On the Undecidability of Artificial Intelligence Alignment: Machines that Halt
<|reference_start|>On the Undecidability of Artificial Intelligence Alignment: Machines that Halt: 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.<|reference_end|>
@article{de melo2024on,
    title={On the Undecidability of Artificial Intelligence Alignment: Machines
  that Halt},
    author={Gabriel Adriano de Melo, Marcos Ricardo Omena De Albuquerque Maximo,
  Nei Yoshihiro Soma, Paulo Andre Lima de Castro},
    journal={arXiv preprint arXiv:2408.08995},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.08995},
    primaryClass={cs.AI}
}