PRISM: Structured Optimization via Anisotropic Spectral Shaping
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910009968820224 |
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| author | Yang, Yujie |
| author_facet | Yang, Yujie |
| contents | We propose PRISM, an optimizer that enhances first-order spectral descent methods like Muon with partial second-order information. It constructs an efficient, low-rank quasi-second-order preconditioner via innovation-augmented polar decomposition. This mechanism enables PRISM to perform anisotropic spectral shaping, which adaptively suppresses updates in high-variance subspaces while preserving update strength in signal-dominated directions. Crucially, this is achieved with minimal computational overhead and zero additional memory compared to first-order baselines. PRISM demonstrates a practical strategy for integrating curvature-adaptive properties into the spectral optimization paradigm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03096 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PRISM: Structured Optimization via Anisotropic Spectral Shaping Yang, Yujie Machine Learning Artificial Intelligence We propose PRISM, an optimizer that enhances first-order spectral descent methods like Muon with partial second-order information. It constructs an efficient, low-rank quasi-second-order preconditioner via innovation-augmented polar decomposition. This mechanism enables PRISM to perform anisotropic spectral shaping, which adaptively suppresses updates in high-variance subspaces while preserving update strength in signal-dominated directions. Crucially, this is achieved with minimal computational overhead and zero additional memory compared to first-order baselines. PRISM demonstrates a practical strategy for integrating curvature-adaptive properties into the spectral optimization paradigm. |
| title | PRISM: Structured Optimization via Anisotropic Spectral Shaping |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.03096 |