Yicheng Lang

Yicheng Lang, Changsheng Wang, Yihua Zhang et al.

Zeroth-order (ZO) optimization provides a gradient-free alternative to first-order (FO) methods by estimating gradients via finite differences of function evaluations, and has recently emerged as a memory-efficient paradigm for fine-tuning large-scale models by avoiding backpropagation. However, ZO optimization has a fundamental tension between accuracy and query efficiency. In this work, we show that ZO optimization can be substantially improved by unifying two complementary principles: (i) a projection-based subspace view that reduces gradient estimation variance by exploiting the intrinsic low-rank structure of model updates, and (ii) Muon-style spectral optimization that applies gradient orthogonalization to extract informative spectral structure from noisy ZO gradients. These findings form a unified framework of subspace gradient orthogonalization, which we instantiate in a new method, ZO-Muon, admitting a natural interpretation as a low-rank Muon optimizer in the ZO setting. Extensive experiments on large language models (LLMs) and vision transformers (ViTs) demonstrate that ZO-Muon significantly accelerates convergence and achieves a win-win improvement in accuracy and query/runtime efficiency. Notably, compared to the popular MeZO baseline, ZO-Muon requires only 24.7% of the queries to reach the same SST-2 performance for LLM fine-tuning, and improves accuracy by 25.1% on ViT-B fine-tuning on CIFAR-100.

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.

Yicheng Lang, Kehan Guo, Yue Huang et al.

Due to the widespread use of LLMs and the rising critical ethical and safety concerns, LLM unlearning methods have been developed to remove harmful knowledge and undesirable capabilities. In this context, evaluations are mostly based on single-value metrics such as QA accuracy. However, these metrics often fail to capture the nuanced retention of harmful knowledge components, making it difficult to assess the true effectiveness of unlearning. To address this issue, we propose UNCD (UNlearning evaluation via Cognitive Diagnosis), a novel framework that leverages Cognitive Diagnosis Modeling for fine-grained evaluation of LLM unlearning. Our dedicated benchmark, UNCD-Cyber, provides a detailed assessment of the removal of dangerous capabilities. Moreover, we introduce UNCD-Agent, which refines unlearning by diagnosing knowledge remnants and generating targeted unlearning data. Extensive experiments across eight unlearning methods and two base models demonstrate that UNCD not only enhances evaluation but also effectively facilitates the removal of harmful LLM abilities.

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.