Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914341408735232 |
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| author | Lang, Yicheng Wang, Changsheng Zhang, Yihua Hong, Mingyi Zhang, Zheng Yin, Wotao Liu, Sijia |
| author_facet | Lang, Yicheng Wang, Changsheng Zhang, Yihua Hong, Mingyi Zhang, Zheng Yin, Wotao Liu, Sijia |
| contents | Zeroth-order (ZO) optimization provides a gradient-free alternative to first-order (FO) methods by estimating gradients via finite differences of function evaluations, and has recently emerged as a memory-efficient paradigm for fine-tuning large-scale models by avoiding backpropagation. However, ZO optimization has a fundamental tension between accuracy and query efficiency. In this work, we show that ZO optimization can be substantially improved by unifying two complementary principles: (i) a projection-based subspace view that reduces gradient estimation variance by exploiting the intrinsic low-rank structure of model updates, and (ii) Muon-style spectral optimization that applies gradient orthogonalization to extract informative spectral structure from noisy ZO gradients. These findings form a unified framework of subspace gradient orthogonalization, which we instantiate in a new method, ZO-Muon, admitting a natural interpretation as a low-rank Muon optimizer in the ZO setting. Extensive experiments on large language models (LLMs) and vision transformers (ViTs) demonstrate that ZO-Muon significantly accelerates convergence and achieves a win-win improvement in accuracy and query/runtime efficiency. Notably, compared to the popular MeZO baseline, ZO-Muon requires only 24.7% of the queries to reach the same SST-2 performance for LLM fine-tuning, and improves accuracy by 25.1% on ViT-B fine-tuning on CIFAR-100. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17155 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization Lang, Yicheng Wang, Changsheng Zhang, Yihua Hong, Mingyi Zhang, Zheng Yin, Wotao Liu, Sijia Machine Learning Zeroth-order (ZO) optimization provides a gradient-free alternative to first-order (FO) methods by estimating gradients via finite differences of function evaluations, and has recently emerged as a memory-efficient paradigm for fine-tuning large-scale models by avoiding backpropagation. However, ZO optimization has a fundamental tension between accuracy and query efficiency. In this work, we show that ZO optimization can be substantially improved by unifying two complementary principles: (i) a projection-based subspace view that reduces gradient estimation variance by exploiting the intrinsic low-rank structure of model updates, and (ii) Muon-style spectral optimization that applies gradient orthogonalization to extract informative spectral structure from noisy ZO gradients. These findings form a unified framework of subspace gradient orthogonalization, which we instantiate in a new method, ZO-Muon, admitting a natural interpretation as a low-rank Muon optimizer in the ZO setting. Extensive experiments on large language models (LLMs) and vision transformers (ViTs) demonstrate that ZO-Muon significantly accelerates convergence and achieves a win-win improvement in accuracy and query/runtime efficiency. Notably, compared to the popular MeZO baseline, ZO-Muon requires only 24.7% of the queries to reach the same SST-2 performance for LLM fine-tuning, and improves accuracy by 25.1% on ViT-B fine-tuning on CIFAR-100. |
| title | Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.17155 |