Machines that halt resolve the undecidability of artificial intelligence alignment

Area of Science:

• Artificial Intelligence
• Theoretical Computer Science
• AI Safety

Background:

• The inner alignment problem questions if AI models satisfy alignment functions.
• This problem is proven undecidable via Rice's theorem, linked to Turing's Halting Problem.
• Current alignment strategies often apply post-hoc adjustments to AI models.

Purpose of the Study:

• To demonstrate the undecidability of the inner alignment problem.
• To advocate for AI alignment as an inherent architectural feature.
• To introduce a halting constraint for AI judge functions to ensure finite execution.

Main Methods:

• Proof sketch reduction to Turing's Halting Problem.
• Analysis of enumerable sets of provably aligned AI operations.
• Conceptual modeling of AI architectures with intrinsic alignment and halting constraints.

Main Results:

• Rigorous proof of the inner alignment problem's undecidability.
• Identification of an enumerable set of provably aligned AI operations.
• Demonstration of AI architectures with built-in alignment and halting guarantees.

Conclusions:

• AI alignment should be a guaranteed property designed into AI architectures from inception.
• Outer alignment judge functions require a halting constraint for reliable AI behavior.
• An intrinsically hard-aligned AI approach ensures safety and predictable termination.