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[2602.18868] Limits of Convergence-Rate Control for Open-Weight Safety
Summary
This paper explores the limitations of convergence-rate control methods for open-weight foundation models, highlighting the challenges in ensuring safety against adversarial attacks.
Why It Matters
As AI models become more widely used, understanding their vulnerabilities is crucial for developing safe and robust systems. This research provides insights into the theoretical limitations of current safety measures, emphasizing the need for innovative approaches to mitigate risks associated with model misuse.
Key Takeaways
- Existing training resistance methods lack theoretical guarantees for safety.
- Convergence-rate control can be linked to the spectral structure of model weights.
- The proposed algorithm, SpecDef, can slow optimization in non-adversarial settings.
- In adversarial contexts, attackers can restore fast convergence with increased model size.
- Future research must explore alternatives to convergence rate control for enhanced safety.
Mathematics > Optimization and Control arXiv:2602.18868 (math) [Submitted on 21 Feb 2026] Title:Limits of Convergence-Rate Control for Open-Weight Safety Authors:Domenic Rosati, Xijie Zeng, Hong Huang, Sebastian Dionicio, Subhabrata Majumdar, Frank Rudzicz, Hassan Sajjad View a PDF of the paper titled Limits of Convergence-Rate Control for Open-Weight Safety, by Domenic Rosati and 6 other authors View PDF HTML (experimental) 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. Comments: Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG) Cite as: arXiv:2602.18868 [m...