate and understate unlearning success. To address this, we propose two principles for future unlearning evaluations: minimal information injection and downstream task awareness. We validate these principles through a series of targeted experiments, showing how violations of each can lead to misleading conclusions.

Large language model (LLM) unlearning has emerged as a crucial post-hoc mechanism for privacy protection and AI safety, yet auditing whether target knowledge is truly erased remains challenging. Existing output-level metrics fail to detect when this knowledge remains recoverable from internal representations. Recent white-box studies reveal such residual knowledge but often rely on auxiliary training or dataset-specific adaptations, leaving no generalizable metric. To address these limitations, we propose the Unlearning Depth Score (UDS), a metric that quantifies the mechanistic depth of unlearning via activation patching. UDS first identifies layers that encode the target knowledge using a retain model baseline, then measures how much of it is erased in the unlearned model on a 0-1 scale. In a meta-evaluation across 20 metrics on 150 unlearned models spanning 8 methods, UDS achieves the highest faithfulness and robustness, confirming our causal approach as the most reliable for unlearning evaluation. Case studies further reveal that white-box metrics can disagree at the layer level and that erasure depth varies across examples. We provide guidelines for integrating UDS into existing benchmarking frameworks and streamlining the evaluation pipeline. Code and data are available at https://github.com/gnueaj/unlearning-depth-score

We address the problem of code generation from multi-turn execution feedback. Existing methods either generate code without feedback or use complex, hierarchical reinforcement learning to optimize multi-turn rewards. We propose a simple yet scalable approach, muCode, that solves multi-turn code generation using only single-step rewards. Our key insight is that code generation is a one-step recoverable MDP, where the correct code can be recovered from any intermediate code state in a single turn. muCode iteratively trains both a generator to provide code solutions conditioned on multi-turn execution feedback and a verifier to score the newly generated code. Experimental evaluations show that our approach achieves significant improvements over the state-of-the-art baselines. We provide analysis of the design choices of the reward models and policy, and show the efficacy of muCode at utilizing the execution feedback. Our code is available at https://github.com/portal-cornell/muCode.

This work investigates the application of Machine Unlearning (MU) for mitigating the impact of trojans embedded in conventional large language models of natural language (Text-LLMs) and large language models of code (Code-LLMs) We propose a novel unlearning approach, LYA, that leverages both gradient ascent and elastic weight consolidation, a Fisher Information Matrix (FIM) based regularization technique, to unlearn trojans from poisoned models. We compare the effectiveness of LYA against conventional techniques like fine-tuning, retraining, and vanilla gradient ascent. The subject models we investigate are BERT and CodeBERT, for sentiment analysis and code defect detection tasks, respectively. Our findings demonstrate that the combination of gradient ascent and FIM-based regularization, as done in LYA, outperforms existing methods in removing the trojan's influence from the poisoned model, while preserving its original functionality. To the best of our knowledge, this is the first work that compares and contrasts MU of trojans in LLMs, in the NL and Coding domain.

In current AI era, users may request AI companies to delete their data from the training dataset due to the privacy concerns. As a model owner, retraining a model will consume significant computational resources. Therefore, machine unlearning is a new emerged technology to allow model owner to delete requested training data or a class with little affecting on the model performance. However, for large-scaling complex data, such as image or text data, unlearning a class from a model leads to a inferior performance due to the difficulty to identify the link between classes and model. An inaccurate class deleting may lead to over or under unlearning. In this paper, to accurately defining the unlearning class of complex data, we apply the definition of Concept, rather than an image feature or a token of text data, to represent the semantic information of unlearning class. This new representation can cut the link between the model and the class, leading to a complete erasing of the impact of a class. To analyze the impact of the concept of complex data, we adopt a Post-hoc Concept Bottleneck Model, and Integrated Gradients to precisely identify concepts across different classes. Next, we take advantage of data poisoning with random and targeted labels to propose unlearning methods. We test our methods on both image classification models and large language models (LLMs). The results consistently show that the proposed methods can accurately erase targeted information from models and can largely maintain the performance of the models.

Optimizing GPU kernels is critical for efficient modern machine learning systems yet remains challenging due to the complex interplay of design factors and rapid hardware evolution. Existing automated approaches typically treat Large Language Models (LLMs) merely as stochastic code generators within heuristic-guided evolutionary loops. These methods often struggle with complex kernels requiring coordinated, multi-step structural transformations, as they lack explicit planning capabilities and frequently discard promising strategies due to inefficient or incorrect intermediate implementations. To address this, we propose Search via Co-Evolving World Model and build K-Search based on this method. By replacing static search heuristics with a co-evolving world model, our framework leverages LLMs' prior domain knowledge to guide the search, actively exploring the optimization space. This approach explicitly decouples high-level algorithmic planning from low-level program instantiation, enabling the system to navigate non-monotonic optimization paths while remaining resilient to temporary implementation defects. We evaluate K-Search on diverse, complex kernels from FlashInfer, including GQA, MLA, and MoE kernels. Our results show that K-Search significantly outperforms state-of-the-art evolutionary search methods, achieving an average 2.10x improvement and up to a 14.3x gain on complex MoE kernels. On the GPUMode TriMul task, K-Search achieves state-of-the-art performance on H100, reaching 1030us and surpassing both prior evolution and human-designed solutions.

Unlearning methods have the potential to improve the privacy and safety of large language models (LLMs) by removing sensitive or harmful information post hoc. The LLM unlearning research community has increasingly turned toward empirical benchmarks to assess the effectiveness of such methods. In this paper, we find that existing benchmarks provide an overly optimistic and potentially misleading view on the effectiveness of candidate unlearning methods. By introducing simple, benign modifications to a number of popular benchmarks, we expose instances where supposedly unlearned information remains accessible, or where the unlearning process has degraded the model's performance on retained information to a much greater extent than indicated by the original benchmark. We identify that existing benchmarks are particularly vulnerable to modifications that introduce even loose dependencies between the forget and retain information. Further, we show that ambiguity in unlearning targets in existing benchmarks can easily lead to the design of methods that overfit to the given test queries. Based on our findings, we urge the community to be cautious when interpreting benchmark results as reliable measures of progress, and we provide several recommendations to guide future LLM unlearning research.

The paper describes LLM unlearning without a retaining dataset, using the ORPO reinforcement learning method with inference enhanced by modified classifier-free guidance. Significant improvement in unlearning, without degradation of the model, is achieved through direct training on synthetic replacement data in CFG-aware training regime, with classifier-free guidance applied during the inference. This article is an extended version of the NeurIPS 2024 LLM-PC submission, which was awarded second prize.

Evolutionary program synthesis systems such as AlphaEvolve, OpenEvolve, and ShinkaEvolve offer a new approach to AI-assisted mathematical discovery. These systems utilize teams of large language models (LLMs) to generate candidate solutions to a problem as human readable code. These candidate solutions are then 'evolved' with the goal of improving them beyond what an LLM can produce in a single shot. While existing mathematical applications have mostly focused on problems of establishing bounds (e.g., sphere packing), the program synthesis approach is well suited to any problem where the solution takes the form of an explicit construction. With this in mind, in this paper we explore the use of OpenEvolve for combinatorial bijection discovery. We describe the results of applying OpenEvolve to three bijection construction problems involving Dyck paths, two of which are known and one of which is open. We find that while systems like OpenEvolve show promise as a valuable tool for combinatorialists, the problem of finding novel, research-level bijections remains a challenging task for current frontier systems, reinforcing the need for human mathematicians in the loop. We describe some lessons learned for others in the field interested in exploring the use of these systems.

Reinforcement Learning with Verifiable Reward (RLVR) has proven effective in improving Large Language Model's (LLM) reasoning ability. However, the learning dynamics of RLVR remain underexplored. In this paper, we reveal a counterintuitive phenomenon: among hard examples that the model initially struggles with, a substantial subset remains unlearnable even when correct rollouts are present. To understand the phenomenon, we first demonstrate that existing optimization and sampling techniques fail to resolve unlearnability. With cross-example gradient analysis, we show that unlearnable examples have fundamental representation issue, characterized by low gradient similarity with the rest of the examples and ungeneralizable reasoning patterns. We further show that representation flaws are difficult to mitigate in RL, as data augmentation does not improve gradient similarity. Our study provides the first systematic characterization of unlearnable data in RLVR training and reveals fundamental limitations in current RL approaches for reasoning tasks. Code and data are available at https://github.com/yulinchen99/unlearnability-rlvr.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

Growing concerns surrounding AI safety and data privacy have driven the development of Machine Unlearning as a potential solution. However, current machine unlearning algorithms are designed to complement the offline training paradigm. The emergence of the Continual Learning (CL) paradigm promises incremental model updates, enabling models to learn new tasks sequentially. Naturally, some of those tasks may need to be unlearned to address safety or privacy concerns that might arise. We find that applying conventional unlearning algorithms in continual learning environments creates two critical problems: performance degradation on retained tasks and task relapse, where previously unlearned tasks resurface during subsequent learning. Furthermore, most unlearning algorithms require data to operate, which conflicts with CL's philosophy of discarding past data. A clear need arises for unlearning algorithms that are data-free and mindful of future learning. To that end, we propose UnCLe, an Unlearning framework for Continual Learning. UnCLe employs a hypernetwork that learns to generate task-specific network parameters, using task embeddings. Tasks are unlearned by aligning the corresponding generated network parameters with noise, without requiring any data. Empirical evaluations on several vision data sets demonstrate UnCLe's ability to sequentially perform multiple learning and unlearning operations with minimal disruption to previously acquired knowledge.

Machine unlearning seeks to selectively remove the "influence" of specific training data on a model's outputs. The ideal goal is Retrain Equivalence--behavior identical to a model trained from scratch on only the retained data. This goal was formulated for models trained on i.i.d. data batches, but modern pipelines often involve multi-stage training, with each stage having a distinct data distribution and objective. Examples include LLM fine-tuning for alignment, reasoning ability, etc. Our study shows via theory and experiments that this shift to multi-stage training introduces a fundamental barrier for machine unlearning. The theory indicates that the outcome of local unlearning--methods that only use gradients computed on the forget set--is path-dependent. That is, a model's behavior during unlearning is influenced by the order of its training stages during learning, making it impossible for path-oblivious algorithms to universally achieve Retrain Equivalence. We empirically demonstrate the same phenomenon in LLM post-training across Llama and Qwen models (1B to 14B) with gradient ascent, NPO, and SimNPO local unlearning algorithms. Models fine-tuned via different orderings of identical training stages diverge in behavior during unlearning, with the degradation in GSM8K accuracy after unlearning varying by over 20% across paths. We also observe that some learning paths consistently produce models that unlearn slowly. During unlearning, whether the probability mass gets squeezed into paraphrasing or alternative concepts is also path-dependent. These results consistently show that Retrain Equivalence is an ill-posed target for local unlearning algorithms, so long as the target models are trained in stages. In situations where access to models' training histories is hard, the current work calls for rethinking the definition and desiderata of machine unlearning.

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.

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

Generative AI technologies have been deployed in many places, such as (multimodal) large language models and vision generative models. Their remarkable performance should be attributed to massive training data and emergent reasoning abilities. However, the models would memorize and generate sensitive, biased, or dangerous information originated from the training data especially those from web crawl. New machine unlearning (MU) techniques are being developed to reduce or eliminate undesirable knowledge and its effects from the models, because those that were designed for traditional classification tasks could not be applied for Generative AI. We offer a comprehensive survey on many things about MU in Generative AI, such as a new problem formulation, evaluation methods, and a structured discussion on the advantages and limitations of different kinds of MU techniques. It also presents several critical challenges and promising directions in MU research. A curated list of readings can be found: https://github.com/franciscoliu/GenAI-MU-Reading.

The study of hardest and easiest fitness landscapes is an active area of research. Recently, Kaufmann, Larcher, Lengler and Zou conjectured that for the self-adjusting (1,lambda)-EA, Adversarial Dynamic BinVal (ADBV) is the hardest dynamic monotone function to optimize. We introduce the function Switching Dynamic BinVal (SDBV) which coincides with ADBV whenever the number of remaining zeros in the search point is strictly less than n/2, where n denotes the dimension of the search space. We show, using a combinatorial argument, that for the (1+1)-EA with any mutation rate p in [0,1], SDBV is drift-minimizing among the class of dynamic monotone functions. Our construction provides the first explicit example of an instance of the partially-ordered evolutionary algorithm (PO-EA) model with parameterized pessimism introduced by Colin, Doerr and F\'erey, building on work of Jansen. We further show that the (1+1)-EA optimizes SDBV in Theta(n^{3/2}) generations. Our simulations demonstrate matching runtimes for both static and self-adjusting (1,lambda) and (1+lambda)-EA. We further show, using an example of fixed dimension, that drift-minimization does not equal maximal runtime.

While Code Language Models (CLMs) have demonstrated superior performance in software engineering tasks such as code generation and summarization, recent empirical studies reveal a critical privacy vulnerability: these models exhibit unintended memorization of sensitive training data, enabling verbatim reproduction of confidential information when specifically prompted. To address this issue, several approaches, including training data de-duplication and differential privacy augmentation, have been proposed. However, these methods require full-model retraining for deployed CLMs, which incurs substantial computational costs. In this paper, we aim to answer the following research question: Can sensitive information memorized by CLMs be erased effectively and efficiently? We conduct a pioneering investigation into erasing sensitive memorization in CLMs through machine unlearning - a post-hoc modification method that removes specific information from trained models without requiring full retraining. Specifically, we first quantify the memorization risks of sensitive data within CLM training datasets and curate a high-risk dataset of 50,000 sensitive memorized samples as unlearning targets. We study two widely used gradient ascent-based unlearning approaches: the vanilla and constraint-based methods, and introduce CodeEraser, an advanced variant that selectively unlearns sensitive memorized segments in code while preserving the structural integrity and functional correctness of the surrounding code. Extensive experiments on three families of CLMs, i.e., CodeParrot, CodeGen-Mono, and Qwen2.5-Coder, validate the effectiveness and efficiency of CodeEraser in erasing targeted sensitive memorization while maintaining model utility.

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the last-iterate to a Nash equilibrium. Although the non-bandit case has been studied extensively, this setting has only been explored recently, with a bound of O(T^{-1/8}) on the exploitability gap. We show that, for uncoupled algorithms, guaranteeing convergence of the policy profiles to a Nash equilibrium is detrimental to the performance, with the best attainable rate being Ω(T^{-1/4}) in contrast to the usual Ω(T^{-1/2}) rate for convergence of the average iterates. We then propose two algorithms that achieve this optimal rate up to constant and logarithmic factors. The first algorithm leverages a straightforward trade-off between exploration and exploitation, while the second employs a regularization technique based on a two-step mirror descent approach.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

Machine unlearning for large language models (LLMs) aims to remove undesired data, knowledge, and behaviors (e.g., for safety, privacy, or copyright) while preserving useful model capabilities. Despite rapid progress over the past two years, research in LLM unlearning remains fragmented, with limited clarity on what constitutes effective unlearning and how it should be rigorously evaluated. In this work, we present a principled taxonomy of twelve recent stateful unlearning methods, grouped into three methodological families: divergence-driven optimization, representation misalignment, and rejection-based targeted unlearning. Building on this taxonomy, we revisit the evaluation of unlearning effectiveness (UE), utility retention (UT), and robustness (Rob), focusing on the WMDP benchmark. Our analysis shows that current evaluations, dominated by multiple-choice question (MCQ) accuracy, offer only a narrow perspective, often overstating success while overlooking the model's actual generation behavior. To address this gap, we introduce open question-answering (Open-QA) metrics that better capture generative performance and reveal the inherent UE-UT tradeoff across method families. Furthermore, we demonstrate that robustness requires finer-grained analysis: for example, vulnerabilities differ substantially between in-domain relearning and out-of-domain fine-tuning, even though both fall under model-level attacks. Through this study, we hope to deliver a full-stack revisit of LLM unlearning and actionable guidance for designing and evaluating future methods.

User specifications or legal frameworks often require information to be removed from pretrained models, including large language models (LLMs). This requires deleting or "forgetting" a set of data points from an already-trained model, which typically degrades its performance on other data points. Thus, a balance must be struck between removing information and keeping the model's other abilities intact, with a failure to balance this trade-off leading to poor deletion or an unusable model. To this end, we propose UPCORE (Utility-Preserving Coreset Selection), a method-agnostic data selection framework for mitigating collateral damage during unlearning. Finding that the model damage is correlated with the variance of the model's representations on the forget set, we selectively prune the forget set to remove outliers, thereby minimizing model degradation after unlearning. We evaluate UPCORE across three standard unlearning methods consistently achieving a superior balance between the competing objectives of deletion efficacy and model preservation. To better evaluate this trade-off, we introduce a new metric, measuring the area-under-the-curve (AUC) across standard metrics. We find that UPCORE improves both standard metrics and AUC, benefitting from positive transfer between the coreset and pruned points while reducing negative transfer from the forget set to points outside of it.

During early optimization passes, compilers must make predictions for machine-dependent characteristics such as execution unit utilization, number of register spills, latency, throughput etc. to generate better code. Often a hand-written static/analytical hardware cost model is built into the compiler. However, the need for more sophisticated and varied predictions has become more pronounced with the development of deep learning compilers which need to optimize dataflow graphs. Such compilers usually employ a much higher level MLIR form as an IR representation before lowering to traditional LLVM-IR. A static/analytical cost model in such a scenario is cumbersome and error prone as the opcodes represent very high level algebraic/arithmetic operations. Hence, we develop a machine learning-based cost model for high-level MLIR which can predict different target variables of interest such as CPU/GPU/xPU utilization, instructions executed, register usage etc. By considering the incoming MLIR as a text input a la NLP models we can apply well-known techniques from modern NLP research to help predict hardware characteristics more accurately. We expect such precise ML-driven hardware cost models to guide our deep learning compiler in graph level optimizations around operator fusion, local memory allocation, kernel scheduling etc. as well as in many kernel-level optimizations such as loop interchange, LICM and unroll. We report early work-in -progress results of developing such models on high-level MLIR representing dataflow graphs emitted by Pytorch/Tensorflow-like frameworks as well as lower-level dialects like affine. We show that these models can provide reasonably good estimates with low error bounds for various hardware characteristics of interest and can be a go-to mechanism for hardware cost modelling in the future.

This paper investigates the impact of loss function selection in deep unfolding techniques for sparse signal recovery algorithms. Deep unfolding transforms iterative optimization algorithms into trainable lightweight neural networks by unfolding their iterations as network layers, with various loss functions employed for parameter learning depending on application contexts. We focus on deep unfolded versions of the fundamental iterative shrinkage thresholding algorithm (ISTA) and the iterative hard thresholding algorithm (IHT), comparing supervised learning using mean squared error with unsupervised learning using the objective function of the original optimization problem. Our simulation results reveal that the effect of the choice of loss function significantly depends on the convexity of the optimization problem. For convex ell_1-regularized problems, supervised-ISTA achieves better final recovery accuracy but fails to minimize the original objective function, whereas we empirically observe that unsupervised-ISTA converges to a nearly identical solution as conventional ISTA but with accelerated convergence. Conversely, for nonconvex ell_0-regularized problems, both supervised-IHT and unsupervised-IHT converge to better local minima than the original IHT, showing similar performance regardless of the loss function employed. These findings provide valuable insights into the design of effective deep unfolded networks for sparse signal recovery applications.

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.

In this work we explore recent advances in instruction-tuning language models on a range of open instruction-following datasets. Despite recent claims that open models can be on par with state-of-the-art proprietary models, these claims are often accompanied by limited evaluation, making it difficult to compare models across the board and determine the utility of various resources. We provide a large set of instruction-tuned models from 6.7B to 65B parameters in size, trained on 12 instruction datasets ranging from manually curated (e.g., OpenAssistant) to synthetic and distilled (e.g., Alpaca) and systematically evaluate them on their factual knowledge, reasoning, multilinguality, coding, and open-ended instruction following abilities through a collection of automatic, model-based, and human-based metrics. We further introduce T\"ulu, our best performing instruction-tuned model suite finetuned on a combination of high-quality open resources. Our experiments show that different instruction-tuning datasets can uncover or enhance specific skills, while no single dataset (or combination) provides the best performance across all evaluations. Interestingly, we find that model and human preference-based evaluations fail to reflect differences in model capabilities exposed by benchmark-based evaluations, suggesting the need for the type of systemic evaluation performed in this work. Our evaluations show that the best model in any given evaluation reaches on average 83% of ChatGPT performance, and 68% of GPT-4 performance, suggesting that further investment in building better base models and instruction-tuning data is required to close the gap. We release our instruction-tuned models, including a fully finetuned 65B T\"ulu, along with our code, data, and evaluation framework at https://github.com/allenai/open-instruct to facilitate future research.

We present MIPS, a novel method for program synthesis based on automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the learned algorithm into Python code. We test MIPS on a benchmark of 62 algorithmic tasks that can be learned by an RNN and find it highly complementary to GPT-4: MIPS solves 32 of them, including 13 that are not solved by GPT-4 (which also solves 30). MIPS uses an integer autoencoder to convert the RNN into a finite state machine, then applies Boolean or integer symbolic regression to capture the learned algorithm. As opposed to large language models, this program synthesis technique makes no use of (and is therefore not limited by) human training data such as algorithms and code from GitHub. We discuss opportunities and challenges for scaling up this approach to make machine-learned models more interpretable and trustworthy.

This paper presents the ZJUKLAB team's submission for SemEval-2025 Task 4: Unlearning Sensitive Content from Large Language Models. This task aims to selectively erase sensitive knowledge from large language models, avoiding both over-forgetting and under-forgetting issues. We propose an unlearning system that leverages Model Merging (specifically TIES-Merging), combining two specialized models into a more balanced unlearned model. Our system achieves competitive results, ranking second among 26 teams, with an online score of 0.944 for Task Aggregate and 0.487 for overall Aggregate. In this paper, we also conduct local experiments and perform a comprehensive analysis of the unlearning process, examining performance trajectories, loss dynamics, and weight perspectives, along with several supplementary experiments, to understand the effectiveness of our method. Furthermore, we analyze the shortcomings of our method and evaluation metrics, emphasizing that MIA scores and ROUGE-based metrics alone are insufficient to fully evaluate successful unlearning. Finally, we emphasize the need for more comprehensive evaluation methodologies and rethinking of unlearning objectives in future research. Code is available at https://github.com/zjunlp/unlearn/tree/main/semeval25.

Various studies have attempted to remove sensitive or private knowledge from a language model to prevent its unauthorized exposure. However, prior studies have overlooked the complex and interconnected nature of knowledge, where related knowledge must be carefully examined. Specifically, they have failed to evaluate whether an unlearning method faithfully erases interconnected knowledge that should be removed, retaining knowledge that appears relevant but exists in a completely different context. To resolve this problem, we first define a new concept called superficial unlearning, which refers to the phenomenon where an unlearning method either fails to erase the interconnected knowledge it should remove or unintentionally erases irrelevant knowledge. Based on the definition, we introduce a new benchmark, FaithUn, to analyze and evaluate the faithfulness of unlearning in real-world knowledge QA settings. Furthermore, we propose a novel unlearning method, KLUE, which updates only knowledge-related neurons to achieve faithful unlearning. KLUE identifies knowledge neurons using an explainability method and updates only those neurons using selected unforgotten samples. Experimental results demonstrate that widely-used unlearning methods fail to ensure faithful unlearning, while our method shows significant effectiveness in real-world QA unlearning.

Machine unlearning (MU) for large language models has become critical for AI safety, yet existing methods fail to generalize to Mixture-of-Experts (MoE) architectures. We identify that traditional unlearning methods exploit MoE's architectural vulnerability: they manipulate routers to redirect queries away from knowledgeable experts rather than erasing knowledge, causing a loss of model utility and superficial forgetting. We propose Geometric Routing Invariance Preservation (GRIP), an algorithm-agnostic framework for unlearning for MoE. Our core contribution is a geometric constraint, implemented by projecting router gradient updates into an expert-specific null-space. Crucially, this decouples routing stability from parameter rigidity: while discrete expert selections remain stable for retained knowledge, the continuous router parameters remain plastic within the null space, allowing the model to undergo necessary internal reconfiguration to satisfy unlearning objectives. This forces the unlearning optimization to erase knowledge directly from expert parameters rather than exploiting the superficial router manipulation shortcut. GRIP functions as an adapter, constraining router parameter updates without modifying the underlying unlearning algorithm. Extensive experiments on large-scale MoE models demonstrate that our adapter eliminates expert selection shift (achieving over 95% routing stability) across all tested unlearning methods while preserving their utility. By preventing existing algorithms from exploiting MoE model's router vulnerability, GRIP adapts existing unlearning research from dense architectures to MoEs.

As AI models are trained on ever-expanding datasets, the ability to remove the influence of specific data from trained models has become essential for privacy protection and regulatory compliance. Unlearning addresses this challenge by selectively removing parametric knowledge from the trained models without retraining from scratch, which is critical for resource-intensive models such as Large Language Models (LLMs). Existing unlearning methods often degrade model performance by removing more information than necessary when attempting to ''forget'' specific data. We introduce Forgetting-MarI, an LLM unlearning framework that provably removes only the additional (marginal) information contributed by the data to be unlearned, while preserving the information supported by the data to be retained. By penalizing marginal information, our method yields an explicit upper bound on the unlearn dataset's residual influence in the trained models, providing provable undetectability. Extensive experiments confirm that our approach outperforms current state-of-the-art unlearning methods, delivering reliable forgetting and better preserved general model performance across diverse benchmarks. This advancement represents an important step toward making AI systems more controllable and compliant with privacy and copyright regulations without compromising their effectiveness.

Machine unlearning aims to solve the problem of removing the influence of selected training examples from a learned model. Despite the increasing attention to this problem, it remains an open research question how to evaluate unlearning in large language models (LLMs), and what are the critical properties of the data to be unlearned that affect the quality and efficiency of unlearning. This work formalizes a metric to evaluate unlearning quality in generative models, and uses it to assess the trade-offs between unlearning quality and performance. We demonstrate that unlearning out-of-distribution examples requires more unlearning steps but overall presents a better trade-off overall. For in-distribution examples, however, we observe a rapid decay in performance as unlearning progresses. We further evaluate how example's memorization and difficulty affect unlearning under a classical gradient ascent-based approach.

Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify these using category theory in order to ease correctness proofs and guide the design of new algorithms. In this paper, we extend CALF to cover learning of algebraic structures that may not have a coalgebraic presentation. Furthermore, we provide a detailed algorithmic account of an abstract version of the popular L* algorithm, which was missing from CALF. We instantiate the abstract theory to a large class of Set functors, by which we recover for the first time practical tree automata learning algorithms from an abstract framework and at the same time obtain new algorithms to learn algebras of quotiented polynomial functors.

Machine learning models often incorporate vast amounts of data, raising significant privacy concerns. Machine unlearning, the ability to remove the influence of specific data points from a trained model, addresses these concerns. This paper explores practical methods for implementing machine unlearning, focusing on a first-epoch gradient-ascent approach. Key findings include: 1. Single vs. Multi-Epoch Unlearning: First-epoch gradient unlearning is more effective than multi-epoch gradients. 2. Layer-Based Unlearning: The embedding layer in GPT-2 is crucial for effective unlearning. Gradients from the output layers (11 and 12) have no impact. Efficient unlearning can be achieved using only the embedding layer, halving space complexity. 3. Influence Functions & Scoring: Techniques like Hessian Vector Product and the dot product of activations and tensors are used for quantifying unlearning. 4. Gradient Ascent Considerations: Calibration is necessary to avoid overexposing the model to specific data points during unlearning, which could prematurely terminate the process. 5. Fuzzy Matching vs. Iterative Unlearning: Fuzzy matching techniques shift the model to a new optimum, while iterative unlearning provides a more complete modality. Our empirical evaluation confirms that first-epoch gradient ascent for machine unlearning is more effective than whole-model gradient ascent. These results highlight the potential of machine unlearning for enhancing data privacy and compliance with regulations such as GDPR and CCPA. The study underscores the importance of formal methods to comprehensively evaluate the unlearning process.

One of the biggest missing capabilities in current AI systems is the ability to learn continuously after deployment. Implementing such continually learning systems have several challenges, one of which is the large memory requirement of gradient-based algorithms that are used to train state-of-the-art LLMs. Evolutionary Strategies (ES) have recently re-emerged as a gradient-free alternative to traditional learning algorithms and have shown encouraging performance on specific tasks in LLMs. In this paper, we perform a comprehensive analysis of ES and specifically evaluate its forgetting curves when training for an increasing number of update steps. We first find that ES is able to reach performance numbers close to GRPO for math and reasoning tasks with a comparable compute budget. However, and most importantly for continual learning, the performance gains in ES is accompanied by significant forgetting of prior abilities, limiting its applicability for training models online. We also explore the reason behind this behavior and show that the updates made using ES are much less sparse and have orders of magnitude larger ell_2 norm compared to corresponding GRPO updates, explaining the contrasting forgetting curves between the two algorithms. With this study, we aim to highlight the issue of forgetting in gradient-free algorithms like ES and hope to inspire future work to mitigate these issues.

Unlearning in Large Language Models (LLMs) aims to enhance safety, mitigate biases, and comply with legal mandates, such as the right to be forgotten. However, existing unlearning methods are brittle: minor query modifications, such as multi-hop reasoning and entity aliasing, can recover supposedly forgotten information. As a result, current evaluation metrics often create an illusion of effectiveness, failing to detect these vulnerabilities due to reliance on static, unstructured benchmarks. We propose a dynamic framework that stress tests unlearning robustness using complex structured queries. Our approach first elicits knowledge from the target model (pre-unlearning) and constructs targeted probes, ranging from simple queries to multi-hop chains, allowing precise control over query difficulty. Our experiments show that the framework (1) shows comparable coverage to existing benchmarks by automatically generating semantically equivalent Q&A probes, (2) aligns with prior evaluations, and (3) uncovers new unlearning failures missed by other benchmarks, particularly in multi-hop settings. Furthermore, activation analyses show that single-hop queries typically follow dominant computation pathways, which are more likely to be disrupted by unlearning methods. In contrast, multi-hop queries tend to use alternative pathways that often remain intact, explaining the brittleness of unlearning techniques in multi-hop settings. Our framework enables practical and scalable evaluation of unlearning methods without the need for manual construction of forget test sets, enabling easier adoption for real-world applications. We release the pip package and the code at https://sites.google.com/view/unlearningmirage/home.

As large language models (LLMs) are increasingly deployed in the real world, the ability to ``unlearn'', or remove specific pieces of knowledge post hoc, has become essential for a variety of reasons ranging from privacy regulations to correcting outdated or harmful content. Prior work has proposed unlearning benchmarks and algorithms, and has typically assumed that the training process and the target model are fixed. In this work, we empirically investigate how learning-time choices in knowledge encoding impact the effectiveness of unlearning factual knowledge. Our experiments reveal two key findings: (1) learning with paraphrased descriptions improves unlearning performance and (2) unlearning individual piece of knowledge from a chunk of text is challenging. Our results suggest that learning-time knowledge encoding may play a central role in enabling reliable post-hoc unlearning.

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