# Universally Empowering Zeroth-Order Optimization via Adaptive Layer-wise Sampling

arXiv: https://arxiv.org/abs/2604.18264 · HTML: https://mlsanity.com/paper/2604.18264/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [WiC: the Word-in-Context Dataset for Evaluating Context-Sensitive Meaning Representations](https://mlsanity.com/paper/1808.09121/) (2018)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [ReCoRD: Bridging the Gap between Human and Machine Commonsense Reading Comprehension](https://mlsanity.com/paper/1810.12885/) (2018)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization](https://mlsanity.com/paper/1910.06513/) (2019)
- [DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training](https://mlsanity.com/paper/2310.02025/) (2023)
- [Variance-reduced Zeroth-Order Methods for Fine-Tuning Language Models](https://mlsanity.com/paper/2404.08080/) (2024)
- [Second-Order Fine-Tuning without Pain for LLMs:A Hessian Informed Zeroth-Order Optimizer](https://mlsanity.com/paper/2402.15173/) (2024)
- [Enhancing Zeroth-order Fine-tuning for Language Models with Low-rank Structures](https://mlsanity.com/paper/2410.07698/) (2024)
- [Zeroth-Order Fine-Tuning of LLMs in Random Subspaces](https://mlsanity.com/paper/2410.08989/) (2024)
- [ZO-AdaMU Optimizer: Adapting Perturbation by the Momentum and Uncertainty in Zeroth-order Optimization](https://mlsanity.com/paper/2312.15184/) (2023)
- [Zeroth-Order Online Alternating Direction Method of Multipliers: Convergence Analysis and Applications](https://mlsanity.com/paper/1710.07804/) (2017)
- [Harmony in Divergence: Towards Fast, Accurate, and Memory-efficient Zeroth-order LLM Fine-tuning](https://mlsanity.com/paper/2502.03304/) (2025)
- [CommonIT: Commonality-Aware Instruction Tuning for Large Language Models via Data Partitions](https://mlsanity.com/paper/2410.03077/) (2024)
- [APT: Improving Specialist LLM Performance with Weakness Case Acquisition and Iterative Preference Training](https://mlsanity.com/paper/2506.03483/) (2025)
- [Dynamic Sampling that Adapts: Self-Aware Iterative Data Persistent Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2505.16176/) (2025)
- [Low-Rank Curvature for Zeroth-Order Optimization in LLM Fine-Tuning](https://mlsanity.com/paper/2511.07971/) (2025)

## Built on by (most cited first, 2 of 2)

- [Coverage, Not Credit: Failure-Credit Routing of Zeroth-Order Perturbation Budgets Does Not Improve On-Pool Sample Efficiency for LLM Agents](https://mlsanity.com/paper/2608.28011/) (2026)
- [Sample-Adaptive Zeroth-Order Post-Training](https://mlsanity.com/paper/2610.12566/) (2026)

## Abstract (arXiv)

Zeroth-Order optimization presents a promising memory-efficient paradigm for fine-tuning Large Language Models by relying solely on forward passes. However, its practical adoption is severely constrained by slow wall-clock convergence and high estimation variance. In this work, we dissect the runtime characteristics of ZO algorithms and identify a critical system bottleneck where the generation of perturbations and parameter updates accounts for over 40% of the training latency. We argue that the standard uniform exploration strategy is fundamentally flawed as it fails to account for the heterogeneous sensitivity of layers in deep networks, resulting in computationally wasteful blind searches. To address this structural mismatch, we propose AdaLeZO, an Adaptive Layer-wise ZO optimization framework. By formulating the layer selection process as a non-stationary Multi-Armed Bandit problem, AdaLeZO dynamically allocates the limited perturbation budget to the most sensitive parameters. We further introduce an Inverse Probability Weighting mechanism based on sampling with replacement, which guarantees unbiased gradient estimation while effectively acting as a temporal denoiser to reduce variance. Extensive experiments on LLaMA and OPT models ranging from 6.7B to 30B parameters demonstrate that AdaLeZO achieves 1.7x to 3.0x wall-clock acceleration compared to state-of-the-art methods. Crucially, AdaLeZO functions as a universal plug-and-play module that seamlessly enhances the efficiency of existing ZO optimizers without incurring additional memory overhead.