AI Noether -- Bridging the Gap Between Scientific Laws Derived by AI Systems and Canonical Knowledge via Abductive Inference
This addresses the challenge of integrating AI-generated scientific insights with established theory, which is crucial for automating and accelerating the scientific method, though it appears incremental as it builds on prior systems like AI Descartes and AI Hilbert.
The paper tackles the problem of bridging the gap between AI-derived scientific laws and canonical knowledge by automating abductive inference, proposing an algebraic geometry-based system that generates minimal missing axioms to explain hypotheses when existing theory is incomplete, and demonstrates its efficacy on examples like Kepler's third law.
A core goal in modern science is to harness recent advances in AI and computer processing to automate and accelerate the scientific method. Symbolic regression can fit interpretable models to data, but these models often sit outside established theory. Recent systems (e.g., AI Descartes, AI Hilbert) enforce derivability from prior axioms. However, sometimes new data and associated hypotheses derived from data are not consistent with existing theory because the existing theory is incomplete or incorrect. Automating abductive inference to close this gap remains open. We propose a solution: an algebraic geometry-based system that, given an incomplete axiom system and a hypothesis that it cannot explain, automatically generates a minimal set of missing axioms that suffices to derive the axiom, as long as axioms and hypotheses are expressible as polynomial equations. We formally establish necessary and sufficient conditions for the successful retrieval of such axioms. We illustrate the efficacy of our approach by demonstrating its ability to explain Kepler's third law and a few other laws, even when key axioms are absent.