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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.10607 |
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| _version_ | 1866910018839773184 |
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| author | Cao, Sansheng Ma, Zhengyu Tian, Yonghong |
| author_facet | Cao, Sansheng Ma, Zhengyu Tian, Yonghong |
| contents | Zeroth-order (ZO) optimization has long been favored for its biological plausibility and its capacity to handle non-differentiable objectives, yet its computational complexity has historically limited its application in deep neural networks. Challenging the conventional paradigm that gradients propagate layer-by-layer, we propose Hierarchical Zeroth-Order (HZO) optimization, a novel divide-and-conquer strategy that decomposes the depth dimension of the network. We prove that HZO reduces the query complexity from $O(ML^2)$ to $O(ML \log L)$ for a network of width $M$ and depth $L$, representing a significant leap over existing ZO methodologies. Furthermore, we provide a detailed error analysis showing that HZO maintains numerical stability by operating near the unitary limit ($L_{lip} \approx 1$). Extensive evaluations on CIFAR-10 and ImageNet demonstrate that HZO achieves competitive accuracy compared to backpropagation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10607 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hierarchical Zero-Order Optimization for Deep Neural Networks Cao, Sansheng Ma, Zhengyu Tian, Yonghong Machine Learning Artificial Intelligence Zeroth-order (ZO) optimization has long been favored for its biological plausibility and its capacity to handle non-differentiable objectives, yet its computational complexity has historically limited its application in deep neural networks. Challenging the conventional paradigm that gradients propagate layer-by-layer, we propose Hierarchical Zeroth-Order (HZO) optimization, a novel divide-and-conquer strategy that decomposes the depth dimension of the network. We prove that HZO reduces the query complexity from $O(ML^2)$ to $O(ML \log L)$ for a network of width $M$ and depth $L$, representing a significant leap over existing ZO methodologies. Furthermore, we provide a detailed error analysis showing that HZO maintains numerical stability by operating near the unitary limit ($L_{lip} \approx 1$). Extensive evaluations on CIFAR-10 and ImageNet demonstrate that HZO achieves competitive accuracy compared to backpropagation. |
| title | Hierarchical Zero-Order Optimization for Deep Neural Networks |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.10607 |