On Surprising Effectiveness of Masking Updates in Adaptive Optimizers

Training large language models requires optimization algorithms that are not only statistically effective, but also computationally and memory efficient at extreme scale. Although Adam remains the dominant optimizer for large-scale language-model pretraining and fine-tuning, recent work has revisited nearly every component of the optimization stack: adaptive moment estimation, decoupled weight decay, memory footprint, curvature approximation, sign-based updates, large-batch stability, low-rank gradient structure, and matrix-wise orthogonalized updates. This survey reviews optimizer design for large language models through a systems-and-optimization lens. We organize the literature into classical first-order optimizers, adaptive optimizers, memory-efficient variants, second-order and curvature-aware methods, sign-based and discovered optimizers, low-rank and projection-based methods, and matrix-based optimizers such as Muon. We also discuss benchmarking methodology, including hyperparameter fairness, scale dependence, wall-clock efficiency, token efficiency, memory overhead, and downstream evaluation. We argue that optimizer research for LLMs is entering a new phase: moving from single-algorithm speedup claims toward rigorous, scale-aware comparisons that jointly evaluate convergence, stability, memory, and implementation complexity.

Memory-efficient optimization methods have recently gained increasing attention for scaling full-parameter training of large language models under the GPU-memory bottleneck. Existing approaches either lack clear convergence guarantees, or only achieve the standard ${\mathcal{O}}(ε^{-4})$ iteration complexity in the nonconvex settings. We propose Omni-Masked Gradient Descent (OMGD), an optimization method based on mask traversal for memory efficient training, and provide a nonconvex convergence analysis that establishes a strictly improved iteration complexity of $\tilde{\mathcal{O}}(ε^{-3})$ for finding an $ε$-approximate stationary point. Empirically, OMGD is a lightweight, plug-and-play approach that integrates seamlessly into most mainstream optimizers, yielding consistent improvements over competitive baselines in both fine-tuning and pre-training tasks.

The large language model (LLM) is typically integrated into the mainstream optimization protocol. However, it remains underexplored whether maintaining the model integrity is indispensable for promising performance. In this work, we introduce Mask Fine-Tuning (MFT), a novel LLM fine-tuning paradigm demonstrating that carefully breaking the model's structural integrity can surprisingly improve performance without updating model weights. MFT learns and applies binary masks to well-optimized models, using the standard LLM fine-tuning objective as supervision. Based on fully fine-tuned models, MFT uses the same fine-tuning datasets to achieve consistent performance gains across domains and backbones (e.g., an average gain of 2.70/4.15 on IFEval with LLaMA2-7B/3.1-8B). Detailed ablation studies and analyses examine the proposed MFT from different perspectives, including the sparse ratio and the loss surface. Additionally, when deployed on well-trained models, MFT is compatible with other LLM optimization procedures to improve overall model performance. Furthermore, this study extends the masking operation beyond its conventional use in network pruning for model compression to encompass a broader range of model capabilities.