On the Origin of Samples: Attribution of Output to a Particular Algorithm

Attribution of artificial outputs to their source algorithms is theoretically impossible in the general case when originators have unlimited computational resources and equal prior probabilities, meaning we cannot definitively prove whether something was created by nature or a specific artificial process without additional constraints.

This impossibility result has practical implications for biosecurity and synthetic biology: as genetic engineering advances and synthetic organisms become more common, we may face fundamental limits in our ability to distinguish natural from artificially-created life forms, which has important policy and safety considerations.

The paper formalizes a generalized version of a classical scientific problem, connecting Darwin's work on distinguishing species origins to modern challenges in AI and synthetic biology, suggesting that fundamental theoretical limits apply across multiple domains of origin attribution.

Computational resource limitations and prior knowledge are critical factors in making origin attribution tractable—the impossibility only holds under idealized conditions, implying that real-world detection may be possible if we can establish reasonable bounds on what algorithms could have created something or assign different probabilities to different originators.

This work is relevant to AI safety research because it addresses how we might verify or audit AI system outputs, suggesting that without additional information or constraints, proving the source of any generated sample presents deep theoretical challenges.