Limits of Convergence-Rate Control for Open-Weight Safety

• URL: http://arxiv.org/abs/2602.18868v1
• Date: Sat, 21 Feb 2026 15:32:27 GMT
• Title: Limits of Convergence-Rate Control for Open-Weight Safety
• Abstract summary: We develop an algorithm that can both provably and empirically slow first- and second-order optimization in non-adversarial settings.<n>In adversarial settings, we establish a fundamental limit on a broad class of convergence rate control methods.
• Score: 23.243652317091456
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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