Chongyu Fan

Chongyu Fan, Jiancheng Liu, Yihua Zhang et al.

With evolving data regulations, machine unlearning (MU) has become an important tool for fostering trust and safety in today's AI models. However, existing MU methods focusing on data and/or weight perspectives often suffer limitations in unlearning accuracy, stability, and cross-domain applicability. To address these challenges, we introduce the concept of 'weight saliency' for MU, drawing parallels with input saliency in model explanation. This innovation directs MU's attention toward specific model weights rather than the entire model, improving effectiveness and efficiency. The resultant method that we call saliency unlearning (SalUn) narrows the performance gap with 'exact' unlearning (model retraining from scratch after removing the forgetting data points). To the best of our knowledge, SalUn is the first principled MU approach that can effectively erase the influence of forgetting data, classes, or concepts in both image classification and generation tasks. As highlighted below, For example, SalUn yields a stability advantage in high-variance random data forgetting, e.g., with a 0.2% gap compared to exact unlearning on the CIFAR-10 dataset. Moreover, in preventing conditional diffusion models from generating harmful images, SalUn achieves nearly 100% unlearning accuracy, outperforming current state-of-the-art baselines like Erased Stable Diffusion and Forget-Me-Not. Codes are available at https://github.com/OPTML-Group/Unlearn-Saliency. (WARNING: This paper contains model outputs that may be offensive in nature.)

Chongyu Fan, Jiancheng Liu, Alfred Hero et al.

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.

Chongyu Fan, Jinghan Jia, Yihua Zhang et al.

The LLM unlearning technique has recently been introduced to comply with data regulations and address the safety and ethical concerns of LLMs by removing the undesired data-model influence. However, state-of-the-art unlearning methods face a critical vulnerability: they are susceptible to ``relearning'' the removed information from a small number of forget data points, known as relearning attacks. In this paper, we systematically investigate how to make unlearned models robust against such attacks. For the first time, we establish a connection between robust unlearning and sharpness-aware minimization (SAM) through a unified robust optimization framework, in an analogy to adversarial training designed to defend against adversarial attacks. Our analysis for SAM reveals that smoothness optimization plays a pivotal role in mitigating relearning attacks. Thus, we further explore diverse smoothing strategies to enhance unlearning robustness. Extensive experiments on benchmark datasets, including WMDP and MUSE, demonstrate that SAM and other smoothness optimization approaches consistently improve the resistance of LLM unlearning to relearning attacks. Notably, smoothness-enhanced unlearning also helps defend against (input-level) jailbreaking attacks, broadening our proposal's impact in robustifying LLM unlearning. Codes are available at https://github.com/OPTML-Group/Unlearn-Smooth.

Chongyu Fan, Gaowen Liu, Mingyi Hong et al.

Muon is a matrix-aware optimizer that leverages Newton-Schulz (NS) iterations to enforce spectral gradient orthogonalization by driving all singular values of the momentum matrix toward 1. While this uniform spectral whitening enhances exploration and outperforms AdamW in LLM pretraining, we show it could lead to fundamental limitations beyond pretraining in two regimes: (i) cross-modality vision-language-action (VLA) training, where inherently low-rank action-module gradients cause amplification of noisy tail directions, and (ii) reinforcement learning with verifiable rewards (RLVR), where low-SNR gradients and the need to preserve per-head specialization from prior training make whitening unstable. To address these challenges, we propose Pion, a drop-in replacement for Muon that preserves its computational efficiency while replacing uniform spectral whitening with a two-stage Promotion+Suppression mechanism, which we call the high-pass NS iteration. This design induces a sharp spectral high-pass effect, anchoring dominant singular values at 1 while suppressing noisy tail components toward 0, with controllable filter strength. To preserve pretrained per-head heterogeneity, Pion also supports a per-head mode that applies updates independently across attention heads via a simple reshape, at no extra cost. In VLA training on LIBERO and LIBERO-Plus, Pion consistently outperforms both baselines across l_1-regression (VLA-Adapter) and flow-matching (VLANeXt) architectures, e.g., reaching 100% success rate on LIBERO Object after 1,500 training steps with VLA-Adapter, vs. 97.0% for Muon and only 32.2% for AdamW. The advantage of Pion further extends to a real Franka Research 3 robot with a pi_0.5 backbone under the DROID setup on three grasp-and-place tasks. In RLVR post-training on Qwen3-1.7B/4B with GRPO and GMPO, Pion also outperforms AdamW on MATH and GSM8K while Muon collapses to zero.

Justin Lee, Zheda Mai, Jinsu Yoo et al.

Machine unlearning--the ability to remove designated concepts from a pre-trained model--has advanced rapidly, particularly for text-to-image diffusion models. However, existing methods typically assume that unlearning requests arrive all at once, whereas in practice they often arrive sequentially. We present the first systematic study of continual unlearning in text-to-image diffusion models and show that popular unlearning methods suffer from rapid utility collapse: after only a few requests, models forget retained knowledge and generate degraded images. We trace this failure to cumulative parameter drift from the pre-training weights and argue that regularization is crucial to addressing it. To this end, we study a suite of add-on regularizers that (1) mitigate drift and (2) remain compatible with existing unlearning methods. Beyond generic regularizers, we show that semantic awareness is essential for preserving concepts close to the unlearning target, and propose a gradient-projection method that constrains parameter drift orthogonal to their subspace. This substantially improves continual unlearning performance and is complementary to other regularizers for further gains. Taken together, our study establishes continual unlearning as a fundamental challenge in text-to-image generation and provides insights, baselines, and open directions for advancing safe and accountable generative AI.

Sijia Liu, Yicheng Lang, Soumyadeep Pal et al.

Zeroth-order (ZO) optimization, learning from finite differences of function evaluations without backpropagation, has recently regained attention in deep learning due to its memory efficiency and applicability to gray- or black-box pipelines. Yet, ZO methods are often dismissed as fundamentally unscalable because of estimator variance and unfavorable query complexity. We argue that this conclusion might be misguided: ZO optimization is underexplored, not underpowered. We show that many perceived limitations stem from myopic development practices, most notably full-space, element-wise, estimator-centric designs. We articulate six positions spanning the algorithmic, systems, and evaluation stack. First, we revisit the feasibility boundaries of estimator-centric ZO methods through variance control, variance-query tradeoffs, and directional-derivative lenses. Then, we identify three underexplored opportunities: (i) subspace and spectral views of ZO that enable interpretable variance reduction with graceful query scaling, (ii) the forward-only nature of ZO as a systems advantage for communication-efficient, pipeline-friendly, and resource-constrained training, and (iii) the need to de-obfuscate ZO evaluations from task complexity. We strongly advocate rethinking ZO optimization around its unique strengths and acting accordingly, opening a viable path toward large-scale, system-aware, and resource-efficient learning with ZO optimization.

Yancheng Huang, Changsheng Wang, Chongyu Fan et al.

Foundation models, such as large language models (LLMs), are powerful but often require customization before deployment to satisfy practical constraints such as safety, privacy, and task-specific requirements, leading to "constrained" optimization problems for model steering and adaptation. However, solving such problems remains largely underexplored and is particularly challenging due to interference between the primary objective and constraint objectives during optimization. In this paper, we propose a subspace control framework for constrained model training. Specifically, (i) we first analyze, from a model merging perspective, how spectral cross-task interference arises and show that it can be resolved via a one-shot solution that orthogonalizes the merged subspace; (ii) we establish a connection between this solution and gradient orthogonalization in the spectral optimizer Muon; and (iii) building on these insights, we introduce SIFT (spectral interference-free training), which leverages a localization scheme to selectively intervene during optimization, enabling controllable updates that mitigate objective-constraint conflicts. We evaluate SIFT across four representative applications: (a) machine unlearning, (b) safety alignment, (c) text-to-speech adaptation, and (d) hallucination mitigation. Compared to both control-based and control-free baselines, SIFT consistently achieves substantial and robust performance improvements across all tasks. Code is available at https://github.com/OPTML-Group/SIFT.

Chongyu Fan, Yihua Zhang, Jinghan Jia et al.

Large reasoning models (LRMs), such as OpenAI's o1 and DeepSeek-R1, harness test-time scaling to perform multi-step reasoning for complex problem-solving. This reasoning process, executed before producing final answers, is often guided by special juncture tokens or textual segments that prompt self-evaluative reflection. We refer to these transition markers and reflective cues as "reflection tokens" (e.g., "wait", "but", "alternatively"). In this work, we treat reflection tokens as a "resource" and introduce the problem of resource allocation, aimed at improving the test-time compute performance of LRMs by adaptively regulating the frequency and placement of reflection tokens. Through empirical analysis, we show that both excessive and insufficient use of reflection tokens, referred to as over-reflection and under-reflection, can degrade model performance. To better understand and manage this trade-off, we draw an analogy between reflection token usage and learning rate scheduling in optimization. Building on this insight, we propose cyclical reflection token scheduling (termed CyclicReflex), a decoding strategy that dynamically modulates reflection token logits using a position-dependent triangular waveform. Experiments on MATH500, AIME2024/2025, and AMC2023 demonstrate that CyclicReflex consistently improves performance across model sizes (1.5B-8B), outperforming standard decoding and more recent approaches such as TIP (thought switching penalty) and S1. Codes are available at https://github.com/OPTML-Group/CyclicReflex.

Yihua Zhang, Chongyu Fan, Yimeng Zhang et al.

The technological advancements in diffusion models (DMs) have demonstrated unprecedented capabilities in text-to-image generation and are widely used in diverse applications. However, they have also raised significant societal concerns, such as the generation of harmful content and copyright disputes. Machine unlearning (MU) has emerged as a promising solution, capable of removing undesired generative capabilities from DMs. However, existing MU evaluation systems present several key challenges that can result in incomplete and inaccurate assessments. To address these issues, we propose UnlearnCanvas, a comprehensive high-resolution stylized image dataset that facilitates the evaluation of the unlearning of artistic styles and associated objects. This dataset enables the establishment of a standardized, automated evaluation framework with 7 quantitative metrics assessing various aspects of the unlearning performance for DMs. Through extensive experiments, we benchmark 9 state-of-the-art MU methods for DMs, revealing novel insights into their strengths, weaknesses, and underlying mechanisms. Additionally, we explore challenging unlearning scenarios for DMs to evaluate worst-case performance against adversarial prompts, the unlearning of finer-scale concepts, and sequential unlearning. We hope that this study can pave the way for developing more effective, accurate, and robust DM unlearning methods, ensuring safer and more ethical applications of DMs in the future. The dataset, benchmark, and codes are publicly available at https://unlearn-canvas.netlify.app/.

Changsheng Wang, Chongyu Fan, Yihua Zhang et al.

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.

Chongyu Fan, Changsheng Wang, Yancheng Huang et al.

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.

Yicheng Lang, Yihua Zhang, Chongyu Fan et al.

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.

Jinghan Jia, Hadi Reisizadeh, Chongyu Fan et al.

Large language models (LLMs) have shown remarkable reasoning capabilities when trained with chain-of-thought (CoT) supervision. However, the long and verbose CoT traces, especially those distilled from large reasoning models (LRMs) such as DeepSeek-R1, significantly increase training costs during the distillation process, where a non-reasoning base model is taught to replicate the reasoning behavior of an LRM. In this work, we study the problem of CoT condensation for resource-efficient reasoning training, aimed at pruning intermediate reasoning steps (i.e., thoughts) in CoT traces, enabling supervised model training on length-reduced CoT data while preserving both answer accuracy and the model's ability to generate coherent reasoning. Our rationale is that CoT traces typically follow a three-stage structure: problem understanding, exploration, and solution convergence. Through empirical analysis, we find that retaining the structure of the reasoning trace, especially the early stage of problem understanding (rich in reflective cues) and the final stage of solution convergence, is sufficient to achieve lossless reasoning supervision. To this end, we propose an Edge-Preserving Condensation method, EPiC, which selectively retains only the initial and final segments of each CoT trace while discarding the middle portion. This design draws an analogy to preserving the "edge" of a reasoning trajectory, capturing both the initial problem framing and the final answer synthesis, to maintain logical continuity. Experiments across multiple model families (Qwen and LLaMA) and benchmarks show that EPiC reduces training time by over 34% while achieving lossless reasoning accuracy on MATH500, comparable to full CoT supervision. To the best of our knowledge, this is the first study to explore thought-level CoT condensation for efficient reasoning model distillation.