On the Undecidability of Artificial Intelligence Alignment: Machines that Halt

TL;DR

This paper proves that the inner alignment problem in AI is undecidable by reduction to the Halting Problem, advocating for architectures that inherently guarantee halting to ensure alignment.

Contribution

It rigorously demonstrates the undecidability of AI inner alignment using Rice's theorem and proposes architecture-based solutions to guarantee halting and alignment.

Findings

Inner alignment is undecidable due to Rice's theorem.

Provenly aligned AIs can be constructed from finite operations.

Architectural guarantees can ensure AI halting and alignment.

Abstract

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, which is also equivalent to a reduction to Turing's Halting Problem, whose proof sketch is presented in this work. 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. Furthermore, while the outer alignment problem is the definition of a judge function that captures human values and preferences, we propose that such a function must also impose a halting constraint that guarantees that the AI model always reaches a terminal state in finite execution steps. Our work presents examples and models that illustrate this constraint and the intricate challenges involved, advancing a compelling case for adopting an intrinsically hard-aligned approach to AI systems architectures that ensures halting.