# Steering the Noise: Turning Random Perturbations into Effective Descent for Memory-Efficient LLM Fine-Tuning

arXiv: https://arxiv.org/abs/2601.04710 · HTML: https://mlsanity.com/paper/2601.04710/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 46 references that are in the map.
- First posted on arXiv 8 Jan 2026.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [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)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Making Pre-trained Language Models Better Few-shot Learners](https://mlsanity.com/paper/2012.15723/) (2020)
- [Exploiting Cloze Questions for Few Shot Text Classification and Natural Language Inference](https://mlsanity.com/paper/2001.07676/) (2020)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [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)
- [ZeRO-Offload: Democratizing Billion-Scale Model Training](https://mlsanity.com/paper/2101.06840/) (2021)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Black-Box Tuning for Language-Model-as-a-Service](https://mlsanity.com/paper/2201.03514/) (2022)
- [ReCoRD: Bridging the Gap between Human and Machine Commonsense Reading Comprehension](https://mlsanity.com/paper/1810.12885/) (2018)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training](https://mlsanity.com/paper/2310.02025/) (2023)
- [Sparse MeZO: Less Parameters for Better Performance in Zeroth-Order LLM Fine-Tuning](https://mlsanity.com/paper/2402.15751/) (2024)
- [Variance-reduced Zeroth-Order Methods for Fine-Tuning Language Models](https://mlsanity.com/paper/2404.08080/) (2024)
- [BBTv2: Towards a Gradient-Free Future with Large Language Models](https://mlsanity.com/paper/2205.11200/) (2022)
- [Second-Order Fine-Tuning without Pain for LLMs:A Hessian Informed Zeroth-Order Optimizer](https://mlsanity.com/paper/2402.15173/) (2024)
- [A Zeroth-Order Block Coordinate Descent Algorithm for Huge-Scale Black-Box Optimization](https://mlsanity.com/paper/2102.10707/) (2021)
- [Gradientless Descent: High-Dimensional Zeroth-Order Optimization](https://mlsanity.com/paper/1911.06317/) (2019)
- [Zeroth-Order Fine-Tuning of LLMs with Extreme Sparsity](https://mlsanity.com/paper/2406.02913/) (2024)
- [ZO-AdaMU Optimizer: Adapting Perturbation by the Momentum and Uncertainty in Zeroth-order Optimization](https://mlsanity.com/paper/2312.15184/) (2023)
- [AdaZeta: Adaptive Zeroth-Order Tensor-Train Adaption for Memory-Efficient Large Language Models Fine-Tuning](https://mlsanity.com/paper/2406.18060/) (2024)

## Abstract (arXiv)

Fine-tuning large language models (LLMs) achieves strong performance but is often limited by the memory overhead of backpropagation. Zeroth-order (ZO) optimization avoids this overhead by estimating gradients through forward passes alone, yet it typically converges slowly because random Gaussian perturbations yield high-variance gradient estimates in high-dimensional parameter spaces. In this paper, we propose a plug-and-play framework that turns random perturbations into more effective descent directions. The key idea is to draw a small pool of candidate perturbations, evaluate their loss values, and then select or combine those that are best aligned with the optimization objective. We develop two instantiations of this idea: MeZO-GV, which forms a guiding vector from the contrast between low-loss and high-loss perturbation groups, and MeZO-Greedy, which keeps the single best perturbation within a fixed evaluation budget. We theoretically show that both strategies yield a larger per-step reduction in the objective than standard ZO estimation, leading to improved convergence rates. Experiments on LLMs of different scales and architectures confirm that the proposed methods integrate naturally with existing ZO optimizers and consistently improve convergence speed and task accuracy. On OPT-13B, our approach outperforms all ZO baselines across 11 benchmarks and exceeds gradient-based methods on 9 of them, while retaining the memory efficiency of forward-only optimization.