Incompleteness of AI Safety Verification via Kolmogorov Complexity

Researchers prove a fundamental theoretical limit in AI safety verification using Kolmogorov complexity theory. They demonstrate that no finite formal verifier can certify all policy-compliant AI instances of arbitrarily high complexity, revealing intrinsic information-theoretic barriers beyond computational constraints.

• →AI safety verification faces fundamental information-theoretic limits that cannot be overcome with more computational resources.
• →Any sound computably enumerable verifier has a complexity threshold beyond which true policy-compliant instances cannot be certified.
• →The limitation is independent of combinatorial complexity and model expressiveness traditionally blamed for verification failures.
• →The findings motivate proof-carrying approaches that provide instance-level correctness guarantees instead of universal verification.
• →This represents a theoretical breakthrough in understanding the mathematical boundaries of AI safety assurance.