Limits of Convergence-Rate Control for Open-Weight Safety
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914342221381632 |
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| author | Rosati, Domenic Zeng, Xijie Huang, Hong Dionicio, Sebastian Majumdar, Subhabrata Rudzicz, Frank Sajjad, Hassan |
| author_facet | Rosati, Domenic Zeng, Xijie Huang, Hong Dionicio, Sebastian Majumdar, Subhabrata Rudzicz, Frank Sajjad, Hassan |
| contents | Open-weight foundation models can be fine-tuned for harmful purposes after release, yet no existing training resistance methods provide theoretical guarantees. Treating these interventions as convergence-rate control problems allows us to connect optimization speed to the spectral structure of model weights. We leverage this insight to develop a novel understanding of convergence rate control through spectral reparameterization and derive an algorithm, SpecDef, that can both provably and empirically slow first- and second-order optimization in non-adversarial settings. In adversarial settings, we establish a fundamental limit on a broad class of convergence rate control methods including our own: an attacker with sufficient knowledge can restore fast convergence at a linear increase in model size. In order to overcome this limitation, future works will need to investigate methods that are not equivalent to controlling convergence rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18868 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limits of Convergence-Rate Control for Open-Weight Safety Rosati, Domenic Zeng, Xijie Huang, Hong Dionicio, Sebastian Majumdar, Subhabrata Rudzicz, Frank Sajjad, Hassan Optimization and Control Machine Learning Open-weight foundation models can be fine-tuned for harmful purposes after release, yet no existing training resistance methods provide theoretical guarantees. Treating these interventions as convergence-rate control problems allows us to connect optimization speed to the spectral structure of model weights. We leverage this insight to develop a novel understanding of convergence rate control through spectral reparameterization and derive an algorithm, SpecDef, that can both provably and empirically slow first- and second-order optimization in non-adversarial settings. In adversarial settings, we establish a fundamental limit on a broad class of convergence rate control methods including our own: an attacker with sufficient knowledge can restore fast convergence at a linear increase in model size. In order to overcome this limitation, future works will need to investigate methods that are not equivalent to controlling convergence rate. |
| title | Limits of Convergence-Rate Control for Open-Weight Safety |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2602.18868 |