# On the Convergence of Zeroth-Order Federated Tuning for Large Language Models

arXiv: https://arxiv.org/abs/2402.05926 · HTML: https://mlsanity.com/paper/2402.05926/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 61 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 30 of 38)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Personalized Federated Learning: A Meta-Learning Approach](https://mlsanity.com/paper/2002.07948/) (2020)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [Towards Building the Federated GPT: Federated Instruction Tuning](https://mlsanity.com/paper/2305.05644/) (2023)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [FederatedScope-LLM: A Comprehensive Package for Fine-tuning Large Language Models in Federated Learning](https://mlsanity.com/paper/2309.00363/) (2023)
- [Cross-Node Federated Graph Neural Network for Spatio-Temporal Data Modeling](https://mlsanity.com/paper/2106.05223/) (2021)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [Federated Full-Parameter Tuning of Billion-Sized Language Models with Communication Cost under 18 Kilobytes](https://mlsanity.com/paper/2312.06353/) (2023)
- [FederatedScope: A Flexible Federated Learning Platform for Heterogeneity](https://mlsanity.com/paper/2204.05011/) (2022)
- [ZeroFL: Efficient On-Device Training for Federated Learning with Local Sparsity](https://mlsanity.com/paper/2208.02507/) (2022)

## Built on by (most cited first, 19 of 19)

- [Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources](https://mlsanity.com/paper/2402.11505/) (2024)
- [Federated Large Language Models: Current Progress and Future Directions](https://mlsanity.com/paper/2409.15723/) (2024)
- [The Synergy between Data and Multi-Modal Large Language Models: A Survey from Co-Development Perspective](https://mlsanity.com/paper/2407.08583/) (2024)
- [Achieving Dimension-Free Communication in Federated Learning via Zeroth-Order Optimization](https://mlsanity.com/paper/2405.15861/) (2024)
- [ElasticZO: A Memory-Efficient On-Device Learning with Combined Zeroth- and First-Order Optimization](https://mlsanity.com/paper/2501.04287/) (2025)
- [Bilevel ZOFO: Efficient LLM Fine-Tuning and Meta-Training](https://mlsanity.com/paper/2502.03604/) (2025)
- [Unity is Power: Semi-Asynchronous Collaborative Training of Large-Scale Models with Structured Pruning in Resource-Limited Clients](https://mlsanity.com/paper/2410.08457/) (2024)
- [FedHL: Federated Learning for Heterogeneous Low-Rank Adaptation via Unbiased Aggregation](https://mlsanity.com/paper/2505.18494/) (2025)
- [Lean Clients, Full Accuracy: Hybrid Zeroth- and First-Order Split Federated Learning](https://mlsanity.com/paper/2601.09076/) (2026)
- [ProtegoFed: Backdoor-Free Federated Instruction Tuning with Interspersed Poisoned Data](https://mlsanity.com/paper/2603.00516/) (2026)
- [Recent Advances in Federated Learning Driven Large Language Models: A Survey on Architecture, Performance, and Security](https://mlsanity.com/paper/2406.09831/) (2024)
- [Efficient Personalization of Quantized Diffusion Model without Backpropagation](https://mlsanity.com/paper/2503.14868/) (2025)
- [VAMO: Efficient Zeroth-Order Variance Reduction for SGD with Faster Convergence](https://mlsanity.com/paper/2505.13954/) (2025)
- [Efficient Zeroth-Order Federated Finetuning of Language Models on Resource-Constrained Devices](https://mlsanity.com/paper/2502.10239/) (2025)
- [GradualDiff-Fed: A Federated Learning Specialized Framework for Large Language Model](https://mlsanity.com/paper/2506.19164/) (2025)
- [Steering the Noise: Turning Random Perturbations into Effective Descent for Memory-Efficient LLM Fine-Tuning](https://mlsanity.com/paper/2601.04710/) (2026)
- [ZorBA: Zeroth-order Federated Fine-tuning of LLMs with Heterogeneous Block Activation](https://mlsanity.com/paper/2603.04436/) (2026)
- [New Hybrid Fine-Tuning Paradigm for LLMs: Algorithm Design and Convergence Analysis Framework](https://mlsanity.com/paper/2604.09940/) (2026)
- [Skillsets on the Chain: A Blockchain-based Zero-Trust Framework for Agentic AI Networking](https://mlsanity.com/paper/2608.00104/) (2026)

## Abstract (arXiv)

The confluence of Federated Learning (FL) and Large Language Models (LLMs) is ushering in a new era in privacy-preserving natural language processing. However, the intensive memory requirements for fine-tuning LLMs pose significant challenges, especially when deploying on clients with limited computational resources. To circumvent this, we explore the novel integration of Memory-efficient Zeroth-Order Optimization within a federated setting, a synergy we term as FedMeZO. Our study is the first to examine the theoretical underpinnings of FedMeZO in the context of LLMs, tackling key questions regarding the influence of large parameter spaces on optimization behavior, the establishment of convergence properties, and the identification of critical parameters for convergence to inform personalized federated strategies. Our extensive empirical evidence supports the theory, showing that FedMeZO not only converges faster than traditional first-order methods such as FedAvg but also significantly reduces GPU memory usage during training to levels comparable to those during inference. Moreover, the proposed personalized FL strategy that is built upon the theoretical insights to customize the client-wise learning rate can effectively accelerate loss reduction. We hope our work can help to bridge theoretical and practical aspects of federated fine-tuning for LLMs, thereby stimulating further advancements and research in this area.