On the Formal Limits of Alignment Verification

2026-03-08

AI Summary

This work investigates whether AI alignment can be formally verified—specifically, whether there exists a program capable of reliably ensuring that a system adheres to prescribed alignment specifications. By integrating insights from computational complexity theory, neural network verification, behavioral identifiability analysis, and finite-evidence reasoning over infinite domains, the paper introduces the “alignment verification trilemma,” which asserts that reliability, universality, and tractability cannot be simultaneously achieved. The study demonstrates that any two of these properties can coexist, but the conjunction of all three leads to infeasibility; however, relaxing any one condition restores the possibility of verification. This result delineates fundamental theoretical limits on alignment guarantees and offers critical guidance for the design of practical alignment systems.

Technology Category

• Philosophy and Ethics of AI: Safety, Robustness & Trustworthiness
• Multiagent Systems: Adversarial Agents
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The goal of AI alignment is to ensure that an AI system reliably pursues intended objectives. A foundational question for AI safety is whether alignment can be formally certified: whether there exists a procedure that can guarantee that a given system satisfies an alignment specification. This paper studies the nature of alignment verification. We prove that no verification procedure can simultaneously satisfy three properties: soundness (no misaligned system is certified), generality (verification holds over the full input domain), and tractability (verification runs in polynomial time). Each pair of properties is achievable, but all three cannot hold simultaneously. Relaxing any one property restores the corresponding possibility, indicating that practical bounded or probabilistic assurance remains viable. The result follows from three independent barriers: the computational complexity of full-domain neural network verification, the non-identifiability of internal goal structure from behavioral observation, and the limits of finite evidence for properties defined over infinite domains. The trilemma establishes the limits of alignment certification and characterizes the regimes in which meaningful guarantees remain possible.

Problem

• AI alignment
• formal verification
• certification
• soundness
• tractability

Innovation

• alignment verification
• trilemma
• formal certification
• computational complexity
• AI safety