Human-level performance via ML was *not* proven impossible with complexity theory [D]

2026-05-13 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, medium

Summary

A recent paper published in *Computational Brain & Behavior* in 2024, titled "Human-level performance via ML was *not* proven impossible with complexity theory," refutes the "Ingenia Theorem" by Van Rooij et al., which claimed to prove the impossibility of Artificial General Intelligence (AGI) via machine learning. The original "Ingenia Theorem" attempted to reduce a known NP-hard problem to learning a human-level classifier from data. However, the refuting paper, also published in *CBB*, identifies a critical flaw: the original authors failed to mathematically define "human-level classifier." Instead, they substituted "distribution of human situation-behaviour tuples" with "for all polytime-sampleable distributions" in their formal proof, which, if applied consistently, would also prove ImageNet classification intractable. This invalidates the core claim that AGI via ML is impossible.

Key takeaway

For AI Scientists and Research Scientists evaluating theoretical claims about AI limitations, you should critically examine the precise definitions and consistency of mathematical constructs used in proofs. The refutation of the "Ingenia Theorem" highlights how subtle shifts in definition, like swapping "human-level classifier" for "polytime-sampleable distributions," can invalidate a proof's conclusions. Always ensure that the problem statement aligns exactly with the formalization to avoid drawing incorrect conclusions about AI's capabilities.

Key insights

A purported proof of AGI impossibility was debunked due to an undefined "human-level classifier" and flawed mathematical substitution.

Principles

• Mathematical definitions must remain consistent.
• Proofs of impossibility require rigorous definitions.

In practice

• Scrutinize definitions in theoretical proofs.
• Verify consistency between problem setup and formal proof.

Topics

• Artificial General Intelligence
• Computational Complexity Theory
• Machine Learning Limitations
• Ingenia Theorem
• Human-Level Classifier

Best for: AI Scientist, Research Scientist, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.