arXiv: Information-Theoretic Proof That Classifier-Based Safety Gates Cannot Allow Unbounded Self-Improvement While Maintaining Bounded Risk

arXiv·medium signal

Scrivens (arXiv:2603.28650) formalizes the safety verification problem for self-improving AI systems and proves that for power-law risk schedules, any classifier-based gate under overlapping safe/unsafe distributions is fundamentally limited by Hölder's inequality — forcing bounded utility. The impossibility can be escaped with continuous probability gates, and the paper provides formal Lipschitz bounds for pre-LayerNorm transformers under LoRA for LLM-scale verification. Validated on GPT-2 with conditional delta=0 at TPR=0.352. This has direct implications for anyone building agent guardrails: binary approve/reject gates have provable limits.