Information-Theoretic Limits of Safety Verification for Self-Improving Systems
Can a safety gate permit unbounded beneficial self-modification while maintaining bounded cumulative risk? We formalize this question through dual conditions -- requiring sum delta_n < infinity (bounded risk) and sum TPR_n = infinity (unbounded utility) -- and establish a theory of their (in)compatibility. Classification impossibility (Theorem 1): For power-law risk schedules delta_n = O(n^{-p}) with p > 1, any classifier-based gate under overlapping safe/unsafe distributions satisfies TPR_n <= C_alpha * delta_n^beta via Holder's inequality, forcing sum TPR_n < infinity. This impossibility is exponent-optimal (Theorem 3). A second independent proof via the NP counting method (Theorem 4) y...
| Authors | Arsenios Scrivens |
|---|---|
| Primary category | cs.LG |
| Published | 30 March 2026 |
| Last updated at source | 2 April 2026 |
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