提出新方法控制模型微调速度，揭示其理论极限。
Limits of Convergence-Rate Control for Open-Weight Safety
- 通过权重谱结构重参数化，实现优化速度的可证明控制
- SpecDef算法在非对抗场景下有效减缓一阶与二阶优化
- 发现攻击者可线性扩大模型规模恢复快速收敛，突破现有控制上限
开放权重的基础模型在发布后可能被微调用于有害目的，而现有训练抗性方法缺乏理论保障。将此类干预视为收敛速率控制问题，可将优化速度与模型权重的谱结构关联。基于此洞察，我们提出一种通过谱重参数化实现收敛速率控制的新理解，并推导出名为SpecDef的算法，在非对抗设置下可同时理论和实证地减缓一阶与二阶优化。在对抗设置中，我们建立了广泛类别的收敛速率控制方法（包括本文方法）的根本极限：拥有足够知识的攻击者可通过线性增加模型规模恢复快速收敛。因此，未来工作需探索不等价于收敛速率控制的方法。
原文摘要 · Abstract (English)
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.
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