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Machines that halt resolve the undecidability of artificial intelligence alignment

Gabriel A. Melo; Marcos R. O. A. Máximo; Nei Y. Soma; Paulo A. L. Castro · 2025 · Scientific Reports 15   evidence medium priority coded

Main argument

Thesis: the inner alignment problem - deciding whether an arbitrary AI model satisfies a non-trivial alignment function - is UNDECIDABLE (via Rice's theorem / reduction to the Halting Problem); but there is an enumerable set of provenly-aligned AIs constructible from a finite set of provenly-aligned operations, so alignment 'should be a guaranteed property from the AI architecture rather than a characteristic imposed post-hoc on an arbitrary AI model'; the outer-alignment judge function must also impose a halting constraint.

Why it matters here

The impossibility theorem for post-hoc alignment verification: whether an ARBITRARY model satisfies a non-trivial alignment property is undecidable (Rice's theorem). Constructive upshot: alignment must be guaranteed BY ARCHITECTURE (built from provenly-aligned operations, with halting constraints), not verified after the fact. A formal cousin of Schuster & Kilov's encoding gap and Kästner's verification problem.

Reading notes

Compact treatment (ITA Brazil; formal). Abstract + argument structure read.

Melo, G. A., Máximo, M. R. O. A., Soma, N. Y., & Castro, P. A. L. (2025). Machines that halt resolve the undecidability of artificial intelligence alignment. Scientific Reports, 15.

Close reading — 1 coded units

#1 · pp. 1 · argument
“The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem [...] Nevertheless, there is an enumerable set of provenly aligned AIs that are constructed from a finite set of provenly aligned operations. Therefore, we argue that the alignment should be a guaranteed property from the AI architecture rather than a characteristic imposed post-hoc on an arbitrary AI model.”
GAP-NO-EMPIRICS RL-CONTROL

Synthesis-matrix row

supports T3-PROCEDURALISM-INCOMPLETE
post-hoc verification undecidable - legitimacy can't be recovered downstream

Memos (1)

theoretical · unit #1
Formal reinforcement for two coded arguments: (a) SCHUSTER_KILOV's encoding gap - if verifying an arbitrary model's alignment is undecidable, then democratic legitimacy for the principles->algorithm step cannot be recovered by after-the-fact verification even in principle, only by construction-time process (strengthening the case that legitimacy must attach to the PROCESS); (b) KAESTNER's MI-as-gold-standard - undecidability bounds what interpretability audits can promise for arbitrary architectures, supporting their restriction of the demand to high-risk/high-stakes contexts and the recommendation of inherently interpretable systems. One-cite in governance chapter: verification-based regulation (audits) has a formal ceiling; architecture/process regulation does not.