No Certificate for Alignment: Two Independent Impossibilities and the Pareto Frontier of Achievable Safety Guarantees
arXiv:2603.08761v2 Announce Type: replace-cross Abstract: We argue that formal certification of AI alignment over open-ended or unbounded input domains is impossible under standard assumptions in computational complexity and learning theory, and characterise what remains achievable. Two structurally independent impossibility theorems support this position. The semantic barrier (Theorem 1): deciding whether a system satisfies any non-trivial alignment property over the full input domain is NP-hard for feedforward networks and undecidable for Turing-complete architectures -- a direct consequence
This research emerges as AI development accelerates, making the question of alignment certificability paramount for safety and governance amidst rapid deployment.
The potential impossibility of formally certifying AI alignment fundamentally alters expectations for AI safety, shifting focus from guaranteed solutions to probabilistic or bounded assurances.
The pursuit of 'perfect' AI alignment certification becomes less viable, necessitating a re-evaluation of safety strategies towards robustness, monitoring, and practical risk mitigation.
- · Researchers in explainable AI
- · Developers of practical AI safety frameworks
- · AI ethics and governance bodies focused on process
- · Advocates for formal, provable AI alignment
- · AI developers promising infallible safety guarantees
- · Regulators expecting certification as an absolute solution
Increased emphasis will be placed on runtime monitoring and human oversight for AI systems, rather than pre-deployment certification.
Investment may shift towards developing robust-by-design AI architectures and continuous learning systems that adapt to unforeseen situations safely.
Public trust in AI systems could be impacted if the inability to certify alignment is widely understood, potentially leading to more cautious adoption.
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Read at arXiv cs.LG