# Zeroth-Order Fine-Tuning of LLMs in Random Subspaces

arXiv: https://arxiv.org/abs/2410.08989 · HTML: https://mlsanity.com/paper/2410.08989/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 70 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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: 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)
- [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)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [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)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [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)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Release Strategies and the Social Impacts of Language Models](https://mlsanity.com/paper/1908.09203/) (2019)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [WiC: the Word-in-Context Dataset for Evaluating Context-Sensitive Meaning Representations](https://mlsanity.com/paper/1808.09121/) (2018)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [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)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [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)

## Built on by (most cited first, 26 of 26)

- [Evolution Strategies at the Hyperscale](https://mlsanity.com/paper/2511.16652/) (2025)
- [Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization](https://mlsanity.com/paper/2602.17155/) (2026)
- [Leveraging Coordinate Momentum in SignSGD and Muon: Memory-Optimized Zero-Order](https://mlsanity.com/paper/2506.04430/) (2025)
- [Conda: Column-Normalized Adam for Training Large Language Models Faster](https://mlsanity.com/paper/2509.24218/) (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)
- [Universally Empowering Zeroth-Order Optimization via Adaptive Layer-wise Sampling](https://mlsanity.com/paper/2604.18264/) (2026)
- [Visualising Policy-Reward Interplay to Inform Zeroth-Order Preference Optimisation of Large Language Models](https://mlsanity.com/paper/2503.03460/) (2025)
- [SeedFlood: A Step Toward Scalable Decentralized Fine-Tuning of LLMs](https://mlsanity.com/paper/2602.18181/) (2026)
- [Learning Dynamics of Zeroth-Order Optimization: A Kernel Perspective](https://mlsanity.com/paper/2605.03373/) (2026)
- [Position: Zeroth-Order Optimization in Deep Learning Is Underexplored, Not Underpowered](https://mlsanity.com/paper/2605.15622/) (2026)
- [Dominant-Layer ZO: A Single Layer Dominates Zeroth-Order Fine-Tuning of LLMs](https://mlsanity.com/paper/2606.05516/) (2026)
- [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)
- [Stochastic Dimension Zeroth-Order Estimator: Stable and Memory-Efficient Training of PINNs](https://mlsanity.com/paper/2603.24002/) (2026)
- [Accelerating Zeroth-Order Spectral Optimization with Partial Orthogonalization from Power Iteration](https://mlsanity.com/paper/2605.09034/) (2026)
- [AR1-ZO: Topology-Aware Rank-1 Zeroth-Order Queries for High-Rank LoRA Fine-Tuning](https://mlsanity.com/paper/2605.19767/) (2026)
- [Unifying Data, Memory, and Compute Efficiency in LLM training: A Survey](https://mlsanity.com/paper/2606.10706/) (2026)
- [LoCA: Forward-Only LLM Tuning after One-Shot Calibration with Local Credit Assignment](https://mlsanity.com/paper/2608.03020/) (2026)
- [SubZero+: Memory-Efficient Adaptive Zeroth-Order LLM Fine-Tuning in Random Subspaces](https://mlsanity.com/paper/2608.15665/) (2026)
- [Escaping Low-Dimensional Overlap: Multi-Task Model Merging via High-Dimensional Sparse Disentanglement](https://mlsanity.com/paper/2608.25354/) (2026)
- [MpSub: A Momentum p-Dimensional Subspace Trust-Region Method for Derivative-Free Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2609.07666/) (2026)
- [AIM-ZO: Activation-Informed Subspace Maintenance for Zeroth-Order LLM Fine-Tuning](https://mlsanity.com/paper/2609.35257/) (2026)
- [Scaling Zero-Order Pretraining through Model Sharding](https://mlsanity.com/paper/2609.37899/) (2026)
- [TACO: Ternary Absolute-max Column-wise One-sparse Optimizer for LLM Fine-Tuning](https://mlsanity.com/paper/2610.02199/) (2026)
- [Which and When to Admit: Gradient Admission for Data-Centric Small Language Model Finetuning](https://mlsanity.com/paper/2610.07553/) (2026)
- [StructZO: Structured Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning](https://mlsanity.com/paper/2610.16451/) (2026)

## Abstract (arXiv)

Fine-tuning Large Language Models (LLMs) has proven effective for a variety of downstream tasks. However, as LLMs grow in size, the memory demands for backpropagation become increasingly prohibitive. Zeroth-order (ZO) optimization methods offer a memory-efficient alternative by using forward passes to estimate gradients, but the variance of gradient estimates typically scales linearly with the model's parameter dimensionunicodex2013a significant issue for LLMs. In this paper, we propose the random Subspace Zeroth-order (SubZero) optimization to address the challenges posed by LLMs' high dimensionality. We introduce a low-rank perturbation tailored for LLMs that significantly reduces memory consumption while improving training performance. Additionally, we prove that our gradient estimation closely approximates the backpropagation gradient, exhibits lower variance than traditional ZO methods, and ensures convergence when combined with SGD. Experimental results show that SubZero enhances fine-tuning performance and achieves faster convergence compared to standard ZO approaches like MeZO across various language modeling tasks. Code is available at https://github.com/zimingyy/SubZero.