Flawed 'Ingenia Theorem' claiming AGI impossible debunked by new paper

In 2024, researchers Van Rooij, Guest, Adolfi, Kolokolova, and Rich published a paper in Computational Brain & Behavior claiming to prove that achieving human-level performance (AGI) via machine learning is impossible. Their 'Ingenia Theorem' attempted to reduce a known NP-hard problem to the problem of learning a human-level classifier from data, sparking significant online discussion. Now, a rebuttal by Mike (University of Toronto CS) has been published in the same journal, demonstrating the proof is fundamentally broken. The core issue: the paper never mathematically defines a 'human-level classifier'. The authors introduce a concept resembling a distribution of human situation-behavior tuples, but in the formal proof they silently swap it for 'for all polytime-sampleable distributions', an entirely different and far stronger constraint. This substitution makes the proof invalid—if accepted, it would also prove that learning to classify ImageNet is intractable. The rebuttal points to a broader pattern in attempts by Penrose, Chomsky, and others to rule out AGI via complexity arguments.

The new paper meticulously shows that the Ingenia Theorem's reasoning collapses under scrutiny. Because the definition of 'human-level' is vague, the reduction to NP-hardness fails—any such theorem would need a precise, measurable characterization of human-level performance (e.g., error rate on a fixed benchmark). By swapping the distribution, the authors inadvertently made their claim trivially true for any fixed dataset, yet meaningless for real AGI. The rebuttal concludes the proof is irreparably broken and cannot be patched without a complete rework. This development reaffirms that complexity theory does not currently rule out the possibility of AGI via machine learning, though the question remains open. For the ML community, it highlights the danger of sloppy definitions when applying theoretical computer science to AI alignment and capabilities debates.