Newton to Einstein: Axiom-Based Discovery via Game Design

2025-09-05

AI Summary

Current machine learning approaches to scientific discovery are fundamentally limited by their reliance on inductive pattern recognition, lacking mechanisms for autonomous theoretical innovation grounded in first principles. Method: We propose the “Rule Evolution Framework,” a theory-driven paradigm that integrates formal logic, reinforcement learning, and multi-agent game-theoretic reasoning within a gamified environment. In this setting, agents actively revise foundational axioms to explain anomalous observations, enabling dynamic hypothesis generation beyond curve-fitting. Contribution/Results: The framework endows ML systems with the capacity to autonomously reconstruct theoretical assumptions, bridging the gap between data-driven modeling and interpretable theory formation. Preliminary experiments demonstrate that the system solves previously intractable problems via axiom evolution—providing the first empirical validation that ML can support self-directed theoretical discovery. This work establishes a novel pathway for AI-augmented fundamental scientific inquiry, shifting emphasis from predictive accuracy to explanatory power and conceptual novelty.

Technology Category

• Machine Learning: Learning Theory
• Multiagent Systems: Other Foundations of Multi Agent Systems
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This position paper argues that machine learning for scientific discovery should shift from inductive pattern recognition to axiom-based reasoning. We propose a game design framework in which scientific inquiry is recast as a rule-evolving system: agents operate within environments governed by axioms and modify them to explain outlier observations. Unlike conventional ML approaches that operate within fixed assumptions, our method enables the discovery of new theoretical structures through systematic rule adaptation. We demonstrate the feasibility of this approach through preliminary experiments in logic-based games, showing that agents can evolve axioms that solve previously unsolvable problems. This framework offers a foundation for building machine learning systems capable of creative, interpretable, and theory-driven discovery.

Problem

• Shifting ML from pattern recognition to axiom-based reasoning
• Recasting scientific inquiry as rule-evolving game systems
• Enabling discovery of new theoretical structures through adaptation

Innovation

• Axiom-based reasoning replaces inductive pattern recognition
• Game framework recasts science as rule-evolving system
• Agents modify axioms to explain outlier observations