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Safety is Non-Compositional: A Formal Framework for Capability-Based AI Systems

arXiv cs.AI / 3/18/2026

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Key Points

  • The paper provides the first formal proof that safety is non-compositional in capability-based AI systems in the presence of conjunctive capability dependencies, showing two individually safe agents can together reach a forbidden goal.
  • It introduces a formal framework capturing these dependencies and emergent behaviors in multi-agent settings.
  • The result demonstrates that preventing forbidden capabilities cannot rely solely on per-agent safeguards; system-level analysis of agent interactions is required.
  • The findings have implications for AI safety research, risk assessment, and governance, emphasizing safeguards against emergent conjunctive failures in multi-agent environments.

Abstract

This paper contains the first formal proof that safety is non-compositional in the presence of conjunctive capability dependencies: two agents each individually inca- pable of reaching any forbidden capability can, when combined, collectively reach a forbidden goal through an emergent conjunctive dependency.

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