Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the Undecidability of Artificial Intelligence Alignment: Machines that Halt

Gabriel Adriano de Melo, Marcos Ricardo Omena De Albuquerque Maximo, Nei Yoshihiro Soma, Paulo Andre Lima de Castro

TL;DR

This work argues that the alignment should be a guaranteed property from the AI architecture rather than a characteristic imposed post-hoc on an arbitrary AI model, and proposes 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.

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.

On the Undecidability of Artificial Intelligence Alignment: Machines that Halt

TL;DR

This work argues that the alignment should be a guaranteed property from the AI architecture rather than a characteristic imposed post-hoc on an arbitrary AI model, and proposes 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.

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.
Paper Structure (12 sections, 4 figures)

This paper contains 12 sections, 4 figures.

Table of Contents

  1. Introduction
  2. Informal Intuition
  3. Formal Proof
  4. Discussions
  5. Final Remarks
  6. Author contributions statement
  7. Data availability statement
  8. Competing interests
  9. Additional information

Figures (4)

  • Figure 1: Construction of an adversarial model that would fool any program that claims to solve the decidability of the alignment problem.
  • Figure 2: The architecture of a model that is guaranteed to be aligned with respect to the judge functions $J_v(i, o)$ by a filtering procedure.
  • Figure 3: A decidable halting model (LLM) in a loop may result in an undecidable halting final AI system (agent).
  • Figure 4: Final system decidability is guaranteed by the $\theta$ parameter that trivializes the LLM after a finite number of iterations.