# Towards Fast LLM Fine-tuning through Zeroth-Order Optimization with Projected Gradient-Aligned Perturbations

arXiv: https://arxiv.org/abs/2510.18228 · HTML: https://mlsanity.com/paper/2510.18228/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 46 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 30 of 41)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [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)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [VisualGPT: Data-efficient Adaptation of Pretrained Language Models for Image Captioning](https://mlsanity.com/paper/2102.10407/) (2021)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [Revisiting Weakly Supervised Pre-Training of Visual Perception Models](https://mlsanity.com/paper/2201.08371/) (2022)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1805.10367/) (2018)
- [DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training](https://mlsanity.com/paper/2310.02025/) (2023)
- [FlightLLM: Efficient Large Language Model Inference with a Complete Mapping Flow on FPGAs](https://mlsanity.com/paper/2401.03868/) (2024)
- [Stochastic Zeroth-order Optimization in High Dimensions](https://mlsanity.com/paper/1710.10551/) (2017)
- [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)
- [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)
- [Improved Zeroth-Order Variance Reduced Algorithms and Analysis for Nonconvex Optimization](https://mlsanity.com/paper/1910.12166/) (2019)
- [Private Fine-tuning of Large Language Models with Zeroth-order Optimization](https://mlsanity.com/paper/2401.04343/) (2024)
- [Accurate LoRA-Finetuning Quantization of LLMs via Information Retention](https://mlsanity.com/paper/2402.05445/) (2024)
- [Efficient On-Chip Learning for Optical Neural Networks Through Power-Aware Sparse Zeroth-Order Optimization](https://mlsanity.com/paper/2012.11148/) (2020)
- [Zeroth order optimization with orthogonal random directions](https://mlsanity.com/paper/2107.03941/) (2021)

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

- [TerMeZO: Ternary Sparse Zeroth-Order Optimization for Fine-tuning BitNet Models at the Edge](https://mlsanity.com/paper/2609.33548/) (2026)
- [Hierarchical Zero-Order Optimization for Deep Neural Networks](https://mlsanity.com/paper/2602.10607/) (2026)

## Abstract (arXiv)

Fine-tuning large language models (LLMs) using zeroth-order (ZO) optimization has emerged as a promising alternative to traditional gradient-based methods due to its reduced memory footprint requirement. However, existing ZO methods suffer from high variance in gradient estimation, leading to slow convergence and suboptimal performance on large-scale models. In this work, we propose P-GAP, a fast LLM fine-tuning approach through zeroth-order optimization with Projected Gradient-Aligned Perturbations. Specifically, we first estimate a low-dimensional gradient space and then align perturbations in projected gradients' direction within the space. This approach enables reduced the number of perturbed parameters and decreased variance, therefore accelerated convergence for LLM fine-tuning. Experiments on LLMs show that P-GAP consistently surpasses the baselines, achieving up to 6% increase in accuracy on classification tasks and up to 12% higher accuracy on generation tasks, with up to about 81% less training iterations and 70% less GPU hours. These results demonstrate that P-GAP enables fast, scalable, and resource-efficient ZO LLM fine-tuning.