Researchers prove AI latent variable theorem with Lean4
A 1771-bound theorem proof emerges after LLM-powered Lean4 formalization
David Lorell and John Wentworth initially believed they had proven a theorem about natural latent variables in AI systems, but their proof was invalidated. After a month of experimentation integrating frontier LLMs (like those used by Resolution) with Lean4 for autoformalization and theorem proving, Lorell reconstructed the proof.
The result is a machine-certified theorem stating that for any measurable latent variable on finite observables, there exists a deterministic function whose sum of deterministic natural latent errors is bounded by a constant (currently 1771, though empirically closer to ~1.838) times the sum of stochastic natural latent errors. The proof, formalized in Lean4 and verified by its kernel, reverses quantifiers compared to earlier attempts, providing a universal deterministic latent that works for all candidate stochastic latents. While the constant 1771 is impractical, empirical testing suggests the true bound is around 2, and Lorell plans to refine it further while exploring more efficient LLM scaffolding for research.
- David Lorell proved a theorem using Lean4 with LLM-powered autoformalization, yielding a machine-certified result after an initial failed attempt.
- The theorem states a deterministic latent exists with error bounded by 1771x (empirically ~1.838x) any stochastic latent’s error, reversing prior quantifier assumptions.
- The proof was formalized in Lean4 and verified by its kernel, with the constant 1771 expected to improve toward empirical values (e.g., ~2).
Why It Matters
This work bridges AI theory and formal verification, enabling provable bounds on latent variable errors for safer, more interpretable models.