Title: Deliberate Evolution: Agentic Reasoning for Sample-Efficient Symbolic Regression with LLMs

Abstract:

Symbolic regression (SR) aims to extract concise mathematical formulas from data. However, contemporary evolutionary approaches utilizing Large Language Models (LLMs) often suffer from low sample efficiency, primarily due to their dependence on scalar feedback metrics like Mean Squared Error (MSE). We pinpoint a fundamental flaw in current methodologies: they merge the tasks of proposing candidates and directing the search process. This forces the LLM to simultaneously determine evolutionary steps, identify errors, and leverage historical insights based solely on a single score. To resolve this, we introduce Deliberate Evolution (DE), an agentic architecture that separates symbolic generation from search management. DE enhances LLM proposals by employing adaptive operators to steer search direction, analytical tools to diagnose structural issues, and a reflective memory system to retain trajectory-level experience. Evaluations on LLM-SRBench demonstrate that DE consistently surpasses leading LLM-based SR baselines across various scientific fields, achieving this superior performance with merely 40% of the conventional sample budget.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC