# Harmony in Divergence: Towards Fast, Accurate, and Memory-efficient Zeroth-order LLM Fine-tuning

arXiv: https://arxiv.org/abs/2502.03304 · HTML: https://mlsanity.com/paper/2502.03304/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 71 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Builds on (most cited first, 30 of 51)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [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)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Making Pre-trained Language Models Better Few-shot Learners](https://mlsanity.com/paper/2012.15723/) (2020)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [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)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [VisualGPT: Data-efficient Adaptation of Pretrained Language Models for Image Captioning](https://mlsanity.com/paper/2102.10407/) (2021)

## Built on by (most cited first, 18 of 18)

- [RCR-Router: Efficient Role-Aware Context Routing for Multi-Agent LLM Systems with Structured Memory](https://mlsanity.com/paper/2508.04903/) (2025)
- [FZOO: Fast Zeroth-Order Optimizer for Fine-Tuning Large Language Models towards Adam-Scale Speed](https://mlsanity.com/paper/2506.09034/) (2025)
- [Structured Agent Distillation for Large Language Model](https://mlsanity.com/paper/2505.13820/) (2025)
- [Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization](https://mlsanity.com/paper/2602.17155/) (2026)
- [Perturbation-efficient Zeroth-order Optimization for Hardware-friendly On-device Training](https://mlsanity.com/paper/2504.20314/) (2025)
- [KerZOO: Kernel Function Informed Zeroth-Order Optimization for Accurate and Accelerated LLM Fine-Tuning](https://mlsanity.com/paper/2505.18886/) (2025)
- [Downgrade to Upgrade: Optimizer Simplification Enhances Robustness in LLM Unlearning](https://mlsanity.com/paper/2510.00761/) (2025)
- [CurvZO: Adaptive Curvature-Guided Sparse Zeroth-Order Optimization for Efficient LLM Fine-Tuning](https://mlsanity.com/paper/2603.21725/) (2026)
- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)
- [Towards Fast LLM Fine-tuning through Zeroth-Order Optimization with Projected Gradient-Aligned Perturbations](https://mlsanity.com/paper/2510.18228/) (2025)
- [When Should a Robot Think? Resource-Aware Reasoning via Reinforcement Learning for Embodied Robotic Decision-Making](https://mlsanity.com/paper/2603.16673/) (2026)
- [Universally Empowering Zeroth-Order Optimization via Adaptive Layer-wise Sampling](https://mlsanity.com/paper/2604.18264/) (2026)
- [AdaMeZO: Adam-style Zeroth-Order Optimizer for LLM Fine-tuning Without Maintaining the Moments](https://mlsanity.com/paper/2605.00650/) (2026)
- [TSLA: A Task-Specific Learning Adaptation for Semantic Segmentation on Autonomous Vehicles Platform](https://mlsanity.com/paper/2508.12279/) (2025)
- [Palette: A Modular, Controllable, and Efficient Framework for On-demand Authorized Safety Alignment Relaxation in LLMs](https://mlsanity.com/paper/2605.24154/) (2026)
- [Dominant-Layer ZO: A Single Layer Dominates Zeroth-Order Fine-Tuning of LLMs](https://mlsanity.com/paper/2606.05516/) (2026)
- [CooperLLM: Cloud-Edge-End Cooperative Federated Fine-tuning for LLMs via ZOO-based Gradient Correction](https://mlsanity.com/paper/2601.12917/) (2026)
- [Why Zeroth-Order Adaptation May Forget Less: A Randomized Shaping Theory](https://mlsanity.com/paper/2605.10658/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excel across various tasks, but standard first-order (FO) fine-tuning demands considerable memory, significantly limiting real-world deployment. Recently, zeroth-order (ZO) optimization stood out as a promising memory-efficient training paradigm, avoiding backward passes and relying solely on forward passes for gradient estimation, making it attractive for resource-constrained scenarios. However, ZO method lags far behind FO method in both convergence speed and accuracy. To bridge the gap, we introduce a novel layer-wise divergence analysis that uncovers the distinct update pattern of FO and ZO optimization. Aiming to resemble the learning capacity of FO method from the findings, we propose Divergence-driven Zeroth-Order (DiZO) optimization. DiZO conducts divergence-driven layer adaptation by incorporating projections to ZO updates, generating diverse-magnitude updates precisely scaled to layer-wise individual optimization needs. Our results demonstrate that DiZO significantly reduces the needed iterations for convergence without sacrificing throughput, cutting training GPU hours by up to 48% on various datasets. Moreover, DiZO consistently outperforms the representative ZO baselines in fine-tuning RoBERTa-large, OPT-series, and Llama-series on downstream tasks and, in some cases, even surpasses memory-intensive FO fine-tuning. Our code is released at https://github.com/Skilteee/DiZO.