Equation Discovery Through Collectively Evolving Effective Hypothesis Generators

Deriving extrapolatable symbolic laws from empirical observations remains a central bottleneck in AI-driven scientific discovery. We propose collective reasoning intelligence for symbolic optimization (CRISO), a multi-agent framework for autonomous equation discovery without expert feedback, task-specific finetuning, or external scientific tools and knowledge bases. CRISO distills collectively selected best hypothesis into reusable scientific statements, accumulates them as shared context, and broadcasts to a population of reasoning agents, thereby implementing a collectively evolving symbolic regression. Consequently, CRISO evolves the hypothesis search toward promising regions without additional finetuning of the backbone LLM. Across ten nonlinear, stochastic, or previously uncharacterized scientific systems, CRISO outperformed or matched state-of-the-art combinatorial and recent LLM-based symbolic regression methods, including under out-of-distribution evaluation. On an in-house chemical reactor whose dynamics lie beyond the backbone LLM's prior knowledge, CRISO derived a symbolic equation with 38.02% lower generalization error than all baselines, demonstrating its scientific discovery capability beyond static LLM priors.